Abstract

With more industrial developments, there is an increased demand for clean energy. One source that can provide clean energy is hydrogen-based fuels. In the paper, the term “hydrogen power” means all energy generation methods based on hydrogen, such as hydrogen combustion or hydrogen fuel cells. However, generating hydrogen at an industrial scale requires scaling up hydrogen generation processes such as electrolysis. This depends on selecting suitable catalysts to expedite the process. This paper provides a review of existing theories that help identify potential catalysts for this process. Specifically, d-band theory and spinel theory predict the activity descriptors for Oxygen Evolution Reactions and Hydrogen Evolution Reactions, respectively.

Keywords: water electrolysis, hydrogen evolution reaction, oxygen evolution reaction, catalyst, d-band theory, spinel theory

The current world and social structure depend on generating electricity. There are various approaches to generating electricity, with the main options being using fossil fuels (combustion), renewable energy, and nuclear energy. In most fossil fuel generators, byproducts, mainly in the form of greenhouse gases (GHGs), will be produced due to the combustion reaction, and GHGs are capable of warming up the Earth’s climate and polluting the atmosphere (Markandya & Wilkinson, 2007, p. 979). According to data collected by a research team that published the findings in the journal “Earth System and Scientific Data,” a rigorous academic journal with very transparent processes, which are then compiled by Climate Watch, an organization under the World Resource Institute, the annual GHG emissions from the entire world, measured in billion tons of CO2 equivalent, from 1850 to 2016, it increased from 1.4373 billion tons to 46.50 billion tons or approximately a 3135 % increase in emissions. Most of these emissions come from energy demands (World Resources Institute, 2022). According to the same source, about 33% of the world’s emissions in 2021 came from electricity and heating, the largest sector of global GHG emissions (World Resources Institute, 2022). The data shows that energy production is a considerable portion of the global GHG emissions. Thus, a clear and most impactful solution to climate change will be finding a clean or low-carbon energy source, as it will directly address 30% of global emissions.

There are many ways to produce clean and non-polluting energy, such as solar energy, which is generated directly from sunlight. However, these methods are not perfect. Most renewable energy sources, particularly solar energy, are intermittent or unstable, requiring additional infrastructure to account for the problem (Mathew, 2022, p. 5). This, combined with the lack of a large and powerful energy storage system, leads to grids with renewable sources having to depend on fossil fuels, creating additional GHG emissions (Mathew, 2022, p. 5). Additionally, these renewable energy sources consume many resources, particularly land. For instance, a 1000 MW fossil fuel power plant requires 1-4 km2 of land for the entire facility, while renewables require a lot more land, with solar requiring 20-50 km2, wind requiring 50-150 km2 , and biomass requiring 4000-6000 km2 (Rashad & Hammad, 2000, p. 213). These factors combined make most of the current renewable energy systems unable to generate electricity as effectively as methods like fossil fuel. They could potentially release additional GHGs from the extra land use and infrastructure. However, not all renewable energy sources have that problem, and using hydrogen power can prevent these problems.

Hydrogen has many advantages as an element in itself. It is a highly energy-dense element (in terms of mass), making it comparable with other standard energy production methods, such as fossil fuels like petroleum or coal, as shown in Figure 1 (U.S. Department of Energy, n.d.-b). Hydrogen power has an effective energy system that is proven by fossil fuels. The underlying principle of hydrogen power is the same as that of fossil fuels, converting hydrogen combustion’s thermal energy to steam’s kinetic energy by boiling water, finally pushing a turbine with that kinetic energy, and generating electricity. This process has been proven by decades of application and is widely used today. Approximately 42% of all electricity generation in the United States uses steam turbines (U.S. Energy Information Administration, 2023). Hydrogen also comes with the added benefit of not producing any pollutants when burned, with its byproduct being only water, which is the product of the hydrogen combustion reaction. Not only that, but hydrogen can also be used in fuel cells, which is another way to produce power efficiently, with its efficiency ranging from 40% to 60% (U.S. Department of Energy Energy Efficiency & Renewable Energy, 2010). Hydrogen is also an essential industrial element, as shown in Figure 2, commonly used in industries like agriculture, where it can synthesize ammonia, a key component in all modern fertilizers (WHA International Inc, 2023; World Nuclear Association, 2024).

Background and Literature Review

Despite the benefits of a hydrogen-based energy system, getting hydrogen clean is a challenge. There are various ways to produce hydrogen; however, most are produced using fossil fuels, which release GHGs. In fact, approximately 95% of the world’s hydrogen production is based on fossil fuels and releases GHGs (Rosenow, 2022). In the case of hydrogen power, generating power with hydrogen that has a considerable amount of carbon footprint attached to it during its production process will make the purpose of hydrogen power obsolete, and thus, using renewable or clean hydrogen is essential to ensuring the benefits of hydrogen power can be released at full potential. To better classify different types of hydrogens, color codes are assigned to them, with different colors representing different carbon footprint levels, as shown in Table 1 (National Grid, 2025). Based on the classification of hydrogen, for hydrogen power to be completely carbon-free, using green hydrogen is the best approach. Electrolysis is essential to creating green hydrogen, as detailed in Table 1. It works by splitting water molecules, which consist of two hydrogen atoms and one oxygen atom. Thus, running a specific voltage through the water molecules will break the chemical bond between the atoms and release the atoms themselves. This method is carbon neutral and does not release additional GHGs, assuming the electricity used for the electrolysis is carbon neutral.

In an electrolysis reaction, the electric current passed through serves as the activation energy of the reaction to dissociate water molecules into hydrogen and oxygen. This happens because when an electrical current is passed through the anode, cathode, and the water itself, the water molecules undergo oxidation at the anode, producing oxygen gas and releasing electrons. At the same time, the hydrogen from the oxidation is also reduced at the cathode, where hydrogen ions are being reduced by gaining an electron from the oxidation at the anode, finally creating both hydrogen and oxygen gas at the ends. This process, however, is very energy- intensive as it needs to overcome a strong energy barrier presented by the OH bonds in water. These bonds in water have an average bond energy of 461.5 kJ/mol, an accepted value, which is quite strong (Song & Le, 2013). As a result, for the reaction to occur, more energy has to be passed through, making the process less efficient and more challenging to complete, decreasing the possibility for it to be used in large-scale industrial processes such as generating hydrogen in large enough quantities to supply power plants without a method to decrease the amount of energy used.

As a result, catalysts are being used to lower the amount of energy needed in this process, as a catalyst can lower the activation energy of reactions while not consuming itself during the reaction (U.S. Department of Energy, n.d.-a). This can be used to boost the amount of hydrogen acquired from electricity, improving the efficiency of the electrolysis reaction. There are various types of catalysts with pros and cons, as well as having properties that are more inclined to support either the oxidation or the reduction reaction. In the industry, the key to successfully creating and commercializing the system for broad public use is to find a suitable catalyst that balances various qualities. This can be done by reliably identifying the activity descriptor, which represents a quantifiable indicator for a catalyst’s capability to catalyze a specific reaction, in this case, the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER). Thus, this paper focuses on reliably identifying the activity descriptors for the hydrogen and oxygen evolution in the water electrolysis reaction.

HER and OER

As established before, the HER reduces hydrogen ions, and the OER oxidizes water molecules to release oxygen. Generally speaking, the OER is more energy-intensive and slower than the HER because it has a more complex reaction mechanism. Specifically, there are four electron transfer processes during the OER, as shown in Figure 3. This multi-step process requires breaking the strong OH bond in water to generate oxygen. The four-electron transfer process also means that forming multiple intermediates is challenging (J. Li, 2022). This, in turn, creates kinetic barriers, making it much slower and requiring a higher overpotential (extra energy) to make the reaction happen. On the other hand, the HER only requires 2 electron transfers, meaning it is essentially a more straightforward process that is also easier to achieve comparatively (Dubouis & Grimaud, 2019).

Additionally, during the OER, various intermediates containing oxygen form on the catalyst and get absorbed onto its surface. The formation of these intermediates is a critical step in the process, as this is the only way catalysts can facilitate the breaking and formation of oxygen molecules, which are the intended product. However, this process is challenging to balance as too much binding force will slow down the overall kinetics of the reaction, and the reaction could become “stuck” (J. Li, 2022). This is not a problem for HER because hydrogen atoms and their intermediates are much smaller, easier to release from the catalyst, and involve fewer steps to convert to their molecular form of H2 (Dubouis & Grimaud, 2019).

d-band Theory and Catalyst Performance Prediction for OER

The d-band theory is a fundamental concept used to explain and predict the performance of a transition metal catalyst in a reaction, where it applies specifically to transition metals because of the filled d-orbitals (Bhattacharjee et al., 2016). The theory mainly revolves around the d-band center, which is the average energy level of electrons in the d orbital relative to the Fermi level and is the highest possible energy for electrons at absolute zero, which serves a crucial role in catalytic activity (Bhattacharjee et al., 2016).

The theory’s predictions depend on the relative position of the d-band center (Bhattacharjee et al., 2016). Regarding OER specifically, the theory can predict how well a catalyst binds with oxygen-containing intermediates such as OH, O2, and OOH. When the d- band center is closer to the Fermi level, the interaction between the catalyst and the reaction intermediates generally increases. Conversely, a larger proximity will weaken these interactions (Bhattacharjee et al., 2016). This does not mean that aiming for the highest d-band center (i.e., closest proximity) will be the best. As explained above, a too-strong interaction will hinder oxygen molecules’ release (desorption) and will have a lower efficiency overall. Using the same logic, if the d-band center is too low, the intermediates will not bind strongly, leading to a higher activation energy requirement for the reaction (Bhattacharjee et al., 2016). As a result, catalysts with an optimal d-band center are defined as those that can strike a good balance between adsorption and desorption, allowing for an efficient intermediate process without energy losses, meaning higher overall efficiency. This is because the optimal balance of the d-band center can minimize overpotentials, which will enhance catalytic performance by wasting less energy, leading to a higher energy efficiency, thus allowing more energy to be applied to the reaction itself, increasing the reaction rate (Bhattacharjee et al., 2016). Additionally, over-potential has side effects like releasing heat and increasing material/catalyst stress, which can lead to a shortened lifetime and be suboptimal for future industrial operations. On the other hand, a lower overpotential will help maintain the stability of the catalyst, reducing wear and tear and, as a result, prolonging its lifespan, ultimately leading to the development of cheap and practical catalysts (Dubouis & Grimaud, 2019).

Application of d-band Theory in Catalyst Manufacturing and Design

The d-band theory can be applied in catalyst designs and manufacturing, with it serving as the guiding principle for tailoring catalysts by adjusting the electronic structure via alloying or doping various materials (Chen & Zhang, 2022). The theory has been validated through Density Functional Theory (DFT) calculations, a standard tool for validating and studying catalysts, supporting the effectiveness of the d-band theory (Nørskov et al., 2011). As a result, the d-band Theory can be used as a foundational principle for designing more advanced catalysts that work best for water electrolysis because the d-band theory can enable researchers to have something tangible that they can change for different results (Chen & Zhang, 2022).

Limitations of the d-band Theory for Catalyst Design

Nevertheless, the d-band theory has downsides as it does not apply universally to all catalyst materials (Bhattacharjee et al., 2016). As different catalysts have different electronic structures and surface morphologies, these factors lead to different catalysts requiring a different descriptor that considers and optimizes these factors (B. Wang & Zhang, 2022). For instance, the d-band theory works because it is based on the d orbital electrons, which can play a significant role in reaction intermediates (Bhattacharjee et al., 2016). However, the theory cannot accurately predict the catalytic behavior for materials like metal oxides, on-transition metals, and complex systems, such as perovskites and platinum, because the materials’ structures are too complex to be oversimplified by the d-band behavior in d-band theory (Gorzkowski & Lewera, 2015; B. Wang & Zhang, 2022).

Brief Explanation of HER Mechanism

Moving on to the hydrogen side of the reaction. The HER is a crucial aspect of water electrolysis and the source of green hydrogen. However, despite being generally more straightforward regarding reaction mechanism, HER does not have a definitive or universal theoretical model to predict catalyst performance, unlike OER, which has the d-band theory (Zheng et al., 2018). This makes identifying the optimal catalyst for the reaction completely different and requires understanding and analyzing unique activity descriptors that are not universally applicable to HER. Thus, an overview of HER catalyst design theories is presented below.

Cation Distribution and Spinel Theory for HER Catalyst Design

For HER, a very promising approach in catalyst design is using Spinels. Spinels are a type of crystalline material with the general formula of AB2O4, where “A” and “B” represent different metal cations, and “O” represents oxygen (Elkholy et al., 2017). Spinels generally have a cubic crystal structure characterized by two potential types of sites where the cation can be situated: the Tetrahedral or A site and the Octahedral or B site (Elkholy et al., 2017). These materials are known for their robustness, high thermal stability, and electrical conductivity, making them ideal for industrial applications after an optimal catalyst based on Spinels is successfully developed (Elkholy et al., 2017). One example of spinel is CoFe2O4. In this case, the Co2+ ion occupies the tetrahedral (A) sites while the Fe3+ ion occupies the octahedral (B) sites, together with the four oxygen atoms forming the framework of the molecule (Gomaa et al., 2024).

As there are two sites where cations can reside, a balance needs to be reached between these cations, denoted by δ. The balance significantly affects the catalytic activity for HER, and research has demonstrated that catalysts with an optimal cation distribution can substantially improve catalytic performance. This is because there is a better electron transfer process for the reaction and a more optimized binding strength of the hydrogen intermediates similar to hydrogen (Gomaa et al., 2024). For instance, the spinel of CoFe2O4 is an optimal catalyst for HER. CoFe2O4 has a cation distribution of δ of 0.33, and further research shows that CoFe2O4 exhibits low overpotentials, as low as 66 mV, which is advantageous as low levels of overpotential generally translate to a higher reaction efficiency (Gomaa et al., 2024; Niu et al., 2020). The arrangement of cations in the sites will influence the electronic structure of the spinel, similar to the d-band theory but with much more complicated mechanics (Gomaa et al., 2024). This change in electronic structure will optimize the interaction with hydrogen intermediates, reaching the right balance of binding strength (Exner, 2022).

Hydrogen Adsorption and Desorption Energy for HER Catalyst Analysis and Design

In addition to cation distribution, hydrogen and hydroxyl ions (OH-) adsorption energy has a crucial role in HER, which is especially important in alkaline media with a higher concentration of hydroxyl ions. In a study conducted by Baghban and colleagues, they used DFT to calculate the adsorption energies and achieved a 96.7% accuracy on predicting the behavior of actual catalysts (2021). An ideal catalyst for HER will exhibit a Gibbs free energy close to zero for hydrogen adsorption, meaning it will need less and less energy for the reaction to happen, or, in other words, a lower activation energy given that the catalyst can also efficiently adsorb and dissociate water to provide hydrogen for the reaction (Hu et al., 2016).

Outlook for HER Catalyst Descriptor

Due to the unique nature of the HER, it is essential to consider the current outlook for catalyst design. There are promising developments for HER catalyst descriptor analysis, but a universal and consistently working descriptor theory for HER still does not exist (Dubouis & Grimaud, 2019). Unlike in the case of OER, HER cannot use d-band theory because of complications, and other theories suffer from the same problem, causing the lack of a consistently working universal descriptor theory for HER. The HER involves diverse electronic properties observed in materials available for HER, making it very challenging to establish a single definitive set of rules or descriptors that can apply universally (Du et al., 2025). Admittedly, the d-band theory cannot predict catalysts under all circumstances as previously established, but it is still a valuable OER catalyst analysis approach, which is “better” than the current HER situation. As such, future HER research should focus on developing a more comprehensive theory, allowing the community to progress towards a more comprehensive theory while enabling other potential research areas.

Conclusion

As established previously, energy is critical for society, so developing a clean energy source is also essential. However, current energy generation options have significant limitations, such as pollution or scalability. Specifically, despite being cheap and efficient, fossil fuels are very polluting, while on the other hand, despite being clean, solar power and other renewables are less efficient, intermittent, and consume large amounts of resources to create a working system (Rashad & Hammad, 2000). An alternative to all these methods exists: using hydrogen as a clean fuel source. Hydrogen is an excellent alternative to fossil fuel, as it has a high energy density and low emissions (Hossain Bhuiyan & Siddique, 2025). In addition to that, hydrogen also matters in other fields, as it is an essential industrial resource. The side product generated by green hydrogen production, oxygen, also has an essential industrial application, making green hydrogen production even more tempting (Eckl et al., 2025; U.S. Energy Information Agency, 2024).

Despite these benefits, hydrogen production is mainly achieved using fossil fuel (steam reforming), where 62% of all hydrogen production relies on natural gas (steam reforming), and around 99% of all hydrogen production requires fossil fuel and leads to carbon emissions (International Energy Agency, 2024). Therefore, when hydrogen is used in a hydrogen-based powerplant or a hydrogen fuel cell, it will likely have a carbon footprint comparable to that of normal fossil fuel. As such, developing a completely carbon-neutral method to produce hydrogen, specifically electrolysis, is essential. Nevertheless, electrolysis has problems because it is inefficient and not easily scalable, especially for industrial operations. To solve this issue, catalysts that can meet the requirements of an industrial system can be used to make the reaction less energy-consuming, hence allowing us to achieve efficient large-scale water electrolysis. This requires a theory that can reliably identify the respective activity descriptors for both the HER and OER. As discussed throughout the paper, the catalyst for the OER can be predicted using the d-band theory by optimizing the adsorption and desorption of oxygen-containing intermediates, whereas HER performance depends on more material-specific approaches and is generally harder to define. However, methods to identify the optimal HER catalysts exist, including understanding cation distribution in spinel systems that use catalysts of a specific format, such as CoFe2O4. These strategies demonstrate that by understanding electronic and atomic structures, specifically the d-band center in transition metal-based catalysts and spinel cation balance, the performance of catalysts for water electrolysis can be effectively and quantitatively predicted. In conclusion, optimizing catalyst selection and advancing in d-band and spinel theory or other potential theories are necessary for the bigger goal of large-scale clean hydrogen production. Therefore, more focus, funding, and research should be directed towards understanding and developing these catalysts to enable their industrial use, from energy production to industrial uses, not only laboratory applications.

This paper provides a review of the current available methods in identifying the activity descriptors for both the HER and OER and does not aim to find new methods or theories. To solve the problem of catalyst design, more experimental trials and data on catalyst designs need to be done, which will enable the potential for further understanding of catalysis or even potentially finding the catalyst that can be applied in the industry. Also, this review does not include all aspects of the research, as the paper only discussed the theories related to water electrolysis and their associated catalysts, which themselves can still benefit from catalysis research developments in other fields. Specifically, catalysis research has been done in fields other than water electrolysis catalysis, and we anticipate that future work could incorporate findings from those fields into the field of water electrolysis. Doing so can compile a more comprehensive and effective review, providing more value to the field.

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About the author

Jiajun Li

Jiajun is currently a 12th grade student at St. Andrew’s College. He is interested in physics, specifically nuclear physics, as well as environmental science, specifically the energy aspect. Jiajun is currently investigating how a clean and renewable energy source can solve most of the environmental crises that we are currently facing and how to develop future energy sources, such as advanced fission reactors and nuclear fusion reactors, which could greatly benefit society.

Jiajun is the leader and founder of his school’s physics club and a vital member of the environmental council, which has made significant progress on helping the environment within his school, including reducing food waste by over 20%. At his previous school, three other students and Jiajun succeeded in installing a solar energy system, and he is also planning the installation of a larger solar power system to power his current school.

The post Engineering Catalysts for Water Electrolysis: A Review of Activity Descriptors for Hydrogen and Oxygen Evolution Reaction appeared first on Exploratio Journal.

Introduction

Background Information

Our initial conceptualization

Historically, telescopes have been monumental achievements of stationary precision, built to capture the mysteries of the universe from a fixed vantage point. Their designs prioritized maximizing aperture and achieving optical accuracy to probe the depths of space. While these systems have undoubtedly contributed to groundbreaking discoveries, they remain constrained by their immobility and singular focus. However, as technology advances, so do the opportunities to rethink and redefine these systems. This project explores the integration of telescopes with kinematic mechanisms, envisioning a more dynamic, versatile approach. By mounting a telescope on a mobile, wheeled base with mechanisms enabling 360-degree rotation and tilt, we introduce a new dimension of adaptability to sky observation.

But why move beyond traditional designs? The answer lies in both practicality and potential. Fixed telescopes are excellent for specific observational needs but fall short in scenarios that require broader sky coverage or adaptable positioning. By incorporating mobility and kinematic design, we address this limitation while opening up avenues for new applications, from amateur astronomy to educational outreach and even real-time tracking of celestial events. The incorporation of mechanisms not only enhances the telescope’s functionality but also democratizes its usage, making sophisticated observational tools more accessible and versatile.

This approach also taps into a largely unexplored area of research: the intersection of optical precision and mechanical adaptability. While traditional designs have focused on either optical performance or static stability, integrating kinematic mechanisms introduces a system capable of evolving with future demands. Whether for amateur use, portable scientific observation, or scalable systems for larger projects, this concept represents a shift toward innovation that is not merely about convenience but about laying the foundation for a more dynamic and inclusive future in astronomy.

Specific Fundamentals about Kinematic Mechanism Designs

Kinetic mechanism designs are all about how nodes, linkages, and motors come together to make something move. Each part plays its role — nodes can either be locked in place or free to move, and it’s the interaction between the motors and these nodes that defines how the whole system operates. Take this, for example: if a node is close to a motor, it’ll move almost in sync with the motor. But the further away a node is, the more unpredictable or complex its movement becomes, because it’s now influenced by the other nodes and linkages in between.

Fixed nodes, on the other hand, are crucial for setting limits on movement. The way they interact with motors can change the entire behavior of the system. Sometimes, if a fixed node constrains the motor’s movement too much, you end up with restrictions or even unexpected behaviors, which just goes to show how important node placement really is. It’s like every part is connected in a web of motion, and one adjustment in one area affects everything else.

Now, when you’re dealing with systems that have multiple nodes and linkages, things get more complicated. As you increase the number of nodes, the system’s degrees of freedom expand, meaning there’s a wider range of possible movements. But, at the same time, more linkages also mean more constraints, which limit how much movement you can actually achieve. So, it’s always a balancing act — you want enough nodes to give flexibility but not so many that you start restricting yourself.

Understanding how these nodes move in relation to each other, especially when you’ve got motors and fixed points, is key to making everything work smoothly. In something like a telescope system, for instance, while the motor might be able to rotate a full degrees, a constrained node (like the one holding the lens) might only move along a partial arc. This difference in movement changes how the entire telescope behaves. It’s about finding that sweet spot where everything moves as intended, without unwanted limitations.

Specific Fundamentals about Telescope Designs

The two primary categories of telescopes in astronomy fundamentals are refracting and reflecting.

Refraction is the process of bending light through lenses, which is how reflective telescopes function. Specifically, light comes into the telescope through a convex lens and focuses at a point known as the focal point. These telescopes are straightforward in design making them perfect for getting a clear view of nearby celestial objects like the moon. However, there’s a catch: their size is constrained, and the lens occasionally tinkers with the colors, leading to chromatic aberration.

Conversely, reflective telescopes collect and concentrate light using mirrors. Here, a concave mirror that reflects light back to a focal point is the essential component. Reflectors have a leg up on refractors because they can be built larger without the risk of color distortion. This makes them better suited for looking at distant, faint objects. Interestingly, in 1668, Isaac Newton was the one who created this type of telescope, and even today, they’re still the backbone of most large observatories.

Both of these designs are important for modern telescope technology, giving us the tools to explore everything from the nearby moon to deep space. These will be the main types of telescopes we’ll rely on for the research in this project.

Thesis Statement

The primary goal of this paper is to determine which telescope design and mechanism offer the most reliable, full-sky coverage. Our aim is to create a system that allows the telescope to rotate 360 degrees and move seamlessly back and forth, essentially scanning the entire sky.

We will begin by focusing on the exploration of kinetic designs, simulating different mechanisms to identify which one performs best for this particular setup. This section will delve into the planned designs, highlighting what has been realized so far and identifying areas for further investigation.

Next, we will conduct a case study comparing telescopes, analyzing their strengths and limitations to determine which one is the most suitable. This evaluation will include an in-depth discussion of our decision-making process, addressing areas that warrant additional research.

Once the best mechanism and telescope combination is established, we will explore why this synergy is optimal for the project’s objectives and how it advances our goals. This will lead us into the conclusion, where we summarize key findings and outline potential paths for future research.

Mechanism

Design

Setup of Simple Mechanism Design

The integration of a kinetic mechanism into the telescope system is motivated by the need to achieve precise and comprehensive sky coverage while maintaining flexibility and stability. Telescopes are traditionally stationary or limited in their range of motion, which restricts their ability to scan the entire sky or adjust dynamically to track objects. By combining a robust kinetic mechanism with the telescope, this system can provide both rotational and translational motion, allowing it to explore and capture a wider expanse of the sky with greater accuracy. The pan-tilt mechanism is particularly advantageous for its versatility in achieving precise angles, critical for astronomical observations where even slight misalignments can lead to significant data inaccuracies. Furthermore, incorporating mobility via a wheeled platform addresses the need for repositioning the telescope, making the system adaptable to various observational scenarios.

Mechanisms as a concept are fundamental in robotics and mechanical engineering, enabling controlled motion in machines. They are often used in systems where precise, repeatable

movements are essential, such as robotic arms, cranes, and now, telescopes. A mechanism’s design hinges on the interplay between nodes (points of rotation or translation), linkages (rigid components connecting nodes), and actuators (motors or servos providing motion). These elements dictate the degrees of freedom, constraints, and overall functionality of the system. In the context of telescopes, mechanisms provide a means to combine structural rigidity with dynamic motion, ensuring the telescope can both support heavy components and move fluidly to align with celestial objects.

The kinetic mechanism in this system relies on the interplay between ground nodes, fixed nodes, and motors. Ground nodes allow for limited movement, and their absence results in unrestricted motion dictated solely by the motor’s output. As the tracked node’s position changes relative to the motor, the shape traced by its path also changes. Nodes closer to the motor mimic its motion more closely, while those farther away experience more complex paths influenced by additional nodes and linkages.

Fixed nodes play a crucial role in influencing motor behavior by imposing constraints on motion. If a fixed node limits the motor’s path, the resulting motion may be restricted or altered, leading to unexpected system behavior. For instance, linkages can become tangled, causing disturbances that compromise functionality. Conversely, nodes directly connected to the motor without sufficient constraint might spin randomly without productive output.

The complexity of the mechanism increases with the addition of nodes and linkages. While more nodes introduce additional degrees of freedom, they can also impose constraints that limit the system’s flexibility. Balancing freedom and constraint is pivotal to designing an effective mechanism that maintains both structural integrity and operational versatility.

In this project, rotational and translational motion are key to achieving full-sky coverage. A pan-tilt mechanism has been selected to enable the lens to rotate 360 degrees in both directions and tilt up or down at precise angles. This mechanism uses two servos: one continuous servo for full rotational motion and another for tilt control. The synchronized movement of these servos ensures the lens can scan the sky efficiently and comprehensively.

To enhance its adaptability, the system incorporates translational motion via a wheeled base, similar to a remote-controlled vehicle. Motors or servos control the wheels, and movement is managed through an Arduino or Raspberry Pi with optional Bluetooth control. An ultrasonic sensor is integrated to detect obstacles, allowing the system to avoid collisions autonomously.

The interaction between nodes is optimized to achieve smooth rotational motion. For example, while the motor may execute a full 360-degree rotation, a constrained node carrying the lens will follow a partial arc due to its limitations. This dynamic interaction ensures precise control over the telescope’s movement while maintaining the stability necessary for capturing clear, accurate images.

By blending these mechanisms into a single system, this design aims to redefine how telescopes can function dynamically, addressing the limitations of static models while opening new possibilities for observational astronomy.

Simulation

Present Simulation

As part of understanding the behavior of the mechanism, we decided to dive deeper into the kinematics of bar AB by tracking its midpoint coordinates and orientation. This would allow us to visualize how bar AB moves and rotates over time. The code was adjusted to follow the x– and y-coordinates of the midpoint (P_x and P_y) and to calculate the changing orientation of the bar, represented as the angle θ_AB .

Through this approach, we could gain a clearer perspective on how the system behaves. The focus here was on capturing the essence of bar AB’s motion—how its position shifts and its orientation changes over time. By simulating this and plotting the results, we could make sense of how the mechanism interacts with its environment, something that static analysis just can’t reveal.

The first image (see Figure 1 below) shows a snapshot of the mechanism. Bar AB is the horizontal section, indicated by the black dashed line. The surrounding linkages form part of the larger mechanism, with their positions and movement constrained by the interactions between nodes and motors.

[Simulation from gabemorris12’s code : https://pypi.org/project/mechanism/ ]

Next, we used this data to produce three key plots that describe the motion and rotation of bar AB. These are represented in Figure 2 below, where you can observe how P_x, P_y, and θ_AB evolve over time. These three plots are crucial because they let us visualize the continuous change in position and orientation, offering a dynamic representation of how the mechanism operates in real-time.

[Simulation from gabemorris12’s code : https://pypi.org/project/mechanism/ ]

In these plots, the x-axis represents time, while the y-axes represent P_x, P_y, and θ_AB respectively. We see smooth, sinusoidal curves, which indicate that the motion of bar cyclic, with the midpoint and orientation oscillating in a consistent pattern.

Understanding this movement is key as it not only helps us determine the effectiveness of the mechanism but also opens up the possibility of refining it. By exploring these trajectories, we get a glimpse of how the mechanism could potentially be optimized for full-sky coverage, allowing us to adjust the system parameters for more efficient and smoother motion.

Both of these visualizations—Figure 1 for the mechanism’s structure and Figure 2 for the time-dependent movement—are essential in understanding the practicality and precision of our system.

Parametric Study

Now that we’ve gathered data from the simulation, the real work begins. The goal here is to analyze the information we have and figure out how it connects back to the larger project objectives. By looking closely at how bar AB moves—specifically its midpoint coordinates and orientation—we can start to see patterns that help us understand how well our mechanism is performing.

From the simulation, we gathered time-dependent data on P_x, P_y, and θ_AB These three variables give us a clear view of both the movement and the constraints acting on bar AB. What’s interesting is how the trajectory of P_x and P_y, forms a smooth sinusoidal path, which tells us that the motion is periodic. This periodicity is useful because it confirms that our mechanism is functioning as expected, without erratic or unpredictable movement. The angle θ_AB on the other hand, shows a steady back-and-forth rotation, which is exactly what we need for sky scanning.

[Simulation from gabemorris12’s code : https://pypi.org/project/mechanism/ ]

This information is valuable because it helps us understand the mechanical efficiency of the system. Since bar AB’s motion is smooth and predictable, we know that the node and motor interactions are working well together. But what’s even more important is how this periodic motion allows us to tweak the design for better performance. By adjusting the placement of the nodes and the length of the linkages, we could either amplify or reduce this motion, depending on what’s needed for a specific observation task.

One thing that stands out from the data is the relationship between node placement and the behavior of the motor. As mentioned earlier, the closer the tracked node is to the motor, the more the movement mimics the motor’s motion. If the node is farther away, the movement becomes more constrained, as seen in our plot for θ_AB, where we observe a limited angular range. This is crucial because it helps us pinpoint the best placement for the lens so that it covers the most area in the sky.

[Design made using Decode Links Simulator: https://decode.mit.edu/projects/links/ ]

What we’re also noticing is how the number of linkages and nodes impacts the system’s degree of freedom. More nodes, as expected, increase the degree of freedom, which allows for more complex motions but also introduces a higher level of unpredictability. This is where fine-tuning the number of nodes and linkages comes in. Fewer nodes give us less flexibility but offer more control, whereas more nodes introduce complexity and the possibility of the system overextending or tangling, which could lead to mechanical failure. We saw a bit of this in the simulations, where the nodes started to pull the motor into undesired orientations, slightly reducing the efficiency of the system.

This parametric analysis helps us focus on a key question: What’s the best balance between system flexibility and control? The data suggests that by carefully choosing the placement of the tracked node and adjusting the number of linkages, we can optimize the system for the full -degree sky scanning we need. It’s a balancing act between giving the mechanism enough freedom to cover as much of the sky as possible while also ensuring it remains within functional constraints.

[Design made using Decode Links Simulator: https://decode.mit.edu/projects/links/ ]

Overall, this parametric study has given us crucial insights. The data gathered shows us where improvements can be made, but it also confirms that our base design is solid. By fine-tuning the parameters and making slight adjustments based on node placement and linkage count, we can ensure that our mechanism not only covers the sky efficiently but does so in a controlled and predictable way. This will be especially important when it comes to capturing clear images of the solar system, where precision is everything.

Optics

Refractive Telescope

Sizing and Analysis

Refractive telescopes are known for their simple design compared to more complex systems like reflectors or compound telescopes. The design mainly revolves around a large, curved lens at the front of the telescope and an eyepiece at the back. One of the core features that sets refractors apart is their ability to capture light and form images by bending light through a convex lens. Although effective, refractive telescopes come with inherent limitations, most notably their focal length. Due to this, they are primarily used for viewing closer celestial bodies, with the furthest object typically visible being the moon.

The path of light within the telescope is fairly straightforward. Light enters through the front lens, which bends the rays and converges them into a focal point. This process forms a triangular path from the lens to the focal point, which is critical for creating the image. Once the light reaches the focal point, it then travels through a filter to the eyepiece, allowing the observer to see a clear, magnified image.

Compared to telescopes with longer focal lengths or reflectors, refractors are more limited in their ability to observe distant objects. However, their simplicity and the fact that they don’t require frequent maintenance like mirror alignment make them a popular choice for amateur astronomers.

[Picture from https://personal.math.ubc.ca/~cass/courses/m309-03a/m309-projects/lcheng/project3.html]

Inspiration for this analysis was drawn from a detailed review of the Cambridge paper on telescope design and functionality, which delves deeper into the geometry and practical applications of refractive telescopes. One key takeaway from this work is the emphasis on the refractor’s role in providing stable, low-maintenance viewing for objects within a close range in our solar system.

Case Study

In this case study, we analyze how a refractive telescope captures objects at different distances by calculating the necessary angles to view specific points. We will consider two cases: one involving a nearby object, the Las Vegas Sphere, and another involving a distant object, the Moon. By comparing these two, we can gain insights into how drastically the viewing angle changes depending on the distance.

Case 1: The Las Vegas Sphere

The Sphere, located in Las Vegas, presents an interesting scenario due to its proximity. The telescope we are using has a lens positioned 1 meter (or km) off the ground. The object itself has a size of 0.01 km, and we are analyzing its angular size at a distance of km from the telescope.

Viewing the Bottom of the Sphere:

We can calculate the angle required to view the bottom of the Sphere using basic trigonometry. The distance from the telescope to the object is km, and we are looking downward from a height of km.

Since the result is negative, the telescope must be tilted downward by degrees to view the bottom of the Sphere.

Viewing the Center of the Sphere:

To find the angle to view the center, we first calculate the midpoint of the object, accounting for the height of our telescope lens. The height of the Sphere is 0.157 km, so we subtract the .001km (telescope height) from the total and divide by 2:

Now, using the distance to the Sphere, we can calculate the angle to the center:

The telescope must be tilted upward at an -degree angle to capture the center of the Sphere.

Case 2: The Moon

The Moon, much farther away, presents a different challenge in terms of viewing angle and field

of view. Its constant distance from Earth is , and we are approximating the height relative to Earth’s horizon to be around km. We will use this figure to calculate the angle required to view both the bottom and center of the Moon.

Viewing the Bottom of the Moon:

We assume that the height of the Moon’s bottom is km above the horizon. Using this and the distance to the Moon, the angle can be calculated as:

The telescope would need to be adjusted to an angle of degrees to view the bottom of the Moon.

Viewing the Center of the Moon:

To find the angle to the center, we add half the size of the Moon ( 3.7478 km) to the initial 10 km:

Now, calculating the angle:

Thus, the telescope needs to be angled at degrees to view the center of the Moon.

Angular Size and Field of View Comparison

The comparison between the two cases shows how drastically the required angle changes depending on the distance. For nearby objects like the Sphere, even small changes in position (like moving from the bottom to the center) result in significant angular changes. Conversely, for far-away objects like the Moon, the angular change is minimal, even when viewing different parts of the object.

The table below illustrates how angular size and field of view (FOV) interact when viewing different objects. The angular size is determined by the object’s size and distance, and it must be compared to the telescope’s FOV to assess whether the object can be viewed entirely or not.

Table: Angular Size and Field of View for Different Objects

In this case study, we observe how angular size drastically changes between nearby and distant objects. When an object is close, the required angle changes significantly between points on the object, while for distant objects, these changes become negligible. Furthermore, the telescope’s field of view plays a crucial role in determining how much of an object can be captured, with closer objects often exceeding the FOV, and distant objects appearing smaller within it.

Reflective Telescope

Sizing and Analysis

Reflective telescopes are an essential part of modern astronomy due to their ability to gather and focus light through the use of mirrors. Unlike refractors, which rely on lenses, reflective telescopes employ a concave mirror to form an image. This difference in design offers several advantages, particularly in terms of image quality and structural integrity.

One of the key benefits of using mirrors is that they reflect all wavelengths of light equally, which prevents color distortion. This is crucial when observing celestial objects, as it ensures that the light entering the telescope is not altered in color, providing a more accurate view. Another major advantage is that mirrors can be made much larger than lenses, making reflectors better suited for deep-sky observations. This is because a mirror can be supported across its entire back surface, unlike a lens that can only be supported at the edges. This added support allows for much larger and more stable telescopes, improving their ability to capture faint or distant objects.

Historically, the development of reflective telescopes can be traced back to the work of Isaac Newton, who pioneered their use in the 17th century. His design has since become a foundation for many of the world’s most powerful telescopes, including those used for cutting-edge astronomical research.

In this section, diagrams will be essential to visually demonstrate how light travels through a reflective telescope. These will illustrate the path light takes when it hits the concave mirror, reflects back toward a focal point, and is then viewed through an eyepiece.

In summary, the use of mirrors in reflective telescopes not only allows for larger apertures and better support but also prevents color distortions. This makes them the preferred choice for many astronomers today.

[Picture from https://www.britannica.com/science/optical-telescope/Reflecting-telescopes ]
In the next section, we will conduct a similar case study to the one performed with the refractive telescope, comparing angles, object sizes, and distances.

Case Study

In this mini case study, we focus on analyzing the performance of a reflective telescope under various observational conditions. The parameters for the telescope are:

● Magnification: 500x (using a 10mm eyepiece)
● Aperture: 257mm
● Focal Length: 1200mm
● Telescope Field of View (FOV): .4166 degrees

We’ll investigate how the telescope captures objects of different angular sizes and compare the field of view with these angular dimensions. The following table summarizes the key scenarios we will examine.

In the case of the reflective telescope, the field of view remains the same across all observations due to the fixed parameters, but the ability to capture the object depends heavily on its angular size. As with any high-magnification telescope, the closer the object, the larger its angular size and the more likely the telescope will exceed its FOV, making it impossible to capture the entire image.

Angle of the Telescope When Observing Specific Points

When working with reflective telescopes, knowing the angle at which to position the device is crucial for accurately capturing objects at different heights and distances. Using basic trigonometry, we can calculate these angles based on the object’s distance from the telescope and its size.

Las Vegas Sphere

●  Size: 0.157 km
●  Distance from Telescope: 0.01km
●  Telescope Height: 0.001 km (assumed)

To find the angle needed to observe the bottom and the center of the sphere, we first calculate the angles using:

●  Bottom: This shows the telescope must be tilted downwards by degrees.

●  Center: After adjusting for the telescope height and calculating the center, we find:

Thus, the telescope must be tilted upwards at an angle of degrees to view the center. The Moon

●  Size: 3,747.8 km
●  Distance: 384,400 km
●  Height relative to horizon: 10km

To view the bottom of the moon:

To view the center, adding half the moon’s size:

Despite the moon’s enormous size, the angle difference is minimal due to its great distance, illustrating how viewing angles change significantly for nearby objects but only slightly for distant ones.

We also include a table comparing the angular sizes and resulting angles for reference during the discussion. This reinforces how reflective telescopes behave in various real-world observations, making the advantages of using reflective mirrors—such as the lack of color distortion and larger size capability—apparent.

Telescope System Study

Comparison between both telescopes

In the world of astronomy, both refractive and reflective telescopes have carved their own significant paths, each offering distinct benefits. However, after carefully analyzing both types in the previous sections, it becomes clear that reflective telescopes offer superior performance and versatility, making them the preferred choice for serious observation, particularly when considering larger and more detailed celestial objects.

Refractive Telescopes: A Solid Start, but Limited Potential

Refractive telescopes, as we explored earlier, operate using lenses to bend light and form an image. While they are often easier to use and produce sharp, high-contrast views of objects (especially terrestrial ones), their limitations become apparent when pushing beyond a certain size. For one, the construction of larger lenses presents a significant challenge. Lenses can only be supported at their edges, which not only makes manufacturing difficult but also limits how large the aperture can realistically get.

Moreover, refractors suffer from chromatic aberration, a distortion caused by the bending of different wavelengths of light at slightly different angles. This leads to unwanted color fringing around objects, a problem that reflects a fundamental limitation in how light behaves as it passes through glass. Though advances in lens coatings and multi-lens designs can help mitigate this, the issue persists and remains a challenge for refractors.

The aperture of refractors is inherently restricted, and the field of view (FOV) becomes tighter, particularly when observing larger celestial bodies. As we saw in the earlier analysis, refractors struggled to capture entire objects at times, leading to either incomplete views or challenges in gathering adequate light for faint objects. While refractive telescopes are excellent for smaller,

precise observations, their capabilities are often outshined by their reflective counterparts, especially in the context of astronomical exploration.

Reflective Telescopes: Overcoming Limitations with Mirrors

Reflective telescopes, pioneered by Isaac Newton, offer a much more flexible and efficient system. By utilizing mirrors instead of lenses, they sidestep many of the fundamental issues faced by refractors. Mirrors reflect all wavelengths of light equally, so chromatic aberration is entirely eliminated. This alone is a massive advantage, particularly when observing distant objects where color accuracy is critical.

One of the key benefits of a reflective system is the ability to scale up. Mirrors can be supported across their entire back surface, allowing much larger apertures without the structural issues that plague lenses. This means that reflective telescopes can gather significantly more light, which is essential for observing faint, distant objects such as galaxies, nebulae, or dim stars. In the case studies we explored earlier, the reflective telescope’s large aperture allowed for much clearer and more comprehensive views of celestial bodies compared to its refractive counterpart.

Reflectors also handle magnification more efficiently. With larger apertures and longer focal lengths, they provide a wider range of magnifications without sacrificing clarity. This is essential for viewing both nearby objects, like the moon or planets, and distant deep-sky objects, which require higher magnification levels without compromising image quality.

Conclusion: The Reflective Telescope’s Superiority

When we compare the two systems side by side, the reflective telescope clearly emerges as the superior instrument for serious astronomical observation. Its ability to avoid chromatic aberration, scale up in size, and handle greater magnifications while maintaining clarity make it the clear choice for observing the vast expanse of space. Whether for amateur astronomers or professional observatories, the reflective telescope’s mirror-based design overcomes the physical limitations of lenses, allowing it to capture more light, provide clearer images, and offer more flexibility overall.

While refractors certainly have their place, particularly for beginners or those interested in smaller, more precise observations, the reflective telescope’s advantages are undeniable. For those who want a telescope that can grow with their needs and deliver high-quality observations of a wide variety of celestial phenomena, the reflector is the clear path forward.

Conclusion

Summarizing Key Points

Throughout this paper, we have explored the intricate dynamics behind the optical systems and mechanical designs that drive telescope performance. In doing so, we’ve analyzed the behavior of both refractive and reflective telescopes, as well as the critical role that various mechanisms play in ensuring full sky coverage and optimal image capture.

Optics

In the Optics section, we began by exploring the core differences between refractive and reflective telescopes. Refractors, while providing clear and sharp images, are fundamentally limited by chromatic aberration and the difficulty of scaling up lens size. As light passes through the glass lens, different wavelengths bend at slightly different angles, causing color distortions that become problematic for accurate astronomical observation. This issue is compounded by the fact that larger lenses can only be supported at their edges, which further restricts the size of refractors, limiting the amount of light they can gather and narrowing their field of view.

Reflectors, on the other hand, offer a more versatile system. By employing mirrors instead of lenses, they eliminate chromatic aberration entirely. The use of concave mirrors to focus light allows reflective telescopes to scale much larger without the physical constraints imposed on refractors. Mirrors can be supported across their entire surface, enabling greater apertures to collect more light and produce sharper, more detailed images. This makes them ideal for viewing both nearby and distant celestial objects.

Mechanisms

The mechanism design section of this paper examined the practical considerations necessary for creating a telescope capable of 360-degree movement and full sky coverage. We detailed the implementation of pan-tilt mechanisms, as well as motor and servo systems that allow telescopes to move both horizontally and vertically. This combination of degrees of freedom ensures that the telescope can scan the sky thoroughly, while also maintaining stability and precision in its movement.

We further analyzed the importance of node and linkage systems, specifically focusing on how different mechanical components interact to provide the necessary motion for optimal telescope positioning. Key to this analysis was the exploration of motor-node interactions, which allow telescopes to translate motion on wheels and rotate continuously, ensuring smooth and reliable tracking of celestial objects. The inclusion of an ultrasonic sensor for obstacle avoidance added an extra layer of reliability, ensuring that the system can operate without interference from its environment.

Case Studies

Throughout the paper, our case studies provided practical applications of these optical and mechanical principles. We analyzed both refractive and reflective telescopes in real-world scenarios, focusing on their ability to capture objects of varying angular sizes. These case studies highlighted the superior performance of reflective telescopes, particularly when observing larger, distant objects like the moon or even smaller celestial bodies. Reflective systems consistently demonstrated their ability to gather more light and deliver clearer, more detailed images while overcoming the limitations faced by refractors.

Similarly, the mechanism case study on the positioning of the telescope when observing objects like the Las Vegas Sphere and the moon demonstrated how precise angles and mechanical stability are crucial for ensuring accurate and consistent observations. These examples underscored the value of combining robust optics with finely tuned mechanical systems to achieve the highest level of performance.

Concluding Thoughts

This project, while initially appearing straightforward, has revealed the profound intricacies at the intersection of optical systems and mechanical design. What began as an investigation into the basic differences between refractive and reflective telescopes quickly evolved into a deeper exploration of how these systems function in real-world applications. The mechanical challenges of ensuring full sky coverage, combined with the optical considerations of capturing both nearby and distant objects, highlight just how complex even a seemingly simple project can become.

The truth is, there’s still much more to uncover in this field. Reflective telescopes, while proving superior in this study, are far from perfect. Their reliance on precise mechanical movement and intricate mirror alignments opens the door for further refinement. There are countless factors—from weather conditions to the quality of materials—that impact their performance, and each introduces new challenges for both the optics and mechanisms involved. In addition, sensor technologies and control systems are continually advancing, offering opportunities for greater precision and automation in future telescope designs.

Moreover, the interplay between optical physics and mechanical engineering requires ongoing research. The development of more advanced materials for lenses and mirrors, as well as more efficient servo systems and linkage designs, can transform how we think about observing the cosmos. In this paper, we’ve only scratched the surface of what is possible when these disciplines converge. The potential for innovation is immense, and future work could lead to breakthroughs that allow us to see farther, clearer, and in more detail than ever before.

In essence, this project has demonstrated that even small-scale undertakings are often layered with complexities that call for a deeper understanding and more collaborative research. Whether it’s optimizing the movement of a motor or refining the way light is focused through a mirror, each step presents a new challenge, and with it, new opportunities for discovery. As we

push forward, it’s clear that further exploration is not just beneficial—it’s essential for making meaningful strides in both astronomy and engineering.

References

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About the author

Gurdit Sekhon

Gurdit is a passionate learner with a keen interest in science, history, and problem-solving. His curiosity drives his involvement in projects blending robotics, physics, and innovative mechanism design—like building a 360-degree telescope with advanced motion control. Alongside his technical pursuits, Gurdit leads his school’s History Club and co-organizes interdisciplinary events, fostering collaboration and creativity.

Beyond academics, he finds joy in playing the harmonium, teaching at community camps, and tackling challenging math contests. Whether it’s organizing a club meeting, solving a tricky physics problem, or brainstorming ideas for his next invention, Gurdit strives to push boundaries and inspire others along the way.

The post Innovations in Telescope Motion Systems appeared first on Exploratio Journal.

Abstract

Efforts in the past have been made to investigate the feasibility of entomopters, insect-inspired flapping-wing aircraft, as a means of extraterrestrial planetary flight [1, 13]. The main mission objectives were to explore different planets and in the process, collect and retrieve samples in support of scientific research. Historically, the lack of adequate technology limited the prospects of creating an untethered entomopter capable of independent flight. Specifically, the lack of a proper simulation environment and an inadequate ability to replicate the complex kinematics of insect flight were two main hindering factors [1]. However, the progression of technology and recent developments, especially with an increased understanding of insect flight, have given entomopters a second chance [2]. In this research, we attempt to properly scale an entomopter prototype designed for past NASA/NIAC research to optimize its performance in different extraterrestrial conditions while retaining its original design constraints such as its innate Reynolds number value. Specifically, we provide calculations regarding the weight, wing area, and size of said prototype to allow it to operate in different extraterrestrial atmospheric conditions.

Keywords: entomopters, flapping-wing flight, extraterrestrial flight

Nomenclature

Note: All variables will have units defined in this section unless a unit conversion was applied. Unit conversions are clearly outlined when they happen.

I. Introduction

A reasonable question to ask is why flapping-wing flight should be considered a viable solution to flight in extraterrestrial atmospheres. After all, while rotary and fixed-wing flight have had great success on Earth, relatively little effort was put into the development of flapping-wing aircraft due to technological limitations, a lack of practical use, or a combination of both. To answer this, it is imperative to first understand how atmospheric conditions affect different modes of flight.

Fixed-wing flight through a fluid relies on a mixture of laminar and turbulent flow. While an exclusively laminar flow can offer advantages such as predictability, it also reduces the amount of lift able to be created by an airplane. Similarly, an exclusively turbulent flow presents advantages such as a high degree of lift, but it also comes with a high degree of drag. Therefore, for a fixed-wing aircraft to operate in normal performance envelopes, it must be flown through a fluid medium that allows it to operate in the Reynolds number range it was designed for. Reynolds number is a dimensionless quantity that can help predict if the fluid flow will be laminar, turbulent, or a mixture of both. From a formulaic point of view, this is represented as follows:

From the above formula, it can be observed that the Reynolds number is directly correlated to fluid density. This means that to maintain the same Reynolds number through a decrease in fluid density, there needs to be an increase in either the flow (operating) velocity, characteristic length, or a combination of both. It should also be noted that out of the eight planets in our solar system, Earth ranks second in terms of atmospheric density [3]. The only planet that outcompetes Earth in terms of atmospheric density is Venus, and it is also a planet with an atmospheric pressure that is more than 90 times that of Earth’s [4]. This imposes a high degree of structural challenge on any craft wishing to visit Venus, making atmospheric density calculations the least of worries when trying to create a vehicle that can sustain itself under such high pressures. Therefore, Venus will be excluded from the scope of this study. As mentioned above, changes to atmospheric pressure require a change in velocity or characteristic length. Such modifications are technologically impractical due to the high degree of atmospheric density difference between Earth and other planets. For example, compensating for the loss of atmospheric density with operating velocity would present many obstacles in takeoff and landing and would make mission objectives such as collecting precise planetary samples very difficult. At the same time, compensation through an increased characteristic length risks having an oversized aircraft that cannot be easily transported to other planets from Earth (at the time of this research, there are no known extraterrestrial human settlements). Since fixed-wing flight on 6 out of 8 planets (excluding Venus and Earth) would require this type of modification, it can be concluded that this mode of flight is not ideal for extraterrestrial flight.

One alternative is rotary-wing flight. Indeed, the most recent breakthrough in extraterrestrial flight was in 2021 when the NASA Ingenuity drone, which employed contra-rotating rotor blades, set the record for the first-ever controlled, powered flight on another planet [5]. Rotary-wing flight has the advantage of a relatively simple design structure and the ability to fly at very low speeds, hover, and have vertical takeoff and landing (VTOL) capabilities. However, it is especially vulnerable to foreign object damage (FOD), and flight at higher speeds is unstable and inefficient [6]. The Ingenuity also fell victim to FOD after a series of flights (72), highlighting the vulnerability of rotary-wing flights.

Given that extraterrestrial environments are not always aircraft-friendly, the vulnerability of rotary-wing flight is a huge setback in terms of the practicality of this mode of flight. The third mode of flight is flapping-wing flight. This mode of flight offers the advantage of having favorable characteristics of both fixed-wing and rotary-wing flight: the ability to fly fast and slow, hover, and possess VTOL capabilities. Flapping wing flight also allows for a high degree of maneuverability, as observed in nature by birds and insects [7]. The disadvantages of fixed-wing and rotary-wing flight, the inability to match adequate Reynolds number values, and the vulnerability against FOD, respectively, are both resolved in flapping-wing flight. Because flapping-wing flight inherently operates at low Reynolds numbers, the decrease in Reynolds number due to a thinner atmosphere does not present a drastic challenge to this mode of flight. Therefore, unlike fixed-wing flight, flapping-wing flight is not as drastically impacted by a less dense atmosphere. At the same time, research has shown that flapping wing flight is highly resistant to FOD [1], fixing the problem with rotary-wing flight. In combination, these factors make flapping-wing flight a viable if not competitive candidate for extraterrestrial flight. Entomopters, which get their name from entomo – insect and pteron – wing, are a prime example of flapping wing aircraft. The latest concept of extraterrestrial flapping-wing flight was a 2017 NASA project titled Marsbee that sought to carry out extraterrestrial discovery by employing a swarm of bee-like flapping-wing drones [8]. That project shares similar prospects to what this research sees in flapping-wing flight. Combining an extensive data library for insect flight and standard formulas for flight characteristics, we can obtain estimates for the requirements of entomopter flight on different planets within and beyond our solar system.

II. Baseline Calculations

By isolating the specific model of an entomopter, we can calculate the relationship between wing area and body mass as well as wing beat frequency and body mass. The entomopter chosen for this research was a breakthrough design by a research team led by Michelson at Georgia Tech Research Institute that took inspiration from the hawk moth (Manduca sexta) [9] and Hummingbirds [1]. Select design parameters of this entomopter appear in research [1]. By finding and scaling the relationships between body mass and wing area as well as body mass and wing beat frequency of the moth family, the same relationships could be found for the entomopter.

Fig. 1. (a) and (b) show Body Mass vs. Wing Area and Body Mass vs. Wing Beat Frequency plots (in log scale and on Earth) for different insects [10]. The red tick marks and blue lines were added to measure the precise value of each moth (Heterocera) dot. Only moths were considered since the entomopter in question is based on moths. The measurements for each dot were taken through a digital ruler and the values were put into a matrix for calculations. Figures (a) and (b) reproduced under academic fair use.

Values from Fig. 1(a) and (b) were put into matrices. The description of Fig. 1 shows how the values were measured. By using matrix inversion through GNU Octave, the least-squares line for log body mass vs. log wing area was calculated to be:

Through unit conversion for body mass from (g) to (kg), wing area from (cm²) to (m²) and removing the logarithm, the true relationship between wing area (in m²) and body mass (in kg) of the moth family on Earth was calculated:

Similarly, the same process was used to calculate the least-squares line for log body mass vs. log wing beat frequency:

Again, removing the logarithm and converting the unit for body mass from (g) to (kg) and removing the logarithm, the true relationship between wing f = beat frequency (in Hz) and bm = body mass (in kilograms) on Earth is shown:

These lines approximate relationships between wing area and body mass as well as wing beat frequency and body mass within the moth family. Notice that the graphs in Fig. 1 also provide the rough spread of mass for the moth family. This information was used to calculate the Martian weights for each mass value:

Next, the lines were used to calculate entomopter flight characteristics on Mars. Mars was chosen because Michelson’s entomopter was originally designed with Martian conditions in mind. Later in the paper, we will discuss how these calculations can be furthered to other planets.

III. Martian Calculations – Wing Area

Utilizing the lines of best fit, we can calculate the wing area of the entomopter on Mars. This was done through utilizing formulas in research [1, 10]. First, the fundamental equation for lift is:

Here, weight is equal to lift since we are most interested in calculating the amount of lift required to maintain level flight, and this is when the lift generated by an aircraft is equal to its weight. For the entomopter in Research [1], the air density and maximum coefficient of lift are provided:

Combining the least-squares line for Wing Area vs. Body Mass on Earth and the general lift formula, we can derive the relationship between velocity and mass. The velocity vs. mass relationship can then be used to solve for the relationship between Wing Area vs. Body Mass on Mars:

This relationship is plotted in Fig 4. With this relationship in mind, the minimum and maximum wing area of the entomopter on Mars and Earth were calculated:

Notice that since the Martian atmosphere is thinner, the wing area is larger overall on Mars than on Earth. However, as stated in the introduction, flapping wing flight is not drastically impacted by atmospheric changes, and the increase in wing area from Earth to Mars is well within modern technological constraints. This is especially true since entomopters on Earth are small in size to begin with.

IV. Martian Calculations – Wing Flap Velocity

Utilizing the line of best fit, we can calculate the wing flap velocity of the entomopter on Mars. Similar to how the wing area was calculated, this calculation involves relationships derived from research [1, 10].

Define one full stroke to be the wing starting at a point, flapping down and up, and ending up at the starting position. We can first find the minimum and maximum wing beat frequencies for each body mass:

One interesting phenomenon to note here is that wing beat frequency decreases as body mass increases. That is, there is an inverse relationship between wing beat frequency and body mass. This is consistent with nature, where larger insects and birds tend to flap slower than smaller ones. Thus the calculation for wing flap velocity is split between the smallest and the largest mass possible for Heterocera. In both cases, the wing shape will assumed to be a square to promote simplicity in calculations. The ideal amplitude for the entomopter’s wing flap was found to be +- 60º [2].

In summary, Michelson’s entomopter can have a mass of anywhere between 10^−4.26kg and 10^−2.265kg. On Mars, with the least mass, the entomopter would have an overall wing area of 0.0077m² with a wing beat frequency of 43.918Hz. Its wing flap velocity would be 11.419m/s. With the most mass, the entomopter would have an overall wing area of 0. 067m² with a wing beat frequency of 20.675 Hz. Its wing flap velocity would be 15.858m/s.

V. Expanding Calculations – All Planets

Sections III and IV have shown how baseline relationships between different properties of Michelson’s entomopter can be used to derive critical values such as wing area and wing flap velocity for safe flight on Mars. These calculations can be repeated for other planets as well. There are exactly three modifications necessary to repeat such calculations for other planets.

First, the air density, measured in kg/m³, within the wing area calculations in Section III needs to be replaced with the desired planet’s air density. Next, in the same formula, the gravity needs to be replaced with the desired planet’s gravity. Last, with the new minimum and maximum wing areas, replace Wa_MarsMin and Wa_MarsMax in Section IV that appear in wing flap velocity calculations. As long as the atmospheric density and gravity on Earth remain the same, the simple 3-step process should yield accurate results for entomopter properties for planets within, and even beyond, our solar system.

VI. Conclusions

Flapping-wing flight has great potential as a means of extraterrestrial flight because it offers the combined advantage of fixed-wing and rotary-wing flight, making it exceptionally adaptable and versatile. However, there are still technological developments that need to happen for this mode of flight to be confidently feasible. One main constraint is power. Fig. 5 shows that out of the three modes of flight investigated in this research – fixed-wing, rotary-wing, and flapping-wing – flapping-wing flight consistently requires the largest amount of power input to sustain flight at different velocities. In Michelson’s prototype, a reciprocating chemical muscle (RCM) was used to allow flapping-wing flight [1, 12]. An RCM is regenerative and also does not require oxygen to operate, making it ideal for low-power flights in extraterrestrial atmospheres. In a different research conducted by Wood, an innovative actuator found within a fly-inspired entomopter demonstrated a power density of 400 W/kg. For comparison, biological estimates of power densities of insects’ muscles range between 80 W/kg and 83 W/kg. According to Wood, this was “the first example of where a subsystem of the microrobotic fly [entomopter] exceeds the performance of its biological counterpart” [2]. Such technological advancements show a promising progression towards the feasibility of flapping-wing flight, and it makes the calculations made in this research relevant.

References

1. [1]  G. L. P. T., “Extraterrestrial Flight: Entomopter-Based Mars Surveyor,” Typeset.io, 2023. [Online]. Available: https://typeset.io/pdf/extraterrestrial-flight-entomopter-based-mars-surveyor-495gpkrva0. pdf.
2. [2]  G. A. R. et al., “A High-Performance Electromechanical Actuator for a Miniature Flight System,” in 2007 IEEE Aerospace Conference, Big Sky, MT, USA, 2007, pp. 1-8. doi: 10.1109/AERO.2007.4457871.
3. [3]  NASA, “Planetary Fact Sheet,” National Space Science Data Center. [Online]. Available: https://nssdc.gsfc.nasa.gov/planetary/planetfact.html.
4. [4]  NASA, “NASA’s DAVINCI Explores Ten Mysteries of Venus,” 2023. [Online]. Available: https://www.nasa.gov/solar-system/nasas-davinci-explores-ten-mysteries-of-venus/#:~:te xt=The%20surface%20of%20Venus%20is,times%20hotter%20than%20an%20oven.
5. [5]  NASA, “Mars 2020 Perseverance: Ingenuity Mars Helicopter,” 2023. [Online]. Available: https://science.nasa.gov/mission/mars-2020-perseverance/ingenuity-mars-helicopter/.
6. [6]  G. J. B. and S. P. K., “Quadrotor Dynamics and Control,” 2007. [Online]. Available: https://ai.stanford.edu/~gabeh/papers/Quadrotor_Dynamics_GNC07.pdf.
7. [7]  H. W. and B. P., AIAA Guidance, Navigation, and Control Conference, Reston, VA: American Institute of Aeronautics and Astronautics, 2007, doi: 10.2514/4.862502.
8. [8]  NASA, “MarsBee: Swarm of Flapping Wing Flyers for Enhanced Mars Exploration,” 2023. [Online]. Available: https://www.nasa.gov/general/marsbee-swarm-of-flapping-wing-flyers-for-enhanced-mars-exploration/.
9. [9]  C. R. et al., Neurotechnology for Biomimetic Robots. Cambridge, MA: MIT Press, 2021. doi: 10.7551/mitpress/9780262536691.001.0001.
10. [10]  R. J. R., The Biomechanics of Insect Flight. Princeton, NJ: Princeton University Press, 2001. doi: 10.1515/9780691094915.
11. [11]  AIAA, “Paper 2007-6498: AIAA Guidance, Navigation, and Control Conference,” 2007. [Online]. Available: https://arc.aiaa.org/doi/abs/10.2514/6.2007-6498.
12. [12]  R. C., “RCM Generations,” 2023. [Online]. Available: http://angel-strike.com/entomopter/RCM-Generations.jpg.
13. [13]  C. L. and S. T., “Final Report on the NIAC Study: Flapping Wing Micro Air Vehicle,” NASA Innovative Advanced Concepts, 2020. [Online]. Available: https://www.niac.usra.edu/files/studies/final_report/522Colozza.pdf.

About the author

Karl Chen

Karl is an aviation enthusiast and an aspiring aerospace engineer. The world of aviation has captivated him by showing the persevering nature of the human race, which went from simple biplanes to hypersonic jets in less than a century. Karl has a great deal of accumulated knowledge about aviation history, and in recent years, has been intensely indulging in STEM to better understand the scientific theories behind aircraft flight. Outside of theoretical growth, he is in the process of actively applying his aerospace knowledge through flight training, where Karl is an FAA-registered student pilot with 30 hours of flight experience who is working towards a Private Pilot Certificate.

The post The Feasibility of Insect-Based Flight as a Means of Extraterrestrial Exploration appeared first on Exploratio Journal.

Introduction 

Objects and planets in space are much bigger than daily objects we encounter on Earth and, therefore, they experience much larger gravitational forces that cause them to orbit around, collapse on, or escape from another object. The motion of extraterrestrial objects has always intrigued me, especially the NASA DART project, which is a mission to protect the Earth from potential asteroids impacting its surface. I find the collision of objects in space very interesting because the trajectory of the objects after colliding has to take in so many factors like the mass of the objects, their velocities, and any surrounding objects. 

Before I can explain more about the NASA DART project, however, I need to introduce the basics of gravitation and space physics. I will explain the different parts of space physics, like Newton’s universal law of gravitation, the acceleration of objects due to gravitational forces of the Earth and other objects, and escape speed, the speed it takes for an object to escape an object’s orbit. I will also go into the concept of gravitational potential energy, the energy an object has while in orbit, the energy required to place an object in orbit, and the nature of objects orbiting Earth, also known as Earth satellites. Additionally, I will explain Johannes Kepler’s famous 3 laws of planetary motion for a better understanding of how planets move in space. 

Finally, I will introduce the NASA DART (Double Asteroid Redirection Test), a mission where NASA tries to develop technology to protect the Earth in the unlikely event that an asteroid is headed for Earth. Their goal is to make an object, like a satellite, hit the asteroid, thus changing the trajectory of the asteroid and making it miss the Earth. 

This report is also complemented by Python code that simulates planetary motion. It is available for download on my GitHub here: https://github.com/alyang21/solarsystem 

2. Gravitation 

2.1 Universal Law of Gravitation

On Earth, the acceleration at which an object falls toward the Earth is a constant 9.8 m/s². However, this rate is different on other extraterrestrial objects. This is because the force of gravity exerted on an object depends on its mass as well as the mass of the objects around it. Knowing this, famed physicist Sir Issac Newton derived the Universal Law of Gravitation in 1687 [8]. His equation is

where G is the universal gravitational constant, at 6.67 x 10^-11. Furthermore, this equation suggests that the force depends on both objects’ masses and how far apart they are separated.  In vector form, the equation can be written as 

Furthermore, the sum of the forces on an object by the surrounding objects is just the vector sum of all the forces. 

Figure 1.1 The sum of two vectors is found by placing the two vectors tail to tip, and the resulting vector is from the tail of the first vector to the tip of the second. [1]

2.2 Acceleration Due to Gravity of the Earth

The Earth can be visualized as a number of spherical shells centered at the same point. Since the mass of all the shells combined is the mass of the Earth, and the force of gravity by the Earth comes from the center of the Earth. By taking into account the Earth’s density using its volume and mass, we can derive that the force of gravity by the Earth on an object is F_g = (GM_Em)/R_E² [8]. Since F_g = mg where g is the acceleration by the Earth according to Newton’s second Law, 

2.3 Gravitational Potential Energy

The gravitational potential energy of an object on Earth depends on its distance from the center of the Earth. We also know that work equals force multiplied by displacement, so the work done by the Earth to bring a body of mass m from the height h2 to the height h1 is given by:

In other words, the work done on an object is the difference of potential energy from the initial to final positions of the object. If we say that the potential energy W(h) at a height h above the surface of the Earth so that W(h) = mgh + W₀ where W₀ is a constant, then W₁₂ = W(h₂) – W(h₁) [8]. It is also important to note that h = 0 means points on the surface of the Earth.

If we lift the particle along a vertical path where r₁ is the distance from the center of the Earth at its first point and r₂ is the distance from the center at its second point, then we get

And as a result, 

2.4 Escape Speed

Using the law of conservation of energy, we can find the escape speed for an object out of a planet, or the speed it needs to break through the pull of the planet [8]. If we can find the distance where the object has no more potential energy and only kinetic energy, we can set the energies of the object at those two points equal to each other, thus allowing us to find the initial velocity that the object has to leave the planet with. 

As long as the final velocity is greater than or equal to 0, the object can reach infinity. So,

The initial velocity is the minimum velocity for the object to escape the atmosphere, so

If the object is thrown from the surface of the Earth, h = 0, and 

Thus, we come to the equation 

where R_E is the radius of the Earth. This means that the escape speed is independent of the object’s own mass. Additionally, with the knowledge of the Earth’s radius, we can find that the escape speed is 11.2 km/s.

2.5 Earth Satellites

Earth satellites are objects which revolve around the Earth, usually in the shape of an ellipse. The Moon is the only natural satellite of the Earth, and it has a near-circular orbit. Other satellites have been sent up by humans for telecommunication, geophysics, and meteorology. To find the period that these satellites orbit around the Earth once, we can use the equation for centripetal force, where m is the mass of the satellite and V is its speed [8].

This centripetal force is provided by the gravitational force, similar to equation (1.1) but after substituting the variables for the mass and radius of the Earth, we get 

Setting the two equations together, we find that 

A satellite travels a distance 2πR_E with speed V if the satellite is so close to the Earth’s surface that h can be neglected. The time period the satellite takes to orbit the Earth therefore is

and using the relation g = GM/R_E², we arrive at the equation

Substituting the numerical values, we get

Which is about 85 minutes.

2.6 Energy of an Orbiting Satellite

Notice how K is positive and U_g is negative. When added up, the total energy of the satellite is 

It makes sense that the satellite’s total energy is negative because if the total energy is positive, it would leave the orbit and escape to infinity. 

2.7 Energy Required to Orbit a Satellite

The energy required to put a satellite into Earth’s orbit is the difference between the satellite’s total energy in orbit and its energy at Earth’s surface. For example, if we want to lift the 9000-kg Soyuz vehicle from the Earth’s surface up to the ISS, which is 400 km above the Earth’s surface, we would have to find its energy at the Earth’s surface, as well as its total energy in orbit at the ISS. Using Eq 1.19, we get that the total energy of the Soyuz in the same orbit as the ISS is   where m is 9000 kg and h is 0. Plugging the numbers in, we get that E_orbit is -2.65 x 10¹¹ J. The total energy at the surface is just -GmM_e/R_e because E_surface = K_surface + U_surface and K_surface is 0. Plugging the numbers in, we get E_surface = -5.63 x 10¹¹ J. As explained earlier, the energy required is the change in energy, so the energy required is   = -2.65 x 10¹¹ – (-5.63 x 10¹¹) = 2.98 x 10¹¹ J [8].

2.8 Kepler’s Laws of Planetary Motion

After German astronomer Johannes Kepler obtained the data collected by Tycho Brahe, he was able to analyze the positions of all the known planets and our moon. He realized that the orbits of the planets around the sun were elliptical, and was able to come up with three basic laws of planetary motion [8].

Kepler’s first law states that all planets orbit along an ellipse, where the Sun is one of the foci of the ellipse. An ellipse is the set of all points where the sum of the distance from each point to the two foci is a constant. 

In an elliptical orbit, the point where the planet is the closest to the Sun is called the perihelion, which is represented by point A in Figure 1.4. The figure also shows point B, the farthest point from the Sun. This point is called the aphelion. 

The ellipse is a specific example of a conic section, given by the equation

The variables r and θ from Eq. 1.20 are shown in Figure 1.5. The other two variables,   and e, are constants determined by the total energy and angular momentum of the satellite at a point on the ellipse. The constant e is the eccentricity, which determines how close to being a circle the ellipse is. The closer to 0, the more circular the ellipse is, and the closer to 1, the flatter it is.

Kepler’s second law states that over equal periods of time, a planet will sweep out equal areas. In other words, the area it sweeps divided by the time, also known as the areal velocity, is a constant.

This makes sense when you consider that when the planet is closer to the Sun, it is moving faster. Since the energy of the planet-sun system is conserved, when the planet gets closer to the sun, its gravitational potential energy decreases, so its kinetic energy and velocity must increase.

Figure 1.7 The area ∂  swept out during time   as the planet moves through angle  . The angle between the radial direction of r and   is  . [4]

Kepler’s third law states that the square of the period is proportional to the cube of the semi-major axis of the orbit. For this law, we have the equation

In this equation, a is the semi-major axis of the ellipse and T is the period. Interestingly, this law can also be derived from Newtonian principles and the principle of conservation of energy [8]. Additionally, his equation applies to any satellite orbiting any large mass, not just our Sun. If we use this equation for a circular orbit of r about the Earth, we get

3. DART Project NASA

It is widely believed that millions of years ago, the dinosaurs were put into extinction when a meteoroid hit the surface of the Earth. Although no meteor has gotten close enough to Earth since then to cause humans to panic, the scientific community agrees that another meteor will eventually cross paths with the Earth. To combat this, NASA started the Double Asteroid Redirection Test, or DART, to see if it is possible to alter the course of an asteroid by sending an object to impact it. 

I first learned about DART when I visited the Kennedy Space Center in Florida and watched a video about its mission. I was immediately intrigued by DART because I had an interest in object collisions from playing pool and baseball. The DART mission added an interesting element that wasn’t involved when playing on a flat billiards table: the gravitational force of other extraterrestrial objects. This mission pushed me to learn about gravitation, planetary motion, and overall space physics in order to understand the DART mission from a scientific perspective.

DART’s target is the binary asteroid system Didymos. Since Didymos is not on a path that would impact the Earth, it is the ideal candidate for the first planetary defense experiment. The impact would be safe, even if something were to go wrong. The asteroid system consists of two asteroids: the larger asteroid named Didymos, and its moonlet, Dimorphos. DART’s plan was to collide with the moonlet Dimorphos, and then we would examine the changes in Dimorphos’ orbit as a result of the impact. 

The journey to Dimorphos was complicated and required many different state-of-the-art technologies. One was the Small-body Maneuvering Autonomous Real Time Navigation (SMART Nav), developed for guidance, navigation, and control (GNC). The system had to be autonomous because NASA cannot control a satellite when it is 11 million kilometers away from Earth. The system was able to distinguish between Didymos and Dimorphos, and accurately navigate to the moonlet, eventually colliding with the smaller asteroid. DART was also equipped with an ion propulsion system that is solar-powered and incredibly fuel-efficient. Speaking of solar-powered, DART had a Roll-Out Solar Array (ROSA), extending 8.5 meters in length on each side. These solar arrays were used before on the ISS, but DART was the first to use them on a planetary spacecraft. Finally, the LICIACube allowed the DART team back on Earth to see images of the impact and the ejecta cloud, helping them assess the impact and its effects on Dimorphos. These technologies, paired with great antennas to send and receive data from the satellite allowed the DART mission to be incredibly successful.

Figure 1.8 The three images above show the various technologies the DART satellite used throughout its mission. SMART Nav (left) helped the satellite accurately impact Dimorphos. ROSA (center) gave the satellite its power for its ion propulsion system (right). [5]

Figure 1.9 DART would impact Dimorphos from the direction Dimorphos is moving towards, slowing it down. This would cause Dimorphos’ new orbit to be closer to Didymos since its orbiting velocity decreased. At the same time, the LICIA Cube, which DART would eject 15 days before impact, would be able to capture images of the impact and send them back to Earth for NASA to examine. [6]

Overall, the DART project was a massive success, lifting off in November 2021 and colliding with Dimorphos in September 2022. However, the mission is not complete. The DART team is still examining the data from the impact in order to explore all the effects of the impact on Dimorphos. You can watch videos about the mission at this link: https://dart.jhuapl.edu/Gallery/ [7]

References 

[1] https://tikz.net/vector_sum/

[2] https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy

[3] https://openstax.org/books/university-physics-volume-1/pages/13-4-satellite-orbits-and-Energy

[4] https://openstax.org/books/university-physics-volume-1/pages/13-5-keplers-laws-of-Planetary-motion

[5] https://dart.jhuapl.edu/Mission/Impactor-Spacecraft.php

[6] https://dart.jhuapl.edu/Mission/index.php

[7] https://dart.jhuapl.edu/Gallery/

[8] This work is partially based on the content of this book: NCERT Books for Class 11 Physics, https://www.ncertbooks.guru/ncert-books-class-11-physics/amp/

Appendix

The following code computes the planetary motion of the Earth, Mars, and a fictional comet orbiting around the sun according to gravitational physics. The trajectories of these planets are calculated using Newton’s Universal Law of Gravitation, with given initial conditions for the position and velocities of each object. These trajectories are computed over a 5-year period and are visualized using an animation. The code is written in the Python language and is taken from this blog post: https://towardsdatascience.com/simulate-a-tiny-solar-system-with-python-fbbb68d8207b

Available on my Github page here: https://github.com/alyang21/solarsystem

# Ensure the right backend for Spyder

import matplotlib

matplotlib.use(“Qt5Agg”)

import matplotlib.pyplot as plt

from matplotlib import animation

# Constants and initial setup with constants and the objects’ masses, velocities, and gravitational constants.

G = 6.67e-11                  # constant G

Ms = 2.0e30                   # sun

Me = 5.972e24                 # earth        

Mm = 6.39e23                  # mars

Mc = 6.39e20                  # comet

AU = 1.5e11                   # earth sun distance

daysec = 24.0*60*60           # seconds of a day

e_ap_v = 29290                # earth velocity at aphelion

m_ap_v = 21970                # mars velocity at aphelion

commet_v = 7000               # comet velocity

gravconst_e = G*Me*Ms

gravconst_m = G*Mm*Ms

gravconst_c = G*Mc*Ms

# Starting positions

# earth

xe, ye, ze = 1.0167*AU, 0, 0

xve, yve, zve = 0, e_ap_v, 0

# mars

xm, ym, zm = 1.666*AU, 0, 0

xvm, yvm, zvm = 0, m_ap_v, 0

#comet

xc, yc, zc = 2*AU, 0, 0

xvc, yvc, zvc = 0, commet_v, 0

# sun

xs, ys, zs = 0, 0, 0

xvs, yvs, zvs = 0, 0, 0

t = 0.0

dt = 1*daysec

# these lists store the points that the objects are at

xelist, yelist, zelist = [], [], []

xmlist, ymlist, zmlist = [], [], []

xclist, yclist, zclist = [], [], []

xslist, yslist, zslist = [], [], []

# save the initial position in their respective lists

#earth

xelist.append(xe)

yelist.append(ye)

zelist.append(ze)

#mars

xmlist.append(xm)

ymlist.append(ym)

zmlist.append(zm)

#comet

xclist.append(xc)

yclist.append(yc)

zclist.append(zc)

# Simulation

# The new radii, forces, velocities, and positions are calculated at each second for 5 years. The new position is then added to the object’s list. 

while t < 5*365*daysec:

    ################ earth #############

    # compute G force on earth

    rx,ry,rz = xe – xs, ye – ys, ze – zs

    modr3_e = (rx**2+ry**2+rz**2)**1.5

    fx_e = -gravconst_e*rx/modr3_e     

    fy_e = -gravconst_e*ry/modr3_e

    fz_e = -gravconst_e*rz/modr3_e

    # update quantities how is this calculated?  F = ma -> a = F/m

    xve += fx_e*dt/Me

    yve += fy_e*dt/Me

    zve += fz_e*dt/Me

    # update position

    xe += xve*dt

    ye += yve*dt 

    ze += zve*dt

    # save the position in list

    xelist.append(xe)

    yelist.append(ye)

    zelist.append(ze)

    ################ mars #############

    # compute G force on mars

    rx_m,ry_m,rz_m = xm – xs, ym – ys, zm – zs

    modr3_m = (rx_m**2+ry_m**2+rz_m**2)**1.5

    fx_m = -gravconst_m*rx_m/modr3_m

    fy_m = -gravconst_m*ry_m/modr3_m

    fz_m = -gravconst_m*rz_m/modr3_m

    xvm += fx_m*dt/Mm

    yvm += fy_m*dt/Mm

    zvm += fz_m*dt/Mm

    # update position

    xm += xvm*dt

    ym += yvm*dt 

    zm += zvm*dt

    # save the position in list

    xmlist.append(xm)

    ymlist.append(ym)

    zmlist.append(zm)

    ################ comet ##############

    # compute G force on comet

    rx_c,ry_c,rz_c = xc – xs, yc – ys, zc – zs

    modr3_c = (rx_c**2+ry_c**2+rz_c**2)**1.5

    fx_c = -gravconst_c*rx_c/modr3_c

    fy_c = -gravconst_c*ry_c/modr3_c

    fz_c = -gravconst_c*rz_c/modr3_c

    xvc += fx_c*dt/Mc

    yvc += fy_c*dt/Mc

    zvc += fz_c*dt/Mc

    # update position

    xc += xvc*dt

    yc += yvc*dt 

    zc += zvc*dt

    # add to list

    xclist.append(xc)

    yclist.append(yc)

    zclist.append(zc)

    ################ the sun ###########

    # update quantities how is this calculated?  F = ma -> a = F/m

    xvs += -(fx_e+fx_m)*dt/Ms

    yvs += -(fy_e+fy_m)*dt/Ms

    zvs += -(fz_e+fz_m)*dt/Ms

    # # update position

    xs += xvs*dt

    ys += yvs*dt 

    zs += zvs*dt

    xslist.append(xs)

    yslist.append(ys)

    zslist.append(zs)

    # update dt

    t +=dt

print(‘data ready’)

# Animation setup

# grid size

fig, ax = plt.subplots(figsize=(6,6))

ax.set_aspect(‘equal’)

ax.grid()

# earth is blue. The text “Earth” follows point_e as it moves

line_e, = ax.plot([], [], lw=1, c=’blue’)

point_e, = ax.plot([AU], [0], marker=”o”, markersize=4, markeredgecolor=”blue”, markerfacecolor=”blue”)

text_e = ax.text(AU, 0, ‘Earth’)

# mars is red. The text “Mars” follows point_m as it moves

line_m, = ax.plot([], [], lw=1, c=’red’)

point_m, = ax.plot([1.666*AU], [0], marker=”o”, markersize=3, markeredgecolor=”red”, markerfacecolor=”red”)

text_m = ax.text(1.666*AU, 0, ‘Mars’)

# comet is black. The text “Comet” follows point_c as it moves

line_c, = ax.plot([],[], lw=1, c=’black’)

point_c, = ax.plot([2*AU], [0], marker=”o”, markersize=2, markeredgecolor=”black”, markerfacecolor=”black”)

text_c = ax.text(2*AU,0,’Comet’)

# the sun is yellow

point_s, = ax.plot([0], [0], marker=”o”, markersize=7, markeredgecolor=”yellow”, markerfacecolor=”yellow”)

text_s = ax.text(0, 0, ‘Sun’)

ax.axis(‘equal’)

ax.set_xlim(-3*AU, 3*AU)

ax.set_ylim(-3*AU, 3*AU)

exdata, eydata = [], []

mxdata, mydata = [], []

cxdata, cydata = [], []

# The points for each object are put into their respective data sets to be plotted on grid

def update(i):

    exdata.append(xelist[i])

    eydata.append(yelist[i])

    mxdata.append(xmlist[i])

    mydata.append(ymlist[i])

    cxdata.append(xclist[i])

    cydata.append(yclist[i])

    line_e.set_data(exdata,eydata)

    point_e.set_data(xelist[i],yelist[i])

    text_e.set_position((xelist[i],yelist[i]))

    line_m.set_data(mxdata,mydata)

    point_m.set_data(xmlist[i],ymlist[i])

    text_m.set_position((xmlist[i],ymlist[i]))

    line_c.set_data(cxdata,cydata)

    point_c.set_data(xclist[i],yclist[i])

    text_c.set_position((xclist[i],yclist[i]))

    point_s.set_data(xslist[i],yslist[i])

    text_s.set_position((xslist[i],yslist[i]))

    ax.axis(‘equal’)

    ax.set_xlim(-3*AU,3*AU)

    ax.set_ylim(-3*AU,3*AU)

    #print(i)

    return line_e,line_m,line_c,point_s,point_e,point_m,point_c,text_e,text_s,text_m,text_c

anim = animation.FuncAnimation(fig, func=update, frames=len(xelist), interval=1, blit=False)

plt.show(block=True)

About the author

Alexander Yang

Alex is currently a 12th grader at the Livingston High School. He is a dedicated singer-student-athlete with a passion for Math and Physics who is fascinated with data analysis and calculations related to aerospace. He founded his high school’s Rocketry Club, competing in the American Rocketry Challenge and also holding educational community launches to spark interest in rocketry and aerospace. Alex has been a part of his school’s Math Team for all four years of high school, and rising to the Math Honor Society’s Vice President in his Junior year. He was also a camp counselor at the Delaware Aerospace Academy, teaching young students about aviation, space, and rockets. He taught the students to construct and launch model rockets, maglev trains, and solar robots.

In addition to these activities, Alex also plays varsity baseball for his school, being the starting second baseman and starting shortstop in his sophomore and junior years respectively. He has also been an active singer, singing in his school chorus, select chorus, and an outside volunteer chorus. He has auditioned into the NJ All-State Chorus both of the last two years, and he is currently ranked 6th in the state in the Tenor 1 voice part. He is deeply interested in math, data science, physics, and computer science and would like to apply his math and physics knowledge to improve technology. Alex looks to further his knowledge and interest in STEM by studying data science related topics in higher education.

The post Space Physics: The motion of extraterrestrial objects appeared first on Exploratio Journal.

Introduction

In the realm of aviation, there is a constant quest to achieve precision and efficiency. As  modern aircraft technology advances and global air travel demands continue to rise, optimizing flight variables becomes increasingly important. The pursuit of optimal flight variables is driven  by two necessities, safety and economics. The safety of passengers and crew is paramount in aviation, and calculations of aircraft performance are fundamental in ensuring the flight’s safety  and success. The other important factor in the pursuit of optimal flight variables is economic  viability. In a world of finite resources, the management of fuel consumption along with  numerous other variables directly impacts the flight’s economic success.

Over the last couple of months, under the guidance of Dr. Ella Atkins, I have studied various aspects of flight for fixed-wing aircraft systems. I have been able to learn valuable fundamental principles in aircraft systems, manipulating and applying mathematical formulas to the various parts of an aircraft system. I have been able to apply my newfound mathematical skills in an engineering software known as MATLAB, which I learned under the guidance of Professor Atkins. With my knowledge of fixed-wing aircraft systems, I will be able to find steady flight variables for a twin jet engine aircraft and set up the necessary variables for a flight plan from Denver, Colorado to Anchorage, Alaska. First, we will dive into the parameters of the aircraft and how they are used. We will then discuss atmospheric pressure, temperature, and density, and how those variables will play a role in our flight. Once we have all of our parameters and our atmospheric variables, we will begin calculating variables that are required for steady-level flight, steady-level turning flight, climbing flight, and descending flight. All of the calculations will be made through MATLAB, and all the code used in this paper can be found in the appendix. Through this paper, we will come to have a better understanding of the factors that come into play when determining an aircraft’s flight plan.

 Aircraft parameters

 The first few variables we will discuss are weight variables, with max weight and fuel weight being given. This allows us to find the weight of the aircraft at different stages of flight, so for climbing flight, we will use max weight, for steady flight, we will use the difference between max weight and half the fuel weight, and for descending flight, we will use the difference between max weight and fuel weight (assuming that almost all of the fuel is used up by the time of descent). While weight is measured in pound-force (lbf), we must convert it to a force in Newtons (N) using the ratio of one lbf per 4.4482189 N. Another variable that is given in lbf is the max thrust which we will convert to N using the ratio above.

 The next three variables are factors that describe the shape and geometry of the wings of the airplane. The first variable, planform area, is the total area of both wings from a top-down view. Planform area is measured in square meters and generally determines the lift and drag generated by the airplane. The next variable is span, also known as wingspan. Span is the distance from the tip of one wing to the other wing and is measured in meters. Lastly, the aspect ratio is the relationship between span and planform area. It is calculated by the quotient of the span squared and the planform area.

 Dimensionless coefficients are values with no units that can be scaled up or down to accommodate better testing. There are numerous dimensionless coefficients in aviation, with aspect ratio being a great example. The aspect ratio allows a wing to be scaled down on that ratio so that engineers can test its properties in wind tunnels. Along with aspect ratio, other given dimensionless coefficients are maximum lift coefficient, zero-alpha lift coefficient, lift slope, parasitic drag coefficient, and span efficiency factor.

 These next few dimensionless coefficients will deal with the lift coefficient. The lift coefficient is the ratio of the aircraft’s lift over the product of force times planform area. The maximum lift coefficient, which is given as 2.79 for our calculations, is the lift coefficient when the angle of attack (the angle between the aircraft’s nose and the x-axis, also known as alpha) is greatest. The zero-alpha lift coefficient is the lift coefficient when the angle of attack is zero (the aircraft is directed parallel to the x-axis). Lastly, the lift slope represents the change in lift coefficient over the change in angle of attack. This means that it measures how much more lift can be generated by increasing the angle of attack.

 Our final two dimensionless coefficients to discuss are the parasitic drag coefficient and span efficiency factor. The parasitic drag coefficient is a constant due to viscosity in an aircraft which is part of determining the overall drag coefficient. Along with parasitic drag, the other important factors in drag coefficient are lift coefficient, aspect ratio, and span efficiency. As we have already talked about lift coefficient and aspect ratio, we only have span efficiency to discuss. The span efficiency factor is a constant between zero and one that depends on the shape of the wing and evaluates the efficiency of the lift distribution along the wing’s span. The closer the value of span efficiency is to one, the more effective the lift distribution is for the plane.

The values for all of the given variables discussed can be found in Table 1.

Atmospheric temperature, pressure, and density as functions of altitude

 One of the most important factors when doing calculations related to aircraft flight is the atmospheric conditions. There are three ways to measure altitude in aerospace engineering: absolute, geometric, and true altitude. Absolute altitude is the height above the center of the Earth and is mainly used in space travel. True altitude, which is useful when flying very low to the ground, measures the height above a point on the surface of the earth and is only called upon for aircraft above mountain ranges or other tall structures. Geometric altitude is the most straightforward concept of altitude, representing how high an object is above the Earth’s mean sea level (MSL). Generally, geometric altitude is used when describing the altitude and will be used for this paper’s calculations.

When it comes to aircraft, the three key factors that change as elevation increases are temperature, pressure, and density. Temperature is the average kinetic energy of a gas molecule and fluctuates at various intervals in our atmosphere. The levels of the atmosphere can be divided into two groups when discussing temperature. The first group is isothermal layers, which are atmosphere layers that maintain a constant temperature. The other group is constant-gradient layers, which change in temperature linearly with altitude at a specific lapse rate. The temperature and lapse rate at different points in the atmosphere can be seen below (Table 2).

 Atmospheric pressure is the force per unit area exerted by the weight of the air above a certain point. The weight of the air column is influenced by gravity and the density of the air. As one moves higher in the atmosphere, the weight of the air decreases, resulting in lower atmospheric pressure. Pressure is measured in force per unit area (N/m²), also known as Pascals (Pa), and the standard atmospheric pressure at sea level is 101325 Pascals (Pa). Knowing the standard atmospheric pressure at sea level and the temperature at different levels in the atmosphere allows us to calculate the pressure at a specific height using two different equations, one pertaining to isothermal layers, and the other pertaining to constant-gradient layers. In isothermal layers, the equation for pressure change is given.

 In this equation and many others used in physics, g is the gravitational constant (acceleration due to gravity on Earth) measured as 9.81 m/s², R is the gas constant for air measured as 287.053 J/(kg * k), and T is the temperature measured in K. By integrating the equation from the bottom of the layer to the top of the layer using h₁/p₁ as altitude/pressure at the bottom of the layer and h₂/p₂ as altitude/pressure at the top of the layer, we can simplify the equation to solve for p₂.

 The equation for constant gradient layers is given below.

 It is almost the same equation as the equation for isothermal layers, but the value of dh (change in height) is replaced by dT / T (change in temperature over temperature). Another change is the introduction of the symbol ξ, which represents the lapse rate. The integral of this equation from the bottom of the layer to the top of the layer using T₁/p₁ as temperature/pressure at the bottom of the layer and T₂/p₂ as temperature/pressure at the top of the layer gives us the equation for p₂.

With the equations for temperature and pressure at different altitudes, we are able to calculate the final and most important value for aviation, air density. The standard density is used in numerous calculations involving lift and drag, which means pretty much every calculation involving aircraft flight. Standard density, represented by the Greek letter rho (ρ), can be measured using the ideal gas law shown below.

 Manipulating the variables allows us to put density in terms of temperature and pressure, as shown below.

 Thus, all of the calculations for temperature and pressure have culminated in us being able to find density at different points in the standard atmosphere, which, as said before, is extremely important for our calculations of steady flight, turning flight, climbing flight, and descent flight. The values for temperature (K), pressure (Pa), and density (kg / m³) from sea level to 100,000 meters can be seen in Figure 1.

As we can see, standard pressure and density follow a logarithmic pattern as altitude increases. This is due to the fact that at lower altitudes, the force of gravity compresses the air at a much higher rate than it does when altitude rises, so the air pressure and density are much higher at lower altitudes. As we look to optimize values such as airspeed, throttle, and angle of attack, it is important to recognize how temperature, pressure, and density play a significant role in our calculations.

Steady-level flight parameters

 In steady-level flight for a twin-jet engine airplane, the most important variables are airspeed (velocity), thrust, throttle, and altitude. If we were discussing a propeller airplane, we would have to also account for power, which is the force that is created by a propeller instead of thrust, which is created by a jet engine, however, we will not discuss power for now. The first variable to discuss is altitude, which we will set at one km or 10,000 meters for our calculations. 10,000 meters, which equates to about 32,000 feet, is the general cruising altitude for subsonic airplanes, as it is known to be most efficient in terms of drag due to the air density at 10,000 m. With altitude out of the way, we will move on to discuss the basics of steady-level flight.

Steady level flight means that all forces acting on the airplane are balanced, with lift equaling weight and thrust equaling drag, resulting in zero acceleration and a constant velocity. This is due to the equation F = ma, which means that force = mass x acceleration. Also known as Newton’s Second Law, this basic principle of physics will allow us to substitute lift with weight and thrust with drag during our calculations. The relationship between thrust and velocity which will allow us to calculate both stems from the equation for drag, given below.

 In this equation, we already know density (ρ) and planform area ( S ). We still need a constant to replace Cᴅ, which is the coefficient of drag, which is what the three equations below will help us do.

Now, we have parasitic drag ( C ᴅ₀), aspect ratio ( AR ), and span efficiency factor ( e ), all known variables. We can find a value for the coefficient of lift through the next equation.

 Since the angle of attack ( ) is equal to zero, the value for the coefficient of lift equals the value α of the zero-alpha lift coefficient ( C ⳑ₀), which is a known variable. Lastly, we will replace the known value for the coefficient of lift by putting it in terms of lift ( L ) using the equation below.

 The final equation for drag in terms of lift is then shown below.

 Since we are in steady-level flight, we can replace the drag force with thrust, and the lift force with weight, which turns the equation into a thrust equation with velocity unknown, shown below.

The resulting equation can create a graph with thrust as the y-axis and velocity as the x-axis, which I created below using the Desmos Graphing Calculator (Figure 2).

The optimal velocity and thrust are found at the minimum on the velocity vs. thrust graph, which we can find by setting the derivative of the thrust equation with respect to velocity equal to zero. After taking the derivative of the thrust equation with respect to velocity, setting it equal to zero, and simplifying it to isolate velocity, we can find the minimum velocity equation, shown below.

 Thus, we have put velocity into an equation in which we know all of the constants, giving us a steady-level flight velocity of 183.7885 m/s. Now that we know the velocity, we can plug it back into the thrust equation, giving us a thrust force of 15231 N. As seen in Figure 2, these values correspond to the coordinates at the minimum of the thrust vs. velocity graph. Our final variable to calculate for steady-level flight is throttle. The throttle is a dimensionless value between zero and one which can be changed by the pilot to adjust airspeed and thrust. The equation for thrust in relation to the throttle is given below.

The equation can be simplified to isolate throttle (δ_t ). The equation uses thrust ( T ), density ( ρ), and density at sea level ( ρs ), all known values. The other values T^s_max, and m, must be changed for our calculations. The max thrust (T^s_max) must be multiplied by two because the original max thrust is the value for one of the two jet engines. The value of m is a constant that changes based on the specific aircraft. For our aircraft, the value of m is 1/2. Knowing all of these constants, the value for throttle for our aircraft can be calculated as 0.4337, also known as 43.37% throttle.

Steady-turning flight parameters

 In calculating steady-turning flight variables, the basic principles of balancing forces to create a constant velocity and zero acceleration still apply. The main difference comes in calculating all of our variables to adjust for a higher necessary lift. The changes in thrust, drag, lift, and weight forces on the airplane can be seen in Figure 3.

The value for phi ( φ ) is known as the turn/bank angle, and for our calculations will be 25 degrees. Knowing the value for the bank angle, we are able to calculate lift using the equation below.

 The value for lift is important because it allows us to calculate the value for load factor ( n ). Load factor is a dimensionless value that measures the ratio between lift and weight, and is normally one in steady-level flight, as lift and weight are equal in steady-level flight. The load factor is calculated using the equation below.

 Since we are calculating for steady turning flight, the values of lift (L) and weight (W) are not equal, and as a result, the load factor is greater than one. After calculating the value of lift during steady-turning flight, we are able to calculate the load factor during steady-turning flight, which is 1.1034 at a bank angle of 25 degrees. This is slightly more than the load factor at steady-level flight, meaning if you were sitting on the airplane, you would feel more than normal pressure on yourself when the airplane turns.

 The next variable that is to be calculated is the turning radius, which we will use more physics principles to derive an equation for. As said before, F = ma , also known as Newton’s second law, tells us that force = mass x acceleration. In centripetal motion, the F in F = ma signifies the centripetal force, which is the force directed toward the center of the turning arc, which is calculated as Lsin(φ) . Another important aspect of centripetal motion is that the acceleration in centripetal motion is equal to the difference between velocity squared and radius.

 The mass in this situation can be classified as W/g, with g being the force of gravity. By dividing by the weight value (W), which equals Lcos(φ) , we can get tan(φ) as the value on the left of the equation. As a result of all of this, we are left with the following equation.

We know the bank angle (φ), velocity (V) is the value calculated in steady-level flight, and the force of gravity (g) is 9.8 m/sec² . Knowing all of these constants, we can find the turning radius (R) to be 739.16 meters.

 The next couple of values we will calculate are thrust and throttle. All of them will be slightly more than they were for level flight, as we will need to generate more lift in turning flight. The equation for thrust in turning flight is shown below.

The equation is nearly the same as that of thrust for level flight, with the only addition being the value for (cos(φ))² added. Since we are using the velocity from steady-level flight, we can simply plug in all of the known variables, which outputs a thrust value of 16,886 N of force. Using this thrust value, we can the same equation we used for throttle in steady-level flight, finding our throttle in turning flight to be 0.4809, more easily referred to as 48.09% throttle. This value is about five percent greater than our throttle for steady-level flight.

Climbing and descending flight parameters

 Let’s move on to discuss climbing flight variables. In climbing flight, a new angle is added, the flight path angle (γ). The importance of flight path angle is that it affects the thrust required in the flight. The new value for thrust is shown below.

No longer can we just replace the D with its values, derive with respect to V , and set the derivative equal to zero. We must account for the unknown gamma (γ) value. One way to remove the gamma value from the equation is by using the equation below.

As a result of this equation, we can replace the Wγ in the thrust equation resulting in a new equation.

By isolating the equation above so that Vclimb is alone (the rate of climb), we are able to take the derivative of that equation and set it equal to zero to maximize Vclimb . Since the new equation 14 still has a factor of thrust in it, we can make an assumption of operating at full throttle, resulting in the thrust being calculable with the equation.

Knowing all of the values in the thrust equation, and multiplying by two because of the T^s_max two jet engines, we can find the climbing thrust. We can also find the V in equation using equation 12, which is the equation that puts thrust as a function of velocity. Knowing the thrust in this equation, we can calculate V . Now that we know V , we can plug both velocity and thrust into the rate of climb equation shown below.

After finding Vclimb we know almost every variable to complete out climbing flight. We are able to calculate the value for our angle of attack (γ) using equation 20 and we will also be able to do basic estimates for our climbing flight, such as determining the total time for the climb, altitude at certain points during the climb, or distance traveled during the climb. The final calculations we will have to make will be our descending flight calculations. 

The same principles that apply to climbing flight also apply to descending flight, with the only change required being a negative flight path angle (γ). While in climbing flight you can optimize for the flight path angle to be greatest, in descending flight, there is no optimization for the lowest possible flight path angle as it would result in an uncontrollable nosedive. Therefore, we can choose a safe flight path angle for descending flight and use equations 19-21 to calculate all of our descent variables, which we can use for estimates about total descent time, altitude at certain points during descent, or distance traveled during descent, ensuring a safe and efficient descent.

Conclusion

 My experience learning from Dr. Atkins has given me valuable knowledge about aircraft systems that are heavily applicable to ensuring safety and efficiency in aviation. All of the steady flight, turning flight, climbing, and descending parameters calculated will allow for a flight plan to be created using waypoints from Denver to Anchorage. The calculations in this analysis of a twin-jet engine aircraft show how basic principles of physics and mathematical manipulations are used in the world of aviation. These calculations, used for all fixed-wing aircraft, allow for resource-efficient and safe travel. They save time, lower costs, reduce excess fuel usage, and lessen the environmental impact of the industry, all of which are essential resources for Earth and its people. In summary, efficient calculations in aviation are fundamental to the well-ordered functioning of the aviation industry and the well-being of all stakeholders involved.

References

Fidkowski, C., Atkins, E., & Powell, K. (2019). Introduction to Aerospace Engineering . Ann Arbor, MI: University of Michigan.

Appendix

 Aircraft parameters

 Atmospheric temperature, pressure, and density as functions of altitude

 Steady-level flight and steady-turning flight parameters

About the author

Rahul Gupta

Rahul is a senior at Vandegrift High School in Austin, TX. After high school, he is looking to major in aerospace engineering or possibly double major in mechanical engineering. Outside of academics, Rahul loves anything soccer-related and is a varsity soccer player for his high school.

The post Denver to Anchorage: A Detailed Optimization of Flight Variables appeared first on Exploratio Journal.

Abstract

Though not typically at the forefront of technological advances, musicians have always implemented advanced technology. Technologies continue to self-integrate with music, inevitability expanding the bounds of self-expression. As quantum computers and their capabilities are utilized more by large industries such as cybersecurity and quantum chemistry, a smaller but ever-present inclination appears to adopt this emerging technology into music.

Cross-disciplinary research is already emerging within the field of quantum computing; multiple experimentations exploring the various methods of integrating science and art can be found in the literature (Katz 2010). A primary example is Quantum Computer Music: Foundations, Methods and Advanced Concepts, which culminates various papers and articles into a book (Miranda 2022). Some leverage quantum computers to “solve” music as an optimization problem, balancing various components that define music (Arya et al. 2022). Others approach implementation by developing quantum tools to aid music composed with human ingenuity rather than trying to replicate it (Hamido 2022).

In this experiment, we attempt to create a functioning program through the Qiskit and Python learning languages within IBM’s Quantum Lab. Unlike their classical counterparts, the advantage of using quantum computers to generate music rather than classical computers is that qubits display true randomness when measured. More often than not, this generates a random assortment of notes without any form or inclination to a sort of musical pattern, resulting in unpleasant music.

This article outlines the first phase of this research, which ultimately seeks to utilize quantum computing to create technically “perfect” music based on traditional music theory.

Introduction

Recent explorations of quantum computing’s potential within the arts, particularly music theory and composition, have made significant strides in generating visual arts based on quantum algorithms as well as music sequences (Arya et al. 202). Examples of advancements include the means to control an inverse Fast Fourier Transform (FFT) sound synthesizer and an adaptive musical sequencer, culminating in the composition “Zeno” as a practical demonstration of this technology’s capabilities (Miranda 2021). Others in the field represent music composition as an optimization problem and attempt to solve it using quantum annealing via adiabatic quantum computing to craft melody, rhythm, and harmony. An example of music generation through this method is using D-Wave quantum annealers (Arya et al. 2022.) Another further suggests the development of Quantum-computing Aided Composition (QAC) and the QAC Toolkit Max package, reflecting on Quantum Computing’s role in enhancing creative music practice and addressing the integration challenges and opportunities (Hamido 2022.) While the fields of physics, computer science, and music have been interconnected for decades with the rise of electronic sound boards and synthesizers, quantum computation within the musical industry is fairly new, and possibilities for composition and sound realization are many.

The objective, as a Quantum Music Composer, is to create a foundation in which developing advanced quantum algorithms capable of generating complex sequences of notes and chords can be made more simple by constructing a base from which additions to the composer are easy to implement. This long-term and multiphasic project has two objectives: (1) to contribute to the theoretical understanding of quantum music through exploring quantum circuits and how to prepare the input data and (2) to provide practical tools that composers and musicians can use to explore new auditory landscapes. Doing so, we aspire to open up new dimensions in music composition, where quantum-induced variability and complexity introduce a novel sound aesthetic.

In what follows, we will delve into the background of quantum music, outline the quantum algorithms designed for our Quantum Music Composer, and discuss our work’s potential implications and applications in both the scientific and artistic communities.

History of Quantum Music

Quantum computing, characterized by its ability to process complex calculations at unprecedented speeds due to principles like superposition and entanglement, has found applications across various fields, from cryptography to drug discovery (Bains 2023). Recently, this cutting-edge technology has ventured into the realm of music, birthing the concept of quantum music. Quantum music explores how quantum computing can revolutionize music composition, synthesis, and even performance, pushing the boundaries of creativity and technology.

The pioneering efforts in quantum music have sought to harness quantum algorithms for generating novel musical compositions that may be impossible with classical computing methods (Basak 2022). These endeavors include the generation of sequences of notes or chords that reflect the probabilistic nature of quantum measurements, leveraging quantum randomness for creativity, and modeling musical structures using quantum states (Basak 2022).

Methods

Basics of Quantum Algorithms

To better understand what quantum computing is, one needs first to understand the qubit. A classical bit can be in two states of either 0 or 1, but the qubits can be expressed in any state of 0, 1, or a quantum superposition of both (Watrous 2022). This allows quantum computers to essentially browse possible answers with an inclination to the correct one (Watrous 2022). In theory, quantum entanglement takes this property further. As a single qubit can form a unique connection with every other qubit in a computer, computing power increases exponentially (Watrous 2022). This makes quantum computing faster, and the processing power tackles problems that are currently intractable by classical computers (Watrous 2022).

Basic quantum operations: Bloch Sphere and primitive gates

Quantum algorithms are founded on basic quantum operations as well as the basics of quantum mechanics (Watrous 2022). Still, the heart of quantum computing is formed by operations manipulating qubits, the foundational units of quantum information that can exist in many states simultaneously due to the principle of their superpositions (Watrous 2022).

Below are relevant concepts pertinent to the understanding of the algorithms developed in this experiment.

Quantum Operations: Quantum operations are the processes that manipulate a qubit’s state, whether in superposition or not. These processes are executed using quantum gates, similar to the logical gates used in classical computing. However, unlike those found in classical computers, quantum gates create and handle superpositions and entanglements, forming computation’s exponential power. A Bloch sphere is a three-dimensional representation of the probability that a qubit will likely output when measured (Watrous 2022).

Superposition: In superposition, quantum gates allow qubits to represent 0 and 1 simultaneously. This gives quantum computing power due to the parallel processing ability it grants to a problem’s solution (Watrous 2022).

Entanglement: Another key operation is entanglement, a quantum property in which the ability of one qubit depends on that of another, no matter the distance. This phenomenon allows quantum computers to make certain calculations more quickly than their classical counterparts (Watrous 2022).

Measurement: Measuring a qubit process causes it to jump into one of the classical states (0 or 1) called its measured state. This operation is not only required to retrieve the result of treatment on quantum computing but also provokes the problem of quantum decoherence, a phenomenon in which the quantum state loses its quantum properties of superposition (Watrous 2022).

Resources

This research introduces a previously untested approach to music composition by leveraging quantum computing’s inherent “true randomness:” randomness that does not rely on a key and an algorithm to generate random numbers like that seen in a classical computer. Utilizing the IBM Quantum Lab, a comprehensive platform accessible via the IBM Quantum website, quantum simulators were used to conduct these experiments (IBM 2024). The IBM Quantum Lab was chosen for its seamless integration with IBM’s quantum devices, offering a robust environment for developing and testing quantum algorithms.

Basics of Musical Composition

Our aim is to create a quantum music composer that employs the stochastic nature of qubit measurements to generate random notes and chords. This gives our composer the means of coming up with music reflecting this complexity and the nuanced nature of natural sounds in a closer way than it has ever been. The combination of precision technology and the organic unpredictability of nature would give birth to innovative and dynamic musical pieces, and through quantum computing, the organic aspect of this would be authentic.

Implementation

At the core of our implementation is the use of IBM Qiskit, a versatile quantum computing framework that applies quantum mechanics principles in innovative ways, notably in music creation. Our process begins with establishing a musical scale, such as the C Major scale, for its simplicity, involving only white piano keys. We then designed a quantum circuit with a calculated number of qubits, ensuring that each note in our scale corresponds to a unique quantum state. This setup allows for the random selection of notes upon qubit measurement.

Execution involves repeatedly generating random notes to form chords, thus creating a sequence of musical expressions over time. The outcome of this quantum-inspired composition process is visualized in a “piano roll” format. This graphical representation, akin to a piano roll (a digital grid that shows music notes with pitch/note on the y-axis and time on the x-axis) for composing and editing in a DAW (Digital Audio Workstation), offers an intuitive view of the quantum-generated music sequence, making it accessible and understandable for musicians and composers.

By combining the principles of quantum computing with musical creativity, this research not only explores new frontiers in music composition but also demonstrates the practical application of quantum randomness in artistic endeavors.

Code

The following is the code used to create the quantum music composer. Notes are placed throughout the code to provide critical context.

The Sound of Quantum: Unveiling New Dimensions in Music through Quantum Computing | Submission

Python 

# Importing standard Qiskit libraries 
from qiskit import QuantumCircuit, transpile 
from qiskit.tools.jupyter import * 
from qiskit.visualization import * 
from ibm_quantum_widgets import * 

# qiskit-ibmq-provider has been deprecated. 
# Please see the Migration Guides in https://ibm.biz/provider_migration_guide for more detail. 
from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Estimator, Session, Options 

# Loading your IBM Quantum account(s) 
service = QiskitRuntimeService(channel="ibm_quantum")

# Invoke a primitive. For more details see
https://docs.quantum-computing.ibm.com/run/primitives
# result = Sampler().run(circuits).result()

Python
from qiskit import QuantumCircuit, Aer, execute from qiskit.visualization import plot_histogram
# Step 1: Define the Musical Scale and Notes # Example: C Major scale
notes = ['C', 'D', 'E', 'F', 'G', 'A', 'B']
# Step 2: Create a Markov Chain
# This is a simplified example with equal probabilities
# In a real scenario, you would define these based on musical theory or
existing compositions
# Step 3: Quantum Circuit
# Creating a basic quantum circuit
qc = QuantumCircuit(3) # 3 qubits for 8 possible states (2^3 = 8, including one extra state)

# Apply quantum gates to represent transitions (this is a simplification)
# In a full implementation, the gates would correspond to the probabilities in the Markov chain
qc.h(range(3)) # Applying Hadamard gate for superposition
# Step 4: Measurement and Note Selection
qc.measure_all()
# Execute the circuit
service = QiskitRuntimeService(channel="ibm_quantum")
backend = service.least_busy(operational=True, simulator=False) print(backend.name)
result = execute(qc, backend, shots=1).result()
counts = result.get_counts()

# Selecting the note based on the measurement
measured_state = list(counts.keys())[0] # Get the binary string
note_index = int(measured_state, 2) % len(notes) # Convert to integer and map to the scale

selected_note = notes[note_index] print(f"Selected note: {selected_note}")
# Step 5: Repeat the process to compose a sequence of notes
# This would involve looping the process and potentially updating the Markov
chain based on previous selections

Python
import matplotlib.pyplot as plt
import numpy as np
from qiskit import QuantumCircuit, Aer, execute
# Define the Musical Scale and Notes
notes = ['C', 'D', 'E', 'F', 'G', 'A', 'B']
note_indices = {note: i for i, note in enumerate(notes)}
# Create a Quantum Circuit
qc = QuantumCircuit(3) # Using 3 qubits for this example qc.h(range(3))
qc.measure_all()
# Execute the circuit multiple times to generate a sequence
backend = Aer.get_backend('qasm_simulator')
sequence_length = 8 # Define the length of the music sequence sequence = []

for _ in range(sequence_length):
result = execute(qc, backend, shots=1).result() counts = result.get_counts()
measured_state = list(counts.keys())[0] note_index = int(measured_state, 2) % len(notes) sequence.append(notes[note_index])
# Function to plot a piano roll
def plot_piano_roll(sequence, note_indices): fig, ax = plt.subplots(figsize=(12, 6))
  # Creating a piano roll matrix
piano_roll = np.zeros((len(notes), len(sequence))) for t, note in enumerate(sequence):
piano_roll[note_indices[note], t] = 1

# Plotting the piano roll
ax.imshow(piano_roll, aspect='auto', cmap='Blues', interpolation='nearest')
     # Setting the labels and titles
     ax.set_yticks(np.arange(len(notes)))
     ax.set_yticklabels(notes)
     ax.set_xlabel('Time Step')
     ax.set_ylabel('Notes')
     ax.set_title('Quantum Music Composer - Piano Roll Visualization')
plt.show()
   # Plotting the sequence of notes
plot_piano_roll(sequence, note_indices)

Results

Building the quantum music composer went smoothly. Aside from a handful of typos that produced bugs during the programming phase, there were no significant hurdles. The composer accomplished the task of putting a series of qubits into superposition and measuring them to choose a musical key at random with no resistance. It could also do so in quick succession. Initially, the program was configured to choose a single note for each time slot, but upgrading from this was simple. By repeating the note selection multiple times for each time slot, chords could be generated, enhancing the musical ability of the composer.

However, because the resulting notes were random at this stage of the experiment with no musical arrangement or form (like that of standard chords), more often than not, the composition produced by the program sounded objectively wrong.

Discussion:

Hypothetical Upgraded Quantum Composer

The first stage of this research resulted in creating a truly random chord generator. While rudimentary with a lack of rules to preference chords that create harmony (how well chords work together), the program developed has strength in its ability to also act as a template from which more complex features may be added, like music theory concepts, to provide direction to the process of composition. A method to accomplish this is through Markov Chains, where each key’s chance to be selected depends only on the state immediately before it.

The second phase of research will implement music theory principles to govern the program’s decisions. This will theoretically allow the quantum computer to create technically perfect compositions using Markov chains to model transitions between chords, which is a promising avenue to advance the efficacy and usability of this program (Basak 2022).

In the music industry today, music theory acts more as guidelines than set rules. Examples are commonplace in genres like jazz when notes that “shouldn’t” go together according to traditional theory create tension,a built-up of anticipation with a satisfying resolution that sounds and feels surprisingly good. However, this technicality is difficult to accomplish, so, for simplicity, a hypothetical program that involved music theory through Markov chains would stick strictly to music theory guidelines to ensure that “technically perfect” music is composed, even if the results are arguably uncreative.

Implementing “guides” formatted as music theory represented through Markov Chains presents a problem: music theory is a grand topic with no particular starting point, so what would act as the foundational principles for the program? Ultimately, our next generation of code wille begin with broad music theory guidelines: staying within a key. Once a key is selected, the next step will select different types of chords that best match with one another within the chosen key. Then, notes can be selected for each chord.

It is possible to introduce some probability gradient that lessens as the possible notes in the key stray further from the base note, resulting in the likelihood, but not certainty, that chords will remain within the same one or two octaves. For instance, if the base key of a chord is C4, say C major, which includes the keys C, E, and G, then it would be unlikely for the key of E7 to be selected to be a part of the chord because they are three octaves apart in a piano keyboard. Allowing E7 to remain possible limitedly is an example of an engineered stray feature with a low likelihood of occurring, but is appreciated for enhancing the music arrangement.

It should be mentioned that for most musicians, this is arguably a “boring” way to go about composition. Such experimentation, when following the rules of music theory strictly, is not often seen at the forefront of the music industry. However, an advantage to no experimentation is the lower likelihood of messing up the composition in pursuit of something pleasant, resulting in a process that would create something pleasant to listen to more often than not.

Conclusion

The program constructed and it’s previously laid out hypothetical further advanced version are purposefully simple quantum music composer algorithms because they directly assign an individual note to a collective qubit measurement. Our quantum circuit primarily uses qubit superposition to generate randomness that classical computers cannot reproduce. However, this does little to tap into the enormous potential quantum computing holds, as it does not yet access the quantum potential qubits that superposition offers. In the future, their forms may expand within the domain of music composition to encompass more niche elements of music, becoming increasingly complex in the process.

Current efforts in the field lack a general understanding of leveraging quantum computing’s extensive computational power for artistic creation, a pursuit I’d like to expand. The question remains: can the application of quantum music create structures as sophisticated as those of human composers? On this frontier, quantum computing could minutely appreciate and apply the principles of music theory for crafting compositions that are not merely original but, most crucially, sonically attractive. Creating “perfect music” for many is counterintuitive to the definition of music: an expression of emotion that all humans experience distinctively. However, the idea posits an intriguing possibility: that one-day quantum computing might yield universally moving compositions and proof of the transcendent capabilities of this burgeoning new music, free from any limitations.

Works Cited

A. Arya, L. Botelho, F. Canete, D. Kapadia, and O. Salehi. 2022. “Music Composition Using Quantum Annealing.” in Quantum Computer Music: Foundations, Methods and Advanced Concepts. Pp 373-406.

E. Miranda, S. Basak. (2022). “Quantum Computer Music: Foundations and Initial Experiments”. In: E.R. Miranda (Ed.), Quantum Computer Music: Foundations, Methods and Advanced Concepts. (pp. 43-54)

Hamido, O.C. (2022). QAC: Quantum-Computing Aided Composition. In: Miranda, E.R. (eds) Quantum Computer Music: Foundations, Methods and Advanced Concepts. Pp 159-196.

IBM. (n.d.). IBM Quantum. Retrieved from https://www.ibm.com/quantum

S. Bains, S. Gupta, K. Joshi, B. Kothapalli, S. Sharma and A. Dutt, “Quantum Computing in Cybersecurity: An in-Depth Analysis of Risks and Solutions,” 2023 3rd International Conference on Advance Computing and Innovative Technologies in Engineering (ICACITE), Greater Noida, India, 2023, pp. 1651-1654, doi: 10.1109/ICACITE57410.2023.10183060.

keywords: {Neuroimaging;Vocabulary;Quantum computing;Human intelligence;Standards organizations;Organizations;Search problems;AI;TF-IDF;Data Analysis;TF-GFP;NLP Method;Data Interpretation and IQ},

Watrous, J. (2022). Lesson 01: Single Systems | Understanding Quantum Information & Computation [Video playlist]. Qiskit by IBM. Retrieved from https://www.youtube.com/playlist?list=PLOFEBzvs-VvqKKMXX4vbi4EB1uaErFM SO

Arya, A., Botelho, L., Canete, F., Kapadia, D., & Salehi, O. (2022). Music Composition Using Quantum Annealing. In Quantum Computer Music: Foundations, Methods and Advanced Concepts (pp. 100-145). Springer. https://doi.org/10.1007/978-3-030-72116-9_34

Ableton. (n.d.). Ableton. Retrieved from https://www.ableton.com

Katz, Mark. Capturing Sound: How Technology Has Changed Music. United Kingdom: University of California Press, 2010.

About the author

Lucas Krippendorff

Lucas is currently a senior at Gulliver Prep High School. He enjoys physics, mathematics, engineering, and music. He participates in his school robotics team or composes music in his free time.

The post The Sound of Quantum: Unveiling New Dimensions in Music through Quantum Computing appeared first on Exploratio Journal.

Intro

Starting with the foundations of electricity, we briefly overview the foundation of a particle’s ability to have a charge and phenomena that come with different charges interacting. We qualitatively and quantitatively examine their interaction through forces, fields, flux, electric potential, and capacitance. Most sections are broken into subcategories to explain nuances and provide examples. Multiple figures are used as visual assistance to a descriptive section. Throughout the paper gravity was used as a reference subject because I have previous knowledge pertaining to Newtonian physics and because equations about gravity are symmetrical with equations about charges.

Forces and Fields are both defined as vectors in Physics, so vectors are important to understand electricity. Vectors are also beneficial because they have easy ways to add, subtract, multiply, and divide. Several other calculations like scalar and vector multiplication can also be used with vectors to find important quantities.

Introduction to Vectors

Vectors contain magnitude and direction. For forces and fields this means that they have a relative position and value in space. The properties of vectors are similar to the properties of an arrow drawn on a coordinate plane. A vector needs a point of reference or an origin just like an origin on a cartesian plane. With a point on a 2-D plane having two coordinates (x,y) and three coordinates on a 3-D plane (x,y,z), vectors can be represented as an arrow drawn from the origin to a point.

Adding and Subtracting

When two vectors are drawn on a plane, addition or subtraction of the two vectors can be shown graphically. When adding, a line that is parallel to vector A is drawn from the end point of vector B. After the same is done to vector A, then the intersection of both constructed segments represents the quantities of the summed vectors. The summed vector can then be drawn from the origin to the point of intersection. The complete structure forms a parallelogram structure; hence, the name of the method is parallelogram law of addition of vectors.

For subtraction, the coordinate plane parallelogram structure can also be made to create a visual representation. The difference is seen in the subtlety that A-B = A + (-B). The opposite of a vector is the same as rotating it 180º about the origin or finding the opposites of the x and y coordinates.

Representations of Matrices in 2-D and 3-D

If exact coordinates are known, then the addition and subtraction can also be represented by matrix addition and subtraction. If vector A has coordinates of (3,4) and vector B has coordinates of (2,1), then A + B =

Vectors with three values can be represented by 3-D space. A value for x, y, and z. While a parallelogram figure cannot be constructed, 3 × 1 matrices can be used. A vector with coordinates of (3,4,5) and another of (6,7,8) can be added as shown below.

Coulomb’s Law

Ever since some materials were discovered to have qualities that attract and repel other objects, there has been a need to quantize the phenomena. Through experiments, Coulomb found that relationships between two particles with this weird property depended on a constant, the charges of the particles, and the distance between them. Coulomb’s equation to model the force that two charges can have on each other is F = k · \q_aq_b\ / r² . This equation has the same properties as Newton’s law of gravitation where F = G · m₁m₂ / r². The derivation of the equation to account for the force on one particle to another and the direction of that force is

Meaning of k

Meaning of F

F is the force in newtons of the charges from particle a on particle b or vice versa. Since the force that particle a does on particle b is equal and magnitude and opposite in direction according to Newton’s third law, the forces must be distinguished. F_ab represents the force that particle a experiences by particle b.

Meaning of r

Multiple Forces

Electric Field

Coulomb’s law requires two particles to create a force, but can there be a force with only one particle? When one of the two particles travels farther and farther away, the electric coulomb force between them becomes weaker until almost nonexistent. Now, if we progressively bring this particle closer and closer to the other particle, a Force will come into existence and automatically enact. Therefore, this force exists when there is only one particle carrying charge.

Since the electric field’s existence was proved in the previous section, we now need a way to visually represent it. Electric and gravitational fields can be represented by lines and arrows. Each arrow represents the direction of the field at that point in space.

Electric Field Lines

Single Particles

When one particle is considered in the representation of an electric field, the direction of the arrows depends on whether the charge is negative or positive. If the charge is positive, then the arrows will be facing away from the particle. If the charge is negative, then the arrows will be facing towards the particle.

In Fig 3, the distance of each of the arrows is the same distance away from the center of the particle, so the force of the electric field is equal in magnitude at each arrow. In 3-D space, a hypothetical sphere surrounds a particle and equidistance faces contain forces of equal magnitudes.

Two Particles

When two particles are at play, they create different models of electric field lines. When field lines are closer together, it symbolizes a stronger field. When they are further apart, the field is weaker.

Electric Flux

We know how to calculate the forces and electric fields exerted by one or multiple particles, but fields cannot exist in a surface. Therefore, to quantify the electric field in a surface, electric flux is found.

Understanding Flux

Flux can be better understood when thought of like water. If there is a stream with water flowing to the right and a surface/plane that is in the middle, then flux is the force that the surface feels or the amount of water that is passing through it. When the surface is perpendicular to the stream, then the flux is at a maximum. When the surface is parallel with the stream, then flux is at a minimum. The important quantities when determining flux are the normal (the line perpendicular to the plane) of the surface and the angle between the normal and the direction of the electric field.

Quantifying Flux

Electric Dipoles

The reason dipoles are important to scientists is because they are found in molecules like H₂O. Water has a hydrogen bond with its two hydrogen atoms which creates a dipole. Calculating the force of the charges between dipoles is needed for the study of atoms.

Calculating a Positive and Negative Dipole

The simplistic form of a dipole is with one negative charge and one positive charge on the same plane with a point p. The charges are a distance, a, from the origin. The point, p, is a distance r from the origin so that p is r-a from the positive charge and r+a from the negative charge.

Dipoles in an Electric Field

Combining the electric field and dipoles helps represent how the electric field acts in useful instances. When a dipole with a positively and a negatively charged particle has the charges acting on each other, the force can be represented as a vector line traveling from the negative charge to the positive charge. When this is put into an electric field, each charge also reacts to the field. Since the positive and negative charges react oppositely to the field, they go in different directions. This makes the dipole system spin counterclockwise or clockwise which creates torque on the system.

Torque of a Dipole in a Field

Vector Product

Continuous Charge Distribution

One Dimensional

Two Dimensional

Three Dimensional

Gauss’ Law

The purpose of Gauss’ Law is to try and quantify the amount of flux that any body/surface experiences with an electric field traveling through it.

Proof of Gauss’ Law

Examples

With a charged particle inside of a sphere, the particle creates an electric field. This field passes through the surface of the sphere creating a flux. To measure the flux, the sphere is broken up into several surfaces labeled Δs. The flux at each Δs is calculated, and then added to find the total flux in the sphere.

Gauss’ Law is very important. Its importance can be seen in these applications of manipulating his formula to find resulting formulas for the electric field.

Solving for the Electric Field

One Dimensional Application

Two Dimensional Application

Work

Proving Electric Energy

Proving Electric Energy

Since the route does not matter, it means that electrical and gravitational forces are conservative forces. The work only depends on the starting and ending positions because it is conserved regardless of the path.

Solving for Work

Finding Electric Potential

Point Charge

Electric potential and the electric field have a similar, but different relationship with r. They both decrease when r increases, but electric potential decreases slower as the r gets larger.

Dipole

System of Charges

When multiple charges are acting on the same point, the net force that the point experiences can be calculated by summing the force exerted by each individual charge. This is also the same for an electric field: E = E₁ + E₂ + E₃… Even though electric potential is a scalar quantity, it holds the same principles V = V₁ + V₂ + V₃… This is important because generalizations can be made about the electric potential of systems of charges.

Equipotential Surfaces

One of the generalizations is equipotential surfaces. With a single charge, the equipotential surfaces are the same as circles surrounding the charge. Similarly, a 2-D plane containing a uniform charge will have equipotential surfaces that are square or rectangular and parallel to the charged plane.

Isoipse Lines

Equipotential surfaces can also be described as isoipse lines from a topographical map. The closer the lines, the steeper the change in elevation. In a similar manner, closer lines around a charge signify a greater force. Each line around a dipole or charge represents all the points that feel the same amount of charge.

Conductors

Conductors, usually metal, have a quality that allows electrons to pass through them easily. This lets electrons flow and a current to form. Conductors still follow Gauss’ law, so they cannot have an electrostatic field within. The electrostatic field is always zero because the same amount of field that enters will exit. Because they can have no internal electrostatic field, the surface has to always be normal to the electric field. The electrons on the surface or outside of it can experience a force and field.

Electrostatic Shielding

Since an electric field can exist on the surface of a conductor but not the outside, the field on the outside builds a shield like property. If there is a cavity inside the conductor, the electric field can still not exist inside when there is no internal charge. With the electrostatic shield protecting cavities inside, an external charge will not affect the conductor or the cavity. This is taken advantage of in daily life by Tracuit mountain huts and Faraday cages.

Capacitance and Capacitors

Definition of Capacitance

Capacitors are made of two conductors separated by an insulator like air. The conductors contain opposite charges and an electric potential. The electric potential is proportional to the charge of the two conductors, so capacitance can be defined as C = Q/V. Since the charge and electric potential depend on each other, the only factor that changes the capacitance is the shape and configuration of the two conductors.

Parallel Plate Capacitors

Parallel plate capacitors is a capacitor that contains two parallel plate conductors of opposite charges separated by a small distance. Since the plates are of opposite charge, electrons flow from the positive conductor to the negative conductor. To calculate the electric field we can use the continuous charge distribution formula for a 2-D surface because the plates act as 2-D objects.

Series and Parallel

References

[1] NCERT. (2006). Physics: Textbook for class XII 2 parts. National Council Of Education Research and Training.

[2] Course hero. Boundless Physics | | Course Hero. (n.d.). https://www.coursehero.com/study-guides/boundless-physics/the-electric-field-revisited/

[3]https://physics.stackexchange.com/questions/288172/why-is-electric-field-lines-away-from-an d-toward

[4] Physics Wallah. (2023, July 26). What is electric flux – definition, formula, unit, symbol: PW. Physics Wallah. https://www.pw.live/physics-articles/what-is-electric-flux

[5] Take online courses. earn college credit. Research Schools, Degrees & Careers. Study.com | Take Online Courses. Earn College Credit. Research Schools, Degrees & Careers. (n.d.). https://study.com/academy/lesson/cross-product-right-hand-rule-definition-formula-examples.ht ml

[6] Gauss’s law to Coulomb’s law: Physics and Mathematics, Gauss’s law, learn physics. Pinterest. (2020, June 13). https://www.pinterest.com/pin/591730838531027476/

[7] Three hikers take three different paths to the top of a … – brainly.com. (n.d.). https://brainly.com/question/19277682

[8] Cabane Tracuit: Wallis. AlpineWelten. (n.d.). https://www.alpinewelten.com/cabane-tracuit

[9] Staff. (2023, February 2). Faraday cage. Science Facts. https://www.sciencefacts.net/faraday-cage.html

About the author

Nathaniel Thornell

Nathaniel is currently a senior at Cheyenne Central High School. He enjoys physics and mathematics, as well as finding unique solutions to math problems, jigsaw puzzles, and Rubik’s cubes.

The post Electricity and Electric Phenomena appeared first on Exploratio Journal.

Summary

River pollution is a major global issue that poses a significant threat to the environment and human health. Rivers and other water bodies are affected by pollution from various sources such as untreated sewage, industrial waste, agricultural run-offs, and plastic litter. For example, the Ganges River in India, which is considered the largest river in India and is considered sacred by millions of people, is heavily polluted with untreated sewage and industrial waste. According to a study, over 3,000 million liters of sewage is dumped into the Ganges every day, making it one of the most polluted rivers in the world. In this research paper, we propose a new solution to combat this issue, a machine called as river cleaning machine which will remove floating waste and chemicals from the river using a unique technique. This machine will be boat like structure with a floating conveyor belt which leads upto the boat’s garbage collection can. The floating waste will come via this conveyor and can be stored in a storage can. The river cleaning machine is also equipped with a feature to remove chemicals and oils that float on the river surface. It This machine will be designed to operate in different water conditions and can be transported to different locations, it will be able to remove floating waste, plastics, and chemical pollutants, which are the major pollutants of the rivers and revolutionize the way we clean our rivers, help preserve these vital resources for future generations and improve the lives of aquatic species and to all those who depend on river water, basically everyone.

Introduction

According to NRDC, Unsafe water kills more people each year than war and all other forms of violence combined. Meanwhile, our drinkable water sources are finite: Less than 1 percent of the earth’s freshwater is actually accessible to us. Without action, the challenges will only increase by 2050, when global demand for freshwater is expected to be one-third greater than it is now. The floating debris and toxic floating chemicals cause maximum damage to the society. According to The Pacific Institute for Studies in Development, Environment, and Security – Every day, 2 million tons of sewage, industrial, and agricultural waste is released into water all around the world. This is the equivalent of the weight of 6.8 billion people. This debris waste and toxic chemicals must be removed from the water bodies as our drinkable water sources are finite. The world needs machines to clean this mess that has been created. This model of the machine consists of a floating conveyor belt which leads upto the boat’s garbage collection can. The floating waste will come via this conveyor and can be stored in a storage can (displayed in figure 1). The river cleaning machine is also equipped with a feature to remove chemicals and oils that float on the river surface. This feature is the latest technology of a smart filter with a shape-shifting surface can separate oil and water using gravity alone, an advancement that could be useful in cleaning up environmental oil spills, among other applications, say its University of Michigan developers.

This model of river cleaning machine has made the whole process of river cleaning so efficient with the help of conveyer belt and use of special smart filters for separation of oils/chemicals from water. This model is made keeping the finances in mind. The model can be built at a affordable cost so that the whole world can benefit from this model. This model will be designed to operate in different water conditions and can be transported to different locations, it will be able to remove floating waste, plastics, and chemical pollutants, which are the major pollutants of the rivers and revolutionize the way we clean our rivers, help preserve these vital resources for future generations and improve the lives of aquatic species and to all those who depend on river water, basically everyone.

Results

The aim of this experiment was to evaluate the efficacy of the river cleaning machine model in removing floating debris, plastics, and toxic chemicals from water bodies. The rationale for this experiment was based on the fact that unsafe water kills more people each year than war and all forms of violence combined, and that the world’s drinkable water sources are finite. With the increasing demand for freshwater, it is imperative to take action to preserve these vital resources for future generations.

The experiment was conducted by using the river cleaning machine model in a controlled environment with simulated floating waste and chemicals. The machine was equipped with a floating conveyor belt that led to a garbage collection can, and a smart filter with a shape- shifting surface to separate oil and water.

The results showed that the river cleaning machine was highly effective in removing floating debris and toxic chemicals from the water. The conveyor belt was able to collect the floating waste and store it in the garbage collection can (Figure 3), while the smart filter was able to separate the oil and water with high accuracy (Figure 2).

In conclusion, the river cleaning machine model showed promising results in removing floating debris, plastics, and toxic chemicals from water bodies. This model, designed to operate in different water conditions and be transported to different locations, has the potential to revolutionize the way we clean our rivers and improve the lives of aquatic species and those who depend on river water. Further research can be conducted to further optimize the design and performance of the river cleaning machine.

Discussion

The present study aimed to evaluate the efficacy of a river cleaning machine model in removing floating debris, plastics, and toxic chemicals from water bodies. The criticality of this experiment stems from the fact that contaminated water causes more fatalities annually than all forms of violence, including war. Moreover, with the increasing demand for freshwater, it is imperative to preserve this vital resource for future generations.

The experiment was carried out in a controlled environment, where the river cleaning machine was deployed to remove floating waste and chemicals. The machine was equipped with a floating conveyor belt that led to a garbage collection can, and a smart filter with a shape-shifting surface for oil and water separation. The results indicated that the river cleaning machine was highly efficient in removing floating debris and toxic chemicals from the water. The conveyor belt effectively collected the floating waste and stored it in the garbage collection can, while the smart filter accurately separated the oil and water. However, the large-scale deployment of this machine presents several challenges. The disposal of the collected waste and harmful oil requires proper chemical processes, such as thermal oxidation or bioremediation, which can be costly. In countries with low-income levels, the cost of producing the machines at scale may be a barrier. Thus, it is vital to find ways to reduce production costs and make this technology more accessible to these communities. In addition, the machine may face difficulties in shallow waters, and restricted locations, and may get damaged by submerged tree stumps. Furthermore, small fragments of weed may remain in the water and spread to other locations, thereby aiding in the dispersal of invasive species.

The pollution of rivers and water bodies is a major concern that needs to be addressed to protect human health and preserve these vital resources for future generations. Clean and healthy rivers not only reduce health risks but also improve the quality of life by promoting recreational activities, such as safe walking and running trails. This, in turn, can attract tourists, boosting both the economy and the well-being of the community. In the future, this project can be improved to sort more categories of waste, and advances such as a conveyor system and the use of solar panels can be integrated to increase efficiency and sustainability. Moreover, modifications to the size and capacity of the machine can make it suitable for use in large rivers and lakes, such as the Ganga, and can be utilized for aquatic weed harvesting and aquatic trash collection.

An example of river revitalization is the Iloilo City in the Philippines, where the main river was successfully revived, and a beautiful Esplanade was built, guided by the principles of unity, strategic planning, and political will. It is our responsibility as individuals to make a difference by reducing our own pollution and supporting initiatives like the river cleaning machine model.

In conclusion, the present study has demonstrated the effectiveness of the river cleaning machine model in removing floating debris, plastics, and toxic chemicals from water bodies. However, several challenges need to be addressed for its large-scale deployment, including the disposal of collected waste and reducing production costs. The preservation of our rivers is crucial for protecting human health and preserving these vital resources for future generations.

Materials and Methods

The river cleaning machine is designed as a modified boat, with an open end at the front that elevates the conveyor belt above the river surface by 20-30 centimeters, as illustrated in Figure 4. The boat is equipped with a garbage can to collect waste collected by the conveyor belt from the river surface. A separate water can, with a super membrane attached, is also included to segregate oil and chemicals from water.

Part 1 – The body of river cleaning machine

The river cleaning machine is designed as a floating platform with a conveyor belt on one side, as shown in Figure 4. The outer body of the machine is made of 316L stainless steel for corrosion resistance in harsh conditions, while the inner body is constructed from 304 stainless steel. The machine features rotating blades at the back to propel it through the water, powered by a 3-Phase AC current motor with IP-65 protection and a worm gearbox. The motion of the rotating blades is shown in Figure 5. The conveyor belt is controlled by drive and driven rollers, which move the SS wire mesh belt with gaps to allow water flow. The belt is attached to the garbage bin, as illustrated in Figure 4.

Part 2 – Garbage Bin

The garbage collection bin, which is integral to the functionality of the river cleaning machine, is constructed from durable HDPE plastic material. Its unique design features a rectangular shape that is molded to exact specifications, with a side that opens and closes seamlessly. To further enhance its functionality, the garbage collection bin is equipped with a state-of-the-art hydraulic lifting system that is seamlessly integrated into both the bin and the surface of the boat. This cutting-edge system allows the river cleaning machine to effortlessly remove waste from the bin when it is near the shore, utilizing a smooth and efficient oil-based hydraulic mechanism. The combination of robust materials, advanced design features, and innovative hydraulic technology, makes the garbage collection bin a truly impressive component of the river cleaning machine.

Part 3 – The Membrane and chemicals/oils removal system

The river cleaning machine also features a specialized HDPE plastic can that is specifically designed to hold a range of chemicals, as indicated in Figure 6. This innovative can is a critical component in the efficient operation of the machine and helps to ensure safe and effective chemical management.

Moreover, the river cleaning machine is equipped with a cutting-edge membrane solution that has been developed by researchers to address the challenge of separating oil and water mixtures. The membrane boasts impressive properties, including a coating that enables water molecules to bond with the polymer while oil remains above the filter. This innovative membrane has been tested and proven to efficiently separate oil and water, even in the presence of surfactants and dispersants, such as those that were seen in the Deepwater Horizon oil spill.

To ensure optimal performance, the coated filters have been designed to last for over 100 hours of continuous use without clogging, which represents a significant improvement over existing technology. The HDPE plastic can will feature two water line connections, including a motor-powered water line that draws water from the river body, and a pipe for dispersing purified water back into the river. The placement of the membrane within the can is depicted in Figure 7.

References

1. Tuteja Group – “TUTEJA GROUP DEVELOPS SMART FILTER THAT STRAINS OIL OUT OF WATER” University of Michigan, – mse.engin.umich.edu/about/news/tuteja- group-develops-smart-filter-that-strains-oil-out-of-water
2. UNEP – “Globally, 3 billion people at health risk due to scarce data on water quality” UN Environment Programe – www.unep.org/news-and-stories/story/globally-3-billion- people-health-risk-due-scarce-data-water-quality
3. Geographical UK – “The Ganges: river of life, religion and pollution” 20 Jan 2022. – geographical.co.uk/culture/the-ganges-river-of-life-religion-and- pollution#:~:text=Every%20day%2C%20around%20three%20million,polluted%20wat erways%20in%20the%20world.
4. NRDC – “Water Pollution: Everything You Need to Know ”. Jan 11 2023 – www.nrdc.org/stories/water-pollution-everything-you-need-know
5. Sorgum Waste –” Water Pollution Statistics” November 2022 – https://www.sourgum.com/trash-talks-blog/water-pollution-statistics/

6. Clarion Municipal – ”Floating Debris” – www.clarionmunicipal.com/floating- debris.html#:~:text=Floating%20debris%20affects%20water%20quality,to%20the%2 0municipal%20water%20supply.
7. Mega Cebu – “THE IMPORTANCE OF CLEARING RIVERS ” – 6 August 2015 – https://megacebu2050.wordpress.com/2015/06/08/importance-of-clearing-rivers/
8. Academia – “Silica-decorated Polypropylene Microfiltration Membranes with a Mussel-inspired Intermediate Layer for Oil-in-Water Emulsion Separation ” – www.academia.edu/8099279/Silica_decorated_Polypropylene_Microfiltration_Membr anes_with_a_Mussel_inspired_Intermediate_Layer_for_Oil_in_Water_Emulsion_Sep aration
9. Lake Forest – “Pollution on the Mississippi River ” – www.lakeforest.edu/academics/majors-and-minors/environmental-studies/pollution- on-the-mississippi- river#:~:text=Agricultural%20Runoff%20is%20one%20of,it%20is%20non%2Dpoint% 20source.
10. SSRN – “Research Paper” – 1 July 2020 – papers.ssrn.com/sol3/papers.cfm?abstract_id=3621962
11. Pure Chemicals Group – “Which is the best way to store chemicals?” – www.pure- chemical.com/blog/metal-or-plastic-containers
12. The Pacific Institute for Studies in Development, Environment, and Security – pacinst.org/
13. Business Standard – “Clean Ganga: Essel Infra, National Mission to build Sewage Treatment Plant” – www.business-standard.com/article/economy-policy/clean-ganga- essel-infra-national-mission-to-build-sewage-treatment-plant-117101100842_1.html

Copyright: © 2023 Jay Katariya. All articles are distributed under Attribution- NonCommercial-NoDerivatives 4.0 International

About the author

Jay Katariya

Jay is an 11th grad student based in the Pune/Pimpri-Chinchwad area. He has a strong personal interest in engineering and is constantly fascinated by the science and logic behind new innovations and technologies. Along with his passion for engineering, Jay also has a genuine interest in sports, physics, computer science, and design.

The post Rivers in Crisis: An engineering approach to removing pollutants and garbage with advanced water treatment systems appeared first on Exploratio Journal.

Introduction

Deep space missions have become the interest of space agencies over the past 50 years after humans successfully reached space and our moon. The technology required to explore the solar system and the universe outside our solar system has grown from simple rockets and capsules designed to bring people to the moon to impressive orbiters and satellites equipped with the latest in research technology to expand humanity’s understanding of our solar system and the universe that surrounds us.

This report will present the stories, physics, and science missions of four historic NASA deep space missions: Voyager, Pioneer (10 and 11), Galileo, and Cassini. These missions are of particular interest to me due to their role in boosting human understanding of various planets and the outer edges of the solar system. Voyager used gravity assist and a rare alignment of planets to research Jupiter, Saturn, Uranus, and Neptune. The Pioneer missions both flew by Jupiter and Pioneer 11 also conducted a detailed exploration of Saturn. Galileo sent a probe into Jupiter’s atmosphere and a spacecraft entered the Jovian orbit. Cassini used a probe and spacecraft to learn about Saturn, its rings, and its satellites as well. Combined these missions altered humanity’s concepts of space by confirming existing theories and presenting information that lead to new questions. This paper will analyze the science objectives of each mission, their orbits and launch vehicles, and other particularly interesting information. To conclude, the facts of previous missions will be used to propose ideas for new missions and offer commentary on established plans for future missions as well.

Outline of Missions

Voyager

The Voyager missions were launched in the 1970s to explore deep space beyond what humans had conceived before. Intended to flyby various bodies within the solar system and then continue gathering data outside of our solar system, the Voyager missions have been instrumental in learning about planets within our solar system and about the energy and space outside the solar system as well [1].

Science of the Mission

The Cosmic Ray Subsystem (CRS) looks for energetic particles in plasma and has high sensitivity. Such particles can be found in intense ration fields like the area around Jupiter, or from other stars. The CRS aimed to gather data to provide information on the content of energy and dynamics of cosmic rays across the galaxy in an attempt to better understand ray sources from across the galaxy, even beyond our star [2]. Highly energetic particles can be detected from fields around large planets such as Jupiter. Stars also emit high energy particles which the CRS system tracks. Since Voyager is now beyond our solar system in deep space, these readings provide scientists with important information about the universe that surrounds us.

Voyager also had a three-part Infrared Interferometer Spectrometer (IRIS) which acted as a thermometer, detecting temperature emissions from space bodies, a sensor for different elements and compounds near atmospheres of space bodies, and a radiometer to measure sunlight reflected at ultraviolet, visible, and infrared frequencies. The use of IRIS as a thermometer in space enables more accurate atmospheric dynamic models [3]. This aids the future of space missions, particularly initiatives to find habitable environments for alien life. Although IRIS shut down in 1988, it transmitted important information about Neptune and Uranus which led to our understanding that the two planets have roughly the same temperature. Since Neptune is substantially further away from the Sun, scientists concluded that the similarity in temperature was due to higher methane content trapping more heat on Neptune.

Voyager 1 has the Golden Record: a message from humanity to intelligent alien species including greetings in 55 human languages, pictures of people and places on Earth, and various samples of music. The two sets of Golden Records spin at 16.67 RPM and play a variety of famous songs from classical Mozart to popular American 1970s songs along with various sounds of nature, humans speaking, and other naturally occurring sounds from the planet. The Golden Record also shows a pulsar map to guide any viewers toward Earth [4]. Pulsars are the remains of dying stars whose rapid spinning and magnetic field emit a beam of light, which is why pulsar diagrams show planets around their star connected with beams of light. Figure 1 depicts the Golden Record as presented on the NASA website.

The spacecraft also had an Optical Calibration Target, a flat rectangle with constant color and light properties for cameras and infrared instruments on the spacecraft to calibrate themselves [5]. The Optical Calibration Target served as a visual target with known properties to compare measurements from space, particularly since different cameras and sensors aboard the Voyager satellites had their own characteristics and exhibited different pictures/visual patterns.

Launch Vehicle and Orbit

Voyager’s launch and path is something of a beauty itself, designed to take advantage of an arrangement of planets which only occurs every 175 years. Voyager swung from planet to planet in a process called gravity assist, because the gravitational pull of each planet (Jupiter, Saturn, Uranus and Neptune) bends the flight path and increases its speed enough to swing it to the next destination. This process minimized the propellant and need for engines and cut the flight time to Neptune from 30 years to 12 years.

Gravity assist lies on satellites orbiting about space bodies in an hyperbolic shape, thus conducting their flybys of planets at periapsis. The hyperbolic orbit is determined by the magnitude of the force of gravity acting on the satellite from the planet or moon it orbits. Since energy is conserved in an orbiting system, and periapsis means that the satellite is the closest to the planet as it will ever be, satellites fly very quickly past their planets [6]. The science equipment and data gathering features onboard then have very little time to actually image and collect data about the planets they fly by.

Launching a deep space vehicle like Voyager requires a period of powered flight which carries the vehicle from Earth’s atmosphere to free flight in space. This requires a launch vehicle to thrust the satellite into orbit which eventually falls off at burnout when the satellite is in free flight. In flight, Voyager 1 focused on flybys of Jupiter, Saturn and Titan, Saturn’s largest moon. Voyager 2 continued from Saturn and Jupiter to Uranus and Neptune as well. Both Satellites are now in deep space beyond the solar system, and it is anticipated that they will continue sending information back to Earth for 20-30 years. They are the longest flying and farthest venturing spacecraft in history and provide scientists with valuable information about the nature of energy and radiation in space [7].

Deep Space Networks

Sharing data from deep space satellites like Voyager back to Earth requires precise time synchronization. This is accomplished by the use of Deep Space Networks (DSNs) in California, Australia and Spain which provide coverage for all space missions [6]. Communication with DSN technology requires precise time information because while in orbit, there are times when a satellite cannot directly communicate with Earth. Whether the sun is between Earth and the satellite, or the body that the satellite is orbiting interferes in the signal, DSN systems can only transmit signals at allocated time intervals. To do so, NASA had used a manual system initially but has now adopted a digital, Sequence of Events (SOE) driven automation system. The SOE for Voyager contains information about the state of the spacecraft, any deviance/changes to the flight path, notification for the beginning and end time of orbits, information about the bit size and format of data being transmitted, and changes in the frequency of information being transmitted [8].

Pioneer

Pioneer 10, launched in March 1972, was built to study Jupiter’s atmosphere, the magnetosphere and moons around Jupiter like Io in particular. Pioneer 10 was the first satellite to fly beyond the asteroid belt, and also collected data on the solar wind patterns and dust distribution around Jupiter. Pioneer 10 completed its flyby of Jupiter in 1973 and became the first spacecraft to ever cross the solar system into interstellar space. Due to a failure of the power source, Pioneer 10 stopped transmitting information to Earth in 2003 but its 30 year flight far exceeded the 21 month mission it was assigned for. It is flying with a trajectory to reach the star Aldebaran in roughly two million years [9]. Pioneer 11 was the twin spacecraft of Pioneer 10, launched in April 1973 to primarily study Saturn although it passed Jupiter in gravity assist. Although Pioneer 11 experienced a number of malfunctions like the temporary failure of the Radioisotope Thermographic Generator, the heat and power source, the mission was a success and significantly enhanced human understanding of Saturn [10].

Science of the Mission

Pioneer 10 and 11 carried a tool called a helium vector magnetometer (HVM) which measured magnetic fields around Jupiter. The NVM protruded ~6.5 meters out from the rest of the satellite to reduce the effects of the spacecraft magnetic field and balance the spin of the spacecraft. Scientists had previously been able to observe the interplanetary magnetic partners from orbits around Mars, and they remained curious about the impact of the Sun’s magnetic field controlling the flow of plasma and magnetic energy to the rest of the solar system. With the Pioneer missions, the HVM collected data on the structure of the interplanetary field up to Jupiter, mapped a specific magnetic field of Jupiter itself and evaluated solar wind interactions about Jupiter [11].

Pursuant to the mission to better understand the Sun’s impact deep in our solar system, Pioneer carried a Cosmic Ray Telescope (CRT) to monitor solar rays and track high energy particles from the Sun. The device also measured particles in Jupiter’s orbit. It was composed of three telescopes, one for high energy particles, another for medium energy, and a last for low energy particles [12]. Coupled with data from future missions including Voyager, this data has led to a more precise understanding of Jupiter’s energy and how the Sun’s energy fades at further points in the solar system.

Pioneer was also the first satellite to take detailed pictures of the Great Red Spot, a massive storm on Jupiter larger than Earth. Pioneer 10 made observations of Jupiter’s poles and enabled a much more detailed perception of Jupiter to Earth’s population.

Launch Vehicle and Orbit

Pioneer 10 was the first spacecraft to use gravity assist to reach escape velocity to leave the solar system. By slingshotting from Jupiter to Saturn, Uranus and Neptune, Pioneer 10 escaped on its trajectory into interstellar space and was the furthest human built device from Earth, until it was surpassed by Voyager in the late 1990s.

When Pioneer was launched from Earth, it entered a heliocentric orbit which was tweaked with small thrust maneuvers from the Pioneer Navigation Team until the gravitational field strength of Jupiter exceeded that of the Sun. After the flyby of Jupiter, Pioneer returned to a heliocentric orbit until it reached Saturn [8]. A paper from researchers at the Jet Propulsion Laboratory about the anomalies detected in Pioneer’s orbit also includes an informative image of the paths taken by both Pioneer missions (see Figure 2).

Pioneer 10 and Pioneer 11 Distinctions

Both Pioneer spacecraft were created almost identical and were simply launched with different intended orbits to research different bodies. Pioneer 11 last transmitted data in 1995 and Pioneer 10 last transmitted data in 2003. Both spacecraft served long after they were anticipated to fail and data from the outer brinks of the solar system lead to an understanding of a discrepancy between the anticipated speed of travel and the real speed dubbed the Pioneer Anomaly. The primary science difference between the two mission lies in their trajectory: Pioneer 10 explored Jupiter, its magnetic field and its satellites in great detail, then flew deeper into the solar system while Pioneer 11 hyperbolically sped past Jupiter, still capturing data and images, primarily aiming for Saturn and research on Saturn’s rings, magnetic fields and properties [10]. Pioneer 11 is now hurtling towards the center of the Milky Way although humanity lost contact with it decades ago. The Golden Record is still prominently shown on both spacecraft for any curious intelligent life in the future.

Pioneer Anomaly

Years into both Pioneer flights, it was noticed that the spacecraft were not moving with the acceleration that was predicted. On the outer edges of the solar system, both Pioneer spacecraft slowed down (5000 km per year). This deviation in behavior initially caused concern in the physics community, because without a reasonable explanation, the Newtonian models of physics would have to be questioned. Eventually, Doppler data (information about lightwaves of different wavelengths) were transmitted from Pioneer back to Earth which set the record straight. The reason for the slow down was simply the anisotropic dispersion of the internal heat generated from the science tools onboard each spacecraft. A paper from JPL describes the issue, saying that “Pioneer spacecraft were powered by SNAP-19 (Space Nuclear Ancillary Power) RTGs mounted on long extended booms designed to protect the on-board electronics from heat and radiation impact”. When these SNAPs got hot, the thermal radiation produced could disrupt the balance of forces on Pioneer, but NASA had placed them on specially balanced rods far away from the body of the spacecraft in order to balance each other out. The failure of this system is currently being researched and remains a topic of interest to amend for future missions. Since the balancing mechanism did not work, SNAP emitted thermal photons in an uneven way, which in return caused a recoil force in the opposite direction of the photos. After all, momentum is still conserved within the photon-spacecraft body. This uneven distribution of force is the current accepted explanation for the discrepancy between anticipated and real speed [13].

Galileo

NASA’s Galileo mission was a historic first for human exploration in space and led to an immense growth in understanding Jupiter. Galileo was the first satellite to ever orbit an outer planet, and it spent eight years orbiting Jupiter gathering information on the planet itself and its various moons. Data gathered from Galileo is the basis for future missions to Europa to explore the potential of subsurface water, among other future space missions as well.

Science of the Mission

Galileo used plasma and particle detectors like the Voyager and Pioneer missions, but employed a much more sophisticated set of cameras and sensors for near-Jupiter orbit.

The Solid State Imaging Camera (SSI) was intended to study Jupiter and its satellites using a modified spare of the narrow angle telescope used on Voyager. The camera operated in eight filtered band passes and provided higher resolution, better filters and more effective bandwidth. Although the SSI did not come with an ultraviolet band, the images were clearer and more useful than prior missions. The amended design from the Voyager mission also improved performance in baffling, a process which eliminates visual noise from scattered light. The primary science missions of this advanced camera was to investigate Jupiter’s atmosphere and clouds, measure and determine the properties of Jovian satellites, map the distribution of minerals on the surface of Jupiter’s moons and search for any other behavior or atmospheric emissions, particularly from the night side of Jupiter [14].

Galileo also carried the Heavy Ion Counter (HIC), an engineering experiment to monitor heavy ion activity in order to find information on radiation near Jupiter and determine the parameters for designing future radiation safe electric material for deep space exploration. The experiment included two Low Energy Telescopes (LETs) used to sample a wide range of energies. The information gathered from Galileo, when combined with data from Pioneer and Voyager, has offered important guidance to scientists about the future of electricity and radiation in space.

Since the Galileo mission was orbiting around Juptier and could not escape further into deep space, it was instructed to hurtle towards Jupiter’s atmosphere in 2003 where it was destroyed. The mission was over because it had collected enough relevant data for NASA to use. Galileo also took a number of detailed pictures of Jovian satellites, including the moon Io (see Figure 3).

Launch Vehicle and Orbit

Galileo was the first mission to ever orbit an outer planet. To do so, the spacecraft had to use gravity assist from Venus and Earth to pass the asteroid belt and reach Jupiter. Galileo did one flyby of Venus and one of Earth, gathering enough momentum from the hyperbolic path it traced around both to thrust itself towards Jupiter. Along the way, Galileo even took pictures and gathered data of a few large bodies in the asteroid belt. Galileo was composed of a spacecraft and a probe. The spacecraft was the source of thrust around other bodies while the probe was intended to be a short-lived tool descending in the atmosphere to measure temperature and other atmospheric factors. Six years after leaving Earth, Galileo reached Jupiter and the probe separated from the spacecraft, entering Jupiter’s atmosphere. The probe descended for just under an hour with parachutes and transmitted data on the strong winds, intense heat and unexpected dryness of the Jovian atmosphere before it was vaporized by the head [15].

While the spacecraft relayed this information from the probe back to Earth, mission scientists at NASA had to determine the right moment to activate the engine on the spacecraft to enter Jupiter’s orbit. Too little thrust, and Galileo would sail past Jupiter into deep space, and too much thrust would force the spacecraft to the same short lived life as the probe: melted in the atmosphere. The decisions made were successful and Galileo entered orbit, where it remained for two years. Galileo maintained a long elliptical orbit around Jupiter because the different distances away from the planet enabled the devices onboard to gather data on the planet, the rings around it and conduct flybys of important moons [16].

The Galileo spacecraft and probe were launched by an Inertial Upper Stage (IUS) launch vehicle. IUS is an unpiloted booster used from the 1980s to the early 2000s. After launching from the ground, the IUS employed a second stage launch boosting its payload into higher orbit, or in Galileo’s case, to another planet of the solar system. The IUS was designed by Boeing and the two rocket burns happened one hour, then six and a half hours into flight [17].

Cassini

Cassini was a joint mission between NASA, European Space Agency and the Italian Space Agency to explore Saturn, its moons and its rings. Much like Galileo, Cassini employed a probe called Huygens to explore Titan, Saturn’s largest moon, while a spacecraft orbited Saturn gathering other data.

Science of the Mission

The science devices onboard the Cassini orbiter fall into three categories: Optical Sensing, Fields/Particles and Microwave Sensing.

With regards to Optical Sensing operations, Cassini carried a Visible and Infrared Mapping Spectrometer (VIMS) which collected light that is visible to humans, and infrared light of longer wavelengths. VIMS separated light by the wavelengths it detected which allowed scientists to break down the composition of Saturn’s atmosphere, its rings and its satellites as well. This proved important during orbit because NASA determined that Titan has an ice volcano, and Titan also had clear polarity similar to Earth with cold poles and a warmer center. While VIMS was used to disassemble specific views on Saturn, Cassini also carried an Imaging Science Subsystem (ISS) which functioned as the main eyes for the spacecraft. While VIMS focused on the visible spectrum and infrared light, ISS also caught ultraviolet light [18]. The ISS made Cassini famous both due to its role in navigation and because most of the iconic pictures from Cassini came from ISS. Popular images of Saturn and its rings came from the ISS, along with important data about the surface of Titan. This information came from blocking all but certain wavelengths to see below the atmospheric smog.

To better conceptualize the plasma, electric/magnetic fields and energy systems around Saturn, Cassini also carried a Magnetometer (MAG) and the Cassini Plasma Spectrometer (CAPS). MAG was a simple device similar to tools used in other missions. While the Cassini spacecraft orbited Saturn, it recorded the direction and strength of magnetic fields around the spacecraft to develop a 3-D model of the magnetosphere and understand how it impacts the moons, the rings and gasses around Saturn. Thanks to Cassini’s elliptical path around Saturn, it orbited in and out of the magnetosphere which allowed a more sophisticated model to be built based on observations from inside and outside the zone of interest. Going deep into Saturn’s dense helium core would yield more information as well, but remains a figment of imagination right now because any human built spacecraft would vaporize well before getting to the center of Saturn. Much like the Voyager spacecraft, having a magnetic detector right next to a metal body would significantly skew results, so MAG was actually installed on an 11 meter metal arm as far away from the spacecraft as possible [19]. This arm was folded at takeoff and simply opened two years after it left Earth. CAPS had three sensors: an electron sensor, ion mass spectrometer and ion beam sensor. Each of them measured particle kinetic energy and direction, but the ion mass spectrometer collected data on particle mass as well [20]. Yet again thanks to an elliptical orbit which enabled the spacecraft to interact with Saturn’s atmosphere at different radii from the surface of the planet, CAPS was able to collect information about the composition of the atmosphere and magnetosphere

To collect information on microwave activity, Cassini also carried the Radio Science Subsystem (RSS) which sent its own radio signals towards Saturn and learned about the objects it interacted with by the radio waves which bounced back towards Cassini. This was used to learn about gravity fields, the structure of the rings of Saturn and some of the surface properties as well [21]. Coupled with the visual data from the cameras and the atmosphere information from the probe, this led to a much more complete model of Saturn and deeper understanding of the rings and satellites around it.

Launch Vehicle and Orbit

Cassini’s orbit is a work of gravity and geometric art. While the path appears to be elliptical, Saturn is actually acting much more like a focus point for the orbit. That is to say, Saturn is relatively close to the end of the major axis of the ellipse. In reality, the orbit of Cassini has been a combination of two hyperbolic traces: a choreography between Saturn and Titan, a massive moon. Cassini begins its journey towards Saturn, crossing between the planet and its rings, when it is the furthest away from Saturn: a point known as apoapse. After that point, Cassini swirls around and away from Titan towards Saturn. Prior to the Cassini mission, Titan was only photographed by Voyager and observed from Earth [22]. These close, hyperbolic orbits not only enabled more detailed photography and research, but the Huygens probe was able to get to the surface of Titan and gather important information.

Cassini was guided to space by the Titan IV-B launch vehicle, which was NASA’s most powerful launch vehicle at the time employing a two stage launch system. The Titan series had been used by the Air Force for various military applications, and were employed extensively by NASA due to their reliability and sheer power [23].

Conclusion and Future Missions

Right now, NASA has dozens of plans to conduct flybys of important asteroids and planets in the coming years. Venus and Mercury seem to be of particular interest, which makes sense given the past focus on Jupiter and Saturn. While the space community believes firmly in the importance of such initiatives, and supports the continued research of planets and space bodies, there is interest in the Europa Clipper mission scheduled for 2024 [24]. Prior images of Europa from NASA show a fascinating fractured surface (see Figure 4) which appears interesting to study. The plan is for NASA to send a spacecraft into Jupiter’s orbit in order to conduct numerous fast flybys of Europa, likely employing the same broadly elliptical shaped orbit around Saturn. Given that Europa is known to have icy surfaces and might harbor water, there is also value in sending a probe to Europa’s atmosphere to better understand its habitability. The same techniques from Galileo can be employed and the information from a probe coupled with a spacecraft would likely yield more direction for future missions than just distant observations from a spacecraft [25].

The exploration of space was unthinkable 100 years ago and has become a reality today. Deploying principles like gravity assist, using hyperbolic flybys of planets and manipulating energy across our solar system has enabled humanity to access and explore worlds previously only dreamt of. As the advent of a period of continued space exploration dawns and humanity prepares to take off on the path to understanding the universe around us better, it is important to recall the physics and engineering concepts discovered and proven in past missions while embracing the future of innovation and change to come.

Bibliography

[1] “Voyager – The Interstellar Mission,” voyager.jpl.nasa.gov. http://voyager.jpl.nasa.gov/mission/interstellar-mission/

[2] J. W. | P. Thursday, October 24, and 2019, “40 years later, these Voyager instruments still talk to NASA,” Astronomy.com, Oct. 29, 2019. https://astronomy.com/magazine/2019/10/after-40-years-voyager-still-talks-to-nasa-with-7 -instruments

[3] “Voyager – Spacecraft – Infrared Interferometer Spectrometer and Radiometer (IRIS),” voyager.jpl.nasa.gov. https://voyager.jpl.nasa.gov/mission/spacecraft/instruments/iris/

[4] J. Lee Oakes, “Voyager Golden Record: Through Struggle to the Stars,” Smithsonian Music, Sep. 24, 2019. https://music.si.edu/story/voyager-golden-record-through-struggle-stars

[5] “Ring-Moon Systems Node – Voyager 1 Narrow Angle Camera Description,” pds-rings.seti.org. https://pds-rings.seti.org/voyager/iss/inst_cat_na1.html (accessed Nov. 20, 2022).

[6] R. Braeunig, “Basics of Space Flight: Orbital Mechanics,” www.braeunig.us. http://www.braeunig.us/space/orbmech.htm#launch (accessed Nov. 20, 2022).

[7] NASA, “Voyager 3D Model,” NASA Solar System Exploration, Jul. 26, 2019. https://solarsystem.nasa.gov/missions/voyager-1/in-depth/

[8] R. Hill, S. A. Chien, C. Smyth, K. Fayyad, and T. Santos, “Planning for Deep Space Network Operations,” undefined, 1995, Accessed: Nov. 20, 2022. [Online]. Available: https://www.semanticscholar.org/paper/Planning-for-Deep-Space-Network-Operations-Hill -Chien/64e8702993baffc32f911272ba1122a91bbd3ba3#citing-papers

[9] “The Outer Planets: Missions: Pioneer 10 & 11,” lasp.colorado.edu.https://lasp.colorado.edu/outerplanets/missions_pioneers.php

[10] “Pioneer 10 and 11, outer solar system explorers,” The Planetary Society. https://www.planetary.org/space-missions/pioneer

[11] “In Depth | Pioneer 10 – NASA Solar System Exploration,” NASA Solar System Exploration, Jul. 24, 2019. https://solarsystem.nasa.gov/missions/pioneer-10/in-depth/

[12] F. McDonald, “Cosmic Ray Telescope Experiment (CRT), Pioneer 10/11 Program,” Technical Report, Maryland Univ. College Park, MD United States Inst. for Physical Science and Technology, Jun. 1999, Accessed: Nov. 20, 2022. [Online]. Available: https://ui.adsabs.harvard.edu/abs/1999STIN…9964263M/abstract

[13] S. G. Turyshev and V. T. Toth, “The Pioneer Anomaly,” Living Reviews in Relativity, vol. 13, no. 1, 2010, doi: 10.12942/lrr-2010-4.

[14] “NASA – NSSDCA – Experiment – Details,” nssdc.gsfc.nasa.gov. https://nssdc.gsfc.nasa.gov/nmc/experiment/display.action?id=1989-084B-10#:~:text=Des cription

[15] “Galileo – In Depth,” NASA Solar System Exploration, Aug. 15, 2018. https://solarsystem.nasa.gov/missions/galileo/in-depth/

[16] “Galileo Project Information,” nssdc.gsfc.nasa.gov. https://nssdc.gsfc.nasa.gov/planetary/galileo.html

[17] “Boeing Inertial Upper Stage Space Payload Booster,” National Museum of the United States Air ForceTM. https://www.nationalmuseum.af.mil/Visit/Museum-Exhibits/Fact-Sheets/Display/Article/6 93053/boeing-inertial-upper-stage-space-payload-booster/#:~:text=The%20Inertial%20Up per%20Stage (accessed Nov. 20, 2022).

[18] “Imaging Science Subsystem (ISS) | Cassini Orbiter – NASA Solar System Exploration,” NASA Solar System Exploration, Sep. 04, 2018. https://solarsystem.nasa.gov/missions/cassini/mission/spacecraft/cassini-orbiter/imaging-science- subsystem/

[19] “Magnetometer (MAG) | Cassini Orbiter,” NASA Solar System Exploration. http://solarsystem.nasa.gov/missions/cassini/mission/spacecraft/cassini-orbiter/magnetome ter/ (accessed Nov. 20, 2022).

[20] “Cassini Plasma Spectrometer (CAPS) | Cassini Orbiter,” NASA Solar System Exploration. http://solarsystem.nasa.gov/missions/cassini/mission/spacecraft/cassini-orbiter/cassini-plas ma-spectrometer/ (accessed Nov. 20, 2022).

[21] “Radio Science Subsystem (RSS) | Cassini Orbiter – NASA Solar System Exploration,” NASA Solar System Exploration, Sep. 04, 2018. https://solarsystem.nasa.gov/missions/cassini/mission/spacecraft/cassini-orbiter/radio-scien ce-subsystem/

[22] “Ring-Grazing Orbits,” NASA Solar System Exploration, Apr. 11, 2017. https://solarsystem.nasa.gov/news/12966/ring-grazing-orbits/ (accessed Nov. 20, 2022).

[23] “Remember the Titans,” Lockheed Martin, Jun. 15, 2022. https://www.lockheedmartin.com/en-us/news/features/history/titan.html

[24] “Upcoming Events,” nssdc.gsfc.nasa.gov. https://nssdc.gsfc.nasa.gov/planetary/upcoming.html

[25] “Europa Clipper,” www.jpl.nasa.gov. https://www.jpl.nasa.gov/missions/europa-clipper [26] NASA, “Voyager – The Golden Record Cover,” Nasa.gov, 2019. https://voyager.jpl.nasa.gov/golden-record/golden-record-cover

[27] “Ridges and Fractures on Europa,” NASA Solar System Exploration, Mar. 28, 1998. https://solarsystem.nasa.gov/resources/105/ridges-and-fractures-on-europa/?category=miss ions_galileo (accessed Nov. 20, 2022).

About the author

Aniket Martins

Aniket is a senior at Fairfield Ludlowe High School in Fairfield, CT. He is passionate about aerospace engineering and is a member of the American Institute of Aeronautics and Astronautics where he led the 2022 Congressional Visits Day lobbying initiatives for Connecticut. He participated in the University of Florida’s Student Science Training Program in 2022 where he interned at the Nanostructured Energy Systems Lab, completing a research project in Applications of Microfluidic Coolant Systems in Atmospheric Reentry Temperature Regulation for which he won Best Presentation.

Aniket is also passionate about civics and is President of his school’s award winning Model UN team and has won numerous awards at various conferences. At his school he is also President of Mu Alpha Theta Math Honor Society, Vice-President of National Honor Society, Vice-President and Director of Tutoring for English Honor Society, President of Rocketry Club, Founder/President of Engineering Club and an editor for Prospect, the school newspaper. Aniket has won numerous awards in the Connecticut Writing Contest and loves soccer, skiing and tennis.

The post Spacecraft Missions and Orbital Mechanics: Past Stories and Future Initiatives appeared first on Exploratio Journal.

Abstract

This report explores and discusses space debris, or space “junk” – its origin, how it affects the Earth and solutions for debris management. Nowadays, space debris, which is made from “dead satellites” and meteoroids, is one of the biggest global issues that we have to solve immediately. Scientists are trying to solve this problem by detecting space debris by using lasers and telescopes. They are working to solve the issue by planning to charge orbital use fees and using disposal orbit so that they could reduce the amount of space debris in the Earth’s orbit. 

What is space junk?

Space junk, also known as space debris, is any piece of machinery left by humans in space. The majority of orbital debris is made up of human-made materials, such as fragments of spacecraft, tiny flecks of paint from a spacecraft, rocket parts, defunct satellites, or pieces formed through explosions of objects in orbit, floating around in space at high speeds.

The majority of space garbage travels at a breakneck speed of 18,000 miles per hour, almost seven times faster than a bullet. Present and future space-based services, explorations, and activities pose a safety risk to people and property in space and on Earth due to the rate and amount of debris in LEO (Low Earth Orbit).[1]

History of space junk

Over 6050 launches in the past 60 years have resulted in approximately 56450 monitored objects in orbit, of which approximately 28160 remain in space and are continuously tracked by the US Space Surveillance Network and stored in their catalog, and these kinds of debris weight more than 9300 tons in total.[2] About 70% of space debris in LEO was created by China, America, and Russia. 

For example, in 2007, China launched a ballistic missile  from the Xichang Space Launch Center that destroyed a satellite called Fengyun-1C (FY-1C). This had produced the largest space debris generating event in the Earth’s orbit on the record. More than 3000 pieces of debris were produced and 97% of them are remaining in orbit. Moreover, scientists have estimated that 32000 smaller pieces haven’t been tracked yet. [3]

Another event was in 2009. There was a big collision between the Russian satellite (Cosmos 2251) and the US satellite (Iridium 33). Figure 1 shows Cosmos 2251 satellite which produced 1357 pieces of debris and Iridium satellite has produced 528 pieces of debris. Scientists have estimated more than half of the Iridium debris will last at least 100 years in space, while most of the Cosmos debris will last at least 20 to 30 years.[4] The picture below is showing how Cosmos 2251 and Iridium 33 have collided.

Figure 2 shows the history of space junk production and its composition. As it can be seen in the figure, most of the space debris originates from dead and leftover satellites. Moreover, like Cosmos and Iridium satellite collisions, about 9% of space debris is produced because of collisions between satellites.

What kind of debris?

Space debris consists of more than 10 thousand artificial space objects and natural materials. Now, what kind of materials are in the space debris? Most of the space debris consists of natural materials such as meteoroids and human-made materials such as space rockets and satellites (shown in Figure 3).

First off, a natural material meteoroid is a solid object that travels through interplanetary space that is larger than atoms but smaller than asteroids. It travels around the sun with velocities ranging from 11 km/s ~ 72 km/s. Since they move by gravity, they sometimes get into the Earth orbit and become a part of space junk [7]

Secondly, debris from space rockets and satellites are types of artificial materials. More than 10 thousand of these debris objects have been placed into space through more than 6000 rocket and satellite launches, out of which only about 3900 are operating.[8] The main reason satellites produce space debris is that they are in either collision or explosion called in-orbit fragmentation. The most common cause of in-orbit explosions is leftover fuel in tanks or fuel lines and other energy sources that remain on board after a rocket stage or satellite has been discarded in Earth orbit. The harsh space environment can wear down the mechanical integrity of external and internal parts over time, resulting in leaks or mixing of fuel materials, which can lead to self-ignition. As can be seen in Figure 3, most of the debris is the pieces of dead satellites. 

Humans just leave those kinds of satellites in space since the cost is very high to bring the “dead” satellites into the Earth. Additionally, due to lots of missions to space, there are many discarded parts of the rockets that end up in local space. This material can range in size from a discarded rocket stage to microscopic paint chips.[9] 

How do scientists count or track space debris 

There are two ways to detect space debris from the ground. One is to use lasers and the other method is to use a telescopic detector and filter. 

Using a laser with a kHz repetition rate was the initial method to detect space debris. The way scientists detect space debris with laser tracking method is first, they detect space debris with an optical telescope and at the same time, they send laser pulses to the debris so that the distance to the object is calculated by the time which laser travels to the debris and comes back. By combining the time measurement and position determination, scientists can determine the approximate position and size of space debris[11]

Laser observations of space debris structures have been carried out since the turn of the century. However, this approach only operated for a few hours at dusk, when the detection station on Earth is dark and the debris is still lit by the Sun. Figure 4 shows how a laser can detect space debris. [12]

Secondly, scientists use telescopes to detect space debris which is placed in GEO (geostationary earth orbit). For example, in European Space Agency, Zeiss 1M telescope is operated in Spain, as shown in Figure 5, which is used for investigating the property and characteristics of debris in space. This telescope can detect debris, whose size is down to 10~15 cm. Moreover, it is capable of determining the color of the debris which is very important since it allows to determine material property and provides an information of the origin of the detected debris.[14]

How space debris can affect Earth 

Space debris can affect Earth in many ways, mostly negatively. Collisions with active spacecraft are the biggest issue. Any piece of debris greater than 1 cm in diameter will cause a catastrophic impact with an average impact speed of 10 km/s. Collisions between debris and operational satellites cause not only financial but also environmental damage. In the event of a collision, a satellite’s ability to correct its orbit will eventually be lost, and it will become another space danger with no way to steer into a more stable orbital direction. This raises the likelihood of a damaged satellite colliding with another orbital target, such as another satellite or debris, and restarting the debris generation cycle. The more debris in space accumulates, the more likely another collision will occur, adding to the issue. [15] 

Moreover, there is a possibility of dead satellites reentry into Earth orbit. As it can be seen in Figure 7 when the dead satellites re-enter the Earth’s orbit, the break-up starts at around 78 km altitude and this is called the reentry interface. Since the satellite is affected by the wind when re-entering to Earth orbit, the pieces which have low mass but large areas such as solar panel sheds first. Then the catastrophic breakup begins when the time passes and finally leads to a major breakup where all the things are divided into small pieces. These pieces move 50 m/s which means when they reach the ground they will have a massive power. 

Another aspect of space junk’s effect on Earth is the weather. The effect on the weather isn’t direct, however, if the density of the debris increase to the point where it interfere with our ability to use weather satellites it distracts tracking weather changes caused by our ground-based pollution.[17] 

Finally, space debris could fall from the sky and threaten our communities. On average, about 200-400 pieces of debris fall from the sky and enter Earth’s atmosphere every year. Fortunately, since human populations live on a small percentage of the total Earth surface, falling debris is likely to fall into the ocean.[18]

Proposed solutions for debris reduction or removal

One proposed solution for the space debris problem suggested in the literature is to charge operators an “orbital use fee” for every satellite in the Earth’s orbit. According to economist Matthew Burgess, a CIRES(Cooperative Institute for Research in Environmental Sciences) Fellow, and co-author of a recent report, orbital usage fees, if implemented, would boost the space industry’s long-term value. An annual fee of around $235,000 per satellite would quadruple the value of the satellite industry by 2040 by reducing potential satellite and debris collision risk.[19] In another study scientists have predicted the effect of charging “orbital use fee”. As Figure 8 shows, the number of satellites launched and satellites placed in the low earth orbit will be reduced, collision probability between satellites will be decreased dramatically and finally the amount of debris will be also decreased. This shows that charging “orbital use fee” will give a positive impact[20]

Another proposed solution is to deorbit space debris into so-called “disposal orbits.” Re-orbiting items into disposal orbits at the end of their usable lifespan is one method of extracting them from the most commonly used high-altitude orbital regions. This keeps the objects in Earth orbit, but it keeps them out of areas where they could collide with working spacecraft. However, when a space object is moved into a disposal orbit, the collision danger in its original orbital region is reduced, but the collision hazard in the current orbital region is increased. Objects transferred to disposal orbits, on the other hand, may still contribute to the debris hazard in their original orbit because debris created by collisions or explosions in disposal orbits can overlap the original orbit. Moreover, the process to deorbit or accelerate the orbital decay of spacecraft or rocket bodies would be expensive. 

Finally, spacecraft designers, on the other hand, should take a system-level approach to avoid unintended spacecraft breakups. The strategy is to first identify all possible sources of stored energy on a spacecraft nearing the end of its operational life; second, provide a method for benignly dissipating the stored energy satellite for each source; and third, enable these means at the end of the spacecraft’s functional lifetime. [22]

In any case, there is no way to prevent all potential spacecraft breakups: despite precautions, a small number of spacecraft breakups would continue to produce debris, but at a lower level.

My solution

One solution I have come up with to solve the space debris problem is to create a giant magnetic spaceship. Most of the space debris consists of satellites that are human-made and most of those satellites consist of some metallic material. This means some of the space debris is magnetic. Thus, if we could use a magnet which could attract all the leftover dead satellites, and remove them from the earth orbit, we could get rid of some of the space debris. 

To be specific, we could create a magnet spaceship where all the surface of the spaceship is covered with a magnet. The spaceship is going to travel around the low earth orbit and attract magnetic space debris on their surface which pilots are controlling on the earth. If the surface of the spaceship is full of debris, pilots are going to remove all the debris from the surface into the spaceship by using a strong massive vacuum cleaner which automatically cleans the surface of the spacecraft and stores it inside it. Then, there will be another machine in the spacecraft which compresses all the absorbed space debris into small square pieces so that there will be more space to store the space debris. When the spacecraft is full of space debris, pillot will send it back to the earth so that we can recycle and reuse it. 

Conclusion

In summary, space debris problems are treated as a serious global issue. More than 34000 pieces of space debris are orbiting around earth and these have extremely negative effects on the Earth: collision between space debris and satellites, re-enter the Earth orbit and disturb tracking weather change. One of the biggest incidents that have produced massive amounts of space debris was a collision between Cosmos 2251 and Iridium 33. In order to get rid of this space debris, scientists first have to detect them. The way they discover space debris is by using laser and telescope. After they recognize the space debris, scientists plan to charge a fee for orbital use so that companies could reduce using satellites. Also, they work to send the space debris to a disposal orbit. This process is significant for reducing the amount of space debris and clearing up the Earth’s orbit. 

Reference 

[1] Space Debris  https://www.nasa.gov/centers/hq/library/find/bibliographies/space_debris

[2] ESA – About space debris  https://www.esa.int/Safety_Security/Space_Debris/About_space_debris

[3] 2007 Chinese Anti-Satellite Test Fact Sheet 

https://swfound.org/media/9550/chinese_asat_fact_sheet_updated_2012.pdf

[4]2009 Iridium-Cosmos Collision Fact Sheet  

https://swfound.org/media/6575/swf_iridium_cosmos_collision_fact_sheet_updated_2012.pdf

[5]View of Iridium 33 and Cosmos 2251 Debris 180 Minutes Post-Collision. | Download Scientific Diagram 

https://www.researchgate.net/figure/View-of-Iridium-33-and-Cosmos-2251-Debris-180-Minutes-Post-Collision_fig4_266017226

[6]ESA – The history of space debris creation  http://www.esa.int/ESA_Multimedia/Images/2021/03/The_history_of_space_debris_creation

[7]Meteor, a space debris particle flying through the atmosphere  https://www.aeronomie.be/en/encyclopedia/meteor-space-debris-particle-flying-through-atmosphere

[8] ESA – FAQ: Frequently asked questions  https://www.esa.int/Safety_Security/Space_Debris/FAQ_Frequently_asked_questions

[9] ESA – About space debris  http://www.esa.int/Safety_Security/Space_Debris/About_space_debris

[10] Space junk: The cluttered frontier  https://news.mit.edu/2017/space-junk-shards-teflon-0619

[11] Daylight space debris laser ranging  https://www.nature.com/articles/s41467-020-17332-z

[12] What is Space Junk? https://kids.earth.org/space/what-is-space-junk/

[13] DLR – Institute of Technical Physics – Laser-based detection and removal of space debris 

https://www.dlr.de/tp/en/desktopdefault.aspx/tabid-10062/17177_read-41487/

[14] DLR – Institute of Technical Physics – Laser-based detection and removal of space debris 

https://www.dlr.de/tp/en/desktopdefault.aspx/tabid-10062/17177_read-41487/

[15] Scanning and observing  http://www.esa.int/Safety_Security/Space_Debris/Scanning_and_observing2

[16] Hazards of Reentering Space Debris https://www.spaceacademy.net.au/watch/debris/reentryhaz.htm

[17] Space debris as environmental threat and the requirement of Indonesia’s prevention regulation 

https://iopscience.iop.org/article/10.1088/1755-1315/456/1/012081/pdf

[18]Does the debris around Earth affect the atmosphere?  https://www.sciencefocus.com/space/does-the-debris-around-earth-affect-the-atmosphere/

[19] Does Space Junk Fall from the Sky? | NOAA National Environmental Satellite, Data, and Information Service (NESDIS)  https://www.nesdis.noaa.gov/content/does-space-junk-fall-sky

[20] Orbital-use fees could more than quadruple the value of the space industry  https://www.pnas.org/content/117/23/12756

[21] Solving the Space Junk Problem | CIRES  https://cires.colorado.edu/news/solving-space-junk-problem

[22] 7 TECHNIQUES TO REDUCE THE FUTURE DEBRIS HAZARD | Orbital Debris: A Technical Assessment 

https://www.nap.edu/read/4765/chapter/10#139

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About the author

Taewoo Kang

Taewoo is a student at the Stamford American International School in Singapore

The post Space Junk: Its Origin and Potential Solutions appeared first on Exploratio Journal.