Study of Debris Mitigation Methods for End of Lifetime

Nicholas Dietrich University of Florida [email protected]

Faculty Advisor: Dr. Norman Fitz-Coy University of Florida

ABSTRACT

The space environment is constantly growing more crowded with satellites continually launched into . To allow the space environment to be useful for future generations, it is recommended that satellites be disposed of within 25 years after the end of their mission life-time, either by disintegrating during re-entry of ’s atmosphere or boosting up into a graveyard orbit. The method for disposal must be designed to minimize the risk of colliding with and be cost effective to implement. This paper analyzes five methods for disposal: electric engine, solar sail, electrodynamic tether, deployable drag surface, and chemical propulsion. The orbit trajectories were modelled using the two-body equation and an analysis of the area-time product and mass requirements for each deorbiting method was conducted. in and were analyzed for typical parameters to determine the feasibility of a successful disposal while minimizing the risk of collision with space debris.

Introduction of satellites in low earth orbit (LEO) and (GEO). The methods for disposal will be electric engines, solar The Earth’s satellite population is only set to increase in the sail, electrodynamic tether, deployable drag surface, and coming years. As space becomes more accessible with more chemical engine. All these methods, except for chemical countries and organizations launching satellites, the satellite engine, are low thrust methods that will look to take advantage population will continue to expand. With an increased number of the longer allowable timescale of disposal transfer orbits. of satellites, the probability of collision for satellites will As satellite technology becomes more accessible with the increase and create more space debris that will consequently usage of smaller satellites like nanosatellites and picosatellites, increase the number of collisions in a cycle known as the these satellites potentially pose a great risk of becoming debris [1]. Just in the region of 900 to 1000 km in as these satellites many times do not have on-board propulsion altitude, the projected number of objects in orbit 10 cm or larger systems to perform on-orbit maneuvers. It is currently the is set to triple within 200 years, and the probability of collision standard to place small satellites in orbits no greater than 600 to go up by a factor of 10 [2]. The composition of this debris km in altitude to ensure they meet the 25-year requirement. includes smaller fragments from previous collisions, satellites While this is the current standard, smaller satellites are pushing that have not yet deorbited, and rocket bodies. While it will the boundaries of their capabilities. Just in 2018 the CubeSat prove difficult to remove these debris objects from orbit, MarCO was able to achieve interplanetary travel by making the requirements have been set to reduce the amount of future space trip to Mars [4]. If CubeSats are to be able to expand beyond debris. The current NASA requirement is for the satellite to the limit of 600 km altitudes, cost-effective means of removal deorbit within 25 years after the mission lifetime [3]. There will be essential to achieving that goal. These cost-effective exist two ways for a satellite to be deorbited: either it re-enters methods will also prove to be beneficial to large satellites as Earth’s atmosphere or it is boosted up into a graveyard orbit. fuel on board required for deorbiting could otherwise be used This paper will examine these methods for disposal in the cases in station keeping and extend its operational lifetime.

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Developing effective means for satellite disposal will greatly equator, geostationary orbit (GEO) is one where the period of aid in the efforts for providing a safe and clean space the orbit equals the rotation of the Earth. environment by reducing strains on the satellite population and will help to ensure that space will be accessible for all future 푎3 generations. 푇 = 2휋√ (1) 휇

Slots in this orbit are in high demand as providing coverage over a specific area allows for continuous communication between the ground and the satellite and only a finite number are available for rent. These slots are managed by the International Telecommunications Union (ITU). As of the end of 2018, the Union of Concerned Scientists (UCS) satellite database lists 558 satellites in GEO and include communications, broadcast, weather, and surveillance satellites [5]. At the end of the lifetime of these satellites, if they have the capability to, boost up into a graveyard orbit 300 km higher in Figure 1: MATLAB generated image of satellites in orbit used from current altitude than the GEO belt [7]. However, there exist a number satellite population data [5]. of dead satellites in GEO that possess no propulsion capabilities. These dead satellites will drift east and west within Low Earth Orbit their orbit, resulting in drifts toward the two libration points at latitudes 105 degrees West and 75 degrees East [8]. Only The region of satellites within low earth orbit (LEO) are another satellite will be able to remove these satellites but will those with an altitude below 2000 km. Most satellites and debris come at a high fuel cost. are located in this region of space, totaling 1229 satellites as of To ensure that future satellites do not drift and end up in this the end of 2018 [5]. This region of space thus possesses the liberation point, an orbit transfer must be performed. The GEO greatest risk of collisions for satellites with the greatest risks in belt slots are finite and are highly sought after, so it is within the altitudes between 900 and 1000 km and in polar inclinations the best interest of all organizations and countries to prevent [2]. While it is possible for satellites at the end of their lifetime GEO from becoming overcrowded with space debris. to boost up into a graveyard orbit at a higher altitude, the best mode of removal for LEO is for re-entry into Earth’s Two-Body Problem atmosphere. Using this method will permanently remove the satellite from the space and reduce risk of any future collision. To describe the motion of two celestial bodies, the two-body To further the goal of keeping the space environment as clean equation is used. Assuming that the two bodies are perfectly of debris as possible, this paper will only examine disposing of symmetrical and there is only a gravitational force acting on the satellites in LEO through re-entry of Earth’s atmosphere. An system, the equation of motion can be written as additional risk for satellites re-entering Earth’s atmosphere will be assurance that the satellite does not survive re-entry into 퐺(푀 + 푚) (2) Earth’s atmosphere, or the descent can be controlled to land on 풓̈ = − 3 풓 Earth with a maximum human casualty risk of 1:10,000 [6]. For 푟 passive disposal methods, this may pose a challenge if a component on board the satellite would survive re-entry as the where G is the gravitational constant, M and m are the masses location of re-entry would not be able to be controlled. of the bodies, and r is the position vector from body M to body In LEO, environmental forces from the Earth are able to be m. Assuming that the orbiting body’s mass, m, is much less than employed for providing a deorbit method. The Earth’s gravity, that of the central body, M, it can be found that magnetic field, and atmosphere all provide methods for generating a retarding force that can be taken advantage of for 퐺(푀 + 푚) ≈ 퐺푀 ≡ 휇, (3) lower the orbit altitude. The lower bound of LEO will be defined as 150 km in altitude. This is the altitude the satellite is where µ is defined as the gravitational parameter. Thus, the not able to complete one full revolution and will re-enter Earth’s two-body equation becomes atmosphere to be disposed. 휇 풓̈ + 3 풓 = 0 (4) Geostationary Orbit 푟

This equation of motion will be used to describe the motion of One specific orbit that is of great particular interest to countries the satellite in orbit about the Earth. Additional perturbative and corporations is one that provides continuous coverage over accelerations will be added to model the environmental and the same region of Earth. At an altitude of 35,786 km above the control the forces acting on the satellite. The two-body equation will be solved by a MATLAB integrator, ode113. Dietrich, Nicholas 2

Collision Type 푇 푉푗 퐼 = = (5) 푠푝 푚̇ 𝑔 𝑔 Any debris fragment greater than 10 cm in diameter can produce catastrophic damage [3]. Relative to catastrophic where 푇 is thrust, 푚̇ is the change in mass, 𝑔 is standard collisions, there is a range of potential debris that is generated. gravitational accelerations, and 푉 is the exhaust velocity. For example, if a fragment of debris collides with a satellite’s 푗 fuel tank used for chemical propulsion, the explosion will The fuel used for electric propulsion additionally can be generate a significantly greater amount of debris than a collision significantly safer than chemical engines as they do not required with an inert metal component. Thus, it is important to take into combustion to function [10]. Fuel used in electric engines are consideration the materials used within each removal method. commonly chemically inert noble gases, like Xenon, that pose a low risk of explosion. The velocity at which this fuel is Area-Time Product emitted by the engine is limited by the system power. Higher velocities can be reached given greater available satellite One of the metrics used in this paper to quantify the power. effectiveness of a device removing a satellite from orbit will be There exist three main types of electric propulsion systems: the area-time product. This quantity signifies the potential risk electrothermal, electromagnetic, and electrostatic [10]. An for an object to collide with another while in orbit. The name is electrostatic/ion engine, NEXT, will be used as the means for self-explanatory as it is defined as the cross-sectional area of electric propulsion (Table 1). the satellite multiplied by the time in a transfer orbit. It is crucial to minimize the area-time product to reduce the probability of Table 1 Electric Engine Specifications collision with another debris object. It may be advantageous to significantly increase the cross-sectional area, and potential Engine 퐼푠푝 Power Thrust Mass collision area, to lessen the transfer time considerably. NEXT While the cross-sectional area of the satellite poses the 3400 s 4.70 kW 192 mN Dry: 13.5 kg greatest risk for catastrophic impact, the effective cross- [11] sectional area is larger than the body of the satellite [9]. While this increases the area, this method for calculating area will not To calculate the orbit for a continuous thrust, the acceleration be used for the purposes of this paper. to be added to the two-body equation is given by

퐹푡 Methods for Removal 풂푐푡 = 풗̂ (6) 푚푠푐

While there exist more removal methods than studied in this where 퐹푡 is the force of thrust produced by the engine, 푚푠푐 is paper, only five prominent deorbiting methods will be the mass of the satellite and 풗̂ is the normalized velocity vector examined: low thrust electric engine, solar sail, electrodynamic given by tether, deployable drag surface, and chemical propulsion. All methods examined were chosen as they are mechanism that can 풗 풗̂ = (7) be on-board the satellite, requiring no external mechanism to |풗| assist in the deorbit, and have some form of flight heritage. Solar Sail Low Thrust Electric Engine As opposed to propelling mass on board the satellite out to These engines are very popular for small satellites due to provide thrust as the chemical propulsion and electric engine their light weight and highly efficient 퐼푠푝. To provide a change use, solar sails use the space environment to accomplish this in momentum for an object, two parameters can be changed, goal. The solar radiation from the sun provides a pressure on all either the amount of mass propelled or the velocity of the mass objects in the solar system. Solar radiation is a pressure that propelled. Instead of projecting a large amount of mass at a high reduces moving further from the sun, and this pressure can be velocity like traditional chemical engines, electric engines harnessed to generate a force through a large reflective surface: project mass at a significantly higher velocity. This efficiency a solar sail. As photons emitted from the sun strike the sail, they allows less mass to be required for the same change in velocity reflect off, imparting a change in momentum of the particle and (Δ푣) as a chemical engine. However, this efficiency comes with sail. This change in momentum will manifest as a force on the the tradeoff of the Δ푣 being spread out over a longer period. sail, resulting in a change in velocity for the satellite. Over the Low thrust orbit transfers as a continuous Δ푣 along the transfer surface area of the satellite, this pressure can be felt and is given orbit, increasing the amount of time a potential collision can by occur and requiring trajectory optimization if a specific terminal orbit is required. The efficiency of the engine can be 퐿 푅 2 calculated using the specific impulse 퐼 . 푃 = ⨀ ( ⊗) (8) 푠푝 푠푟 4푐휋푅2 푅

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26 where 퐿⨀ is the radiative power of the sun 퐿⨀ = 3.84 ∗ 10 up of a completely reflective material while the other side is an W, 푐 is the speed of light 푅 is the distance from the sun, and 푅⊗ absorptive material, configuring in such a way to provide thrust is the average distance of the Earth from the sun [12]. At Earth, only in the positive velocity direction [14]. This passive system 푅 2 would reduce risk of requiring the satellite to continue to be the orbit is assumed to be nearly circular, so ( ⊗) = 1, 푅 operational after the solar sails are deployed and offer greater resulting in the solar radiation pressure to roughly be 4.5 µPa. assurance the satellite reaches its terminal orbit. An active However, taking into account the reflectiveness of the solar sail, solution for disposal through re-entry has been to rotate the sail this value is doubled to be 9 µPa [13]. The force that is applied to be perpendicular to the sun’s incident radiation vector when to the solar sail surface is then calculated to be moving towards the sun to provide drag and orienting the sail to be parallel when moving away from the sun [15]. Other 2 푭푠표푙푎푟푠푎푖푙,푑푖푓푓 = 2푃푠푟(풏푠 ⋅ 풏) 푑푆 ⋅ 풏 (9) methods have combined using solar radiation forces and atmospheric drag to deorbit a satellite [16]. Additionally, it is where 풏푠 is the angle of incident solar radiation direction 풏 is found that when analyzing steering laws for solar sails, polar the direction normal to the solar sail surface, and 푑푆 is the orbits possess more efficient steering laws over equatorial differential area (Figure 2). orbits [17]. There are, however, limitations to where solar sails are effective. While solar radiation can provide sizable thrust given enough solar radiation pressure, it is not usable for altitudes below 750 km [18]. Under 750 km, the influences of atmospheric particles are dominant over the solar radiation pressure. This limits the range of use for using a solar sail for deorbiting in LEO. Still at higher altitude orbits where atmospheric drag is nearly non-existent like GEO, the application of a solar sail will be investigated. Solar sail technology is just in the infancy of its technological use. JAXA completed the first successful launch and deployment of a solar sail, IKAROS, in 2010, deploying a 20 m span sail [19] and LightSail successfully deployed a solar sail in 2015. These sails used mylar and Kapton as their primary materials. While it is proven that a thrust can be generated using a solar sail, it still must be answered if solar sails are effective in

Figure 2: Diagram of a solar sail forces [12]. producing enough thrust for the mass they require. Solar sails can produce thrust for a theoretically infinite amount of time given the structure remains intact, however it will need to be Taking 휃 to the angle between 풏푠 and 풏, and integrating over investigated if they will provide enough thrust over the limited the entire solar sail area 퐴푠푎푖푙 assuming the sail’s thrust is normal to the sail, (9) can be simplified to timescale required for meeting the deorbiting standards.

퐹 = 2푃 퐴 cos2 휃 (10) Electrodynamic Tether 푠표푙푎푟푠푎푖푙 푠푟 푠푎푖푙

Similar to the solar sail’s use of the space environment for Thus, the maximum thrust will be generated when the solar sail propulsion, the electrodynamic tether utilizes Earth’s magnetic normal vector is aligned with the incoming solar radiation. The field to provide a thrust for altering a satellite’s orbit. This acceleration caused by the solar sail can thus be expressed as method involves deploying a long, thin conducting wire below

the satellite with a mass attached to the end (Figure 3). As the 2휂푃푠푟퐴푠푎푖푙 2 풂푠표푙푎푟푠푎푖푙 = cos 휃 풗̂ (11) induced current in the wire moves through Earth’s magnetic 푚푠푐 field, a Lorentz force is generated by where 휂 is an efficiency parameter between 0 and 1. To simplify 푭 = 퐿 (푰푥푩) (12) the calculations, 휃 will be assumed to be zero and the solar sail’s 퐸 푇 surface be normal to the thrust vector and satellite’s velocity Where 퐿 is the tether length, 푰 is the induced current vector, vector. 푇 and 푩 is the Earth’s magnetic field vector [20]. The magnetic In real cases, to achieve maximum thrust the solar sail’s field the tether moves through can be given by orientation will need to be continuously adjusted using an active control method so that the normal vector is aligned with the 3 incoming solar radiation. However, a passive system would 푅퐸 퐵 = 퐵 ( ) cos 휆 (13) require no controls and therefore be more beneficial given 푇 퐸 푟 enough thrust was generated. There still exist discussion on designing solar sails to maximize thrust while keeping a simple design. One method is for one side of the solar sail to be made

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unstable state. However, analysis has been done to find the current in the wire can be duty-cycled to control the torque and keep the system stable [21]. While the current is off, the gravity gradient torque will work to stabilize the system.

Deployable Drag Surface

For any satellite in LEO without a means of on-board propulsion, atmospheric drag is the only way for debris to re- enter Earth’s atmosphere. The model of the atmospheric density used will be the CIRA-72 at a constant temperature of 1000 K. This is a static model of the density of the atmosphere that assumes the density to decay exponentially as altitude is increased and that the density is spherically symmetric. Thus, the density at a given altitude can be given by Figure 3: Electrodynamic tether diagram of the Terminator TetherTM design [20]. ℎ − ℎ0 휌 = 휌 exp ( ) (17) 0 퐻 where 퐵 = 31 휇푇 is the magnetic field at the equator, 푅 is the 퐸 퐸 radius of the earth, r is the distance to the satellite from the where 휌 is the reference density, ℎ is the altitude, ℎ is the center of the Earth and 휆 is the orbit inclination with respect to 0 0 reference altitude, and 퐻 is the scale height [22]. The density is the Earth’s geomagnetic equator. The dipole of the Earth’s known only for altitudes less than 1000 km. For the less known magnetic field is tiled from the Earth’s axis by an angle of 휙 = density in the above exosphere, the density was extrapolated 11.5 degrees off the spin axis of the geocentric-equatorial using the exponential model [23]. Other forces will influence coordinate system. To account for this tilt throughout the orbit, the atmospheric density like temperature fluctuations that vary the average inclination 휆 can be calculated from the orbit with the sun’s 11-year solar cycle [24]. These variations will be inclination 𝑖 by ignored for the simpler static atmospheric model. Using the found altitude’s density, the atmospheric drag force is 1 〈cos2 휆〉 = {6 + 2 cos(2𝑖) + 3 cos[2(𝑖 − 휙)] 16 (14) 1 2 + 2 cos(2휙) 퐹퐷푟푎푔 = − 퐶퐷퐴휌푣 (18) + 3 cos[2(𝑖 + 휙)]} 2

where 퐶 is the coefficient of drag taken to be 2.1 and A is the where 〈cos2 휆〉 is the average value of cos2 휆. The drag force is 퐷 cross-sectional area of the satellite normal to the velocity the Lorentz force in the direction of the velocity direction, i.e., vector. Thus, the acceleration caused by atmospheric drag can 퐹 = 푭 ⋅ 풗̂ which yields the acceleration vector 푡푒푡ℎ푒푟 퐸 be seen to be

2 2 퐵푇퐿 푣 2 풂 = − cos 훼 풗̂ (15) 1 퐶퐷퐴 푡푒푡ℎ푒푟 푚 푅 풂 = − 휌 ( ) 푣2풗̂ (19) 푠푐 푇 퐷푟푎푔 2 푚 푠푐 where 훼 is the angle of the tether to the local zenith and 푅 is 푇 푚 the resistance of the tether given by where ( 푠푐 ) is the measure of inertia-to-drag-force, defined as 퐶퐷퐴 the ballistic coefficient. 휌푇퐿푇 To utilize this atmospheric drag for deorbiting, area 푅푇 = (16) 퐴푇 augmentation systems offer a passive method of increasing the area-to-mass ratio of the satellite once deployed. This method where 휌푇 is the resistivity of the tether material and 퐴푇 is the is only viable in lower altitudes due to the reliance on the cross-sectional area of the tether. The angle 훼 is taken to be 30 density of atmospheric particles. From the atmospheric model degrees. in (17), the density experiences an exponential decay with From (13), it can be seen that as the inclination of the orbit is increasing altitude. increased, the effectiveness of the electric tether drops. The The structure to be used to model the atmospheric drag tether is most effective when used for an orbit about the equator device will be based upon the Gossamer Orbit Lower Device and least effective for polar orbits. Additionally, the (GOLD) produced by the Global Aerospace Corporation that is effectiveness of the electric tether drops for higher orbits, a design for an inflatable drag surface [25]. making the tether most effective in LEO. Due to the long length of electrodynamic tethers, the Chemical Propulsion dynamics of the tether need to be carefully examined to ensure the system does not become unstable. The Lorentz force will These engines are already commonly available on large induce a torque on the system that may drive the tether into an satellites that require propulsion systems. This method will

Dietrich, Nicholas 5 primarily serve as a control for the other methods as it is an already a common form of disposal. Deorbiting using chemical 100000 propulsion is the fastest method for removal and the area-time

product is insignificant compared to other deorbit methods. The yr) 10000 - control will be the comparison in mass on board the satellite in 2 Atmospheric Drag Surface the form of fuel. The mass of propellent required is given by the 1000 rocket equation: 5% Tether 90° Inclination 100 −Δ푣

푚푝푟표푝푒푙푙푎푛푡 = 푚푠푐 (1 − exp (− )) (20) 10 5% Tether 0° Inclination

𝑔퐼푠푝 Time Time Product(m -

The corresponding mass of propellant to complete an orbit 1 Area transfer can be calculated from finding the Δ푣 that is calculated Electric Engine from the most efficient orbit transfer, the Hohmann transfer. For 0.1 the analysis in this paper, an 퐼 of 300 s was chosen. (20) can 200 500 800 1100 1400 1700 2000 푠푝 Orbit Altitude (km additionally be used to calculate the mass of propellent for the ) Figure 4: Area-Time Product of deorbiting for re-entry into Earth’s electric engine. 2 A potential danger of using chemical propulsion is that while atmosphere for 1000 kg, 5 m satellite initially in . they provide a highly reliable method for orbit transfer, if a It can be seen that the electric engine provides the least area- collision were to happen with a satellite’s tank of chemical time product, followed by the electrodynamic tether and then propellent, a high-energy catastrophic collision would occur. the deployable drag surface. All these methods were able to meet the 25-year requirement for up to 2000 km except for the Analysis deployable drag surface that is unable to meet requirement beyond altitudes of roughly 1000 km. It was found that while To assess the feasibility and compare the effectiveness of increasing the surface area of the deployable drag surface each deorbiting method, simulations were run to compare the decreased the time for deorbit, the area-time product remained area-time product and mass tradeoffs. All qualitative predominantly the same. Comparing the electrodynamic tether comparison of these methods can be seen in Table 2. at 0° inclination and 90° inclination, the tether was confirmed to be less effective at high inclinations, however the tether still Low Earth Orbit performed better than the deployable drag surface at all inclinations. This data additionally can be scaled to different For the low earth orbit, the simulation was run with a 1000 2 satellite mass as the area-time product scales linearly with mass kg satellite with a cross-sectional area of 5 m . The simulation [20]. was run at various altitudes to calculate the area-time product To compare efficiencies of on-board mass, the rocket of each deorbit method for the transfer orbit from an initial equation (20) was used to calculate the additional necessary circular orbit to an orbit altitude less than 150 km (Figure 4). mass of fuel to complete the orbit transfer (Figure 5). The initial The NEXT ion engine was used for the electric engine, a 5% weight of the engine is not included. The electric engine was duty-cycle tether composed of aluminum weighing 60 kg was 2 assumed to provide continuous thrust throughout the orbit, the used for the electrodynamic tether, and a 1000 m deployed chemical engine mass was calculated for the Δ푣 of a Hohmann surface modeled off GOLD for the drag surface. transfer, and the drag surface and electric tether were taken as constant mass.

Table 2 Comparison of Removal Methods

Active/ Effective Deorbit Method Effective Inclinations Flight Heritage Reliability Collision Energy Passive Altitudes

Chemical Active Any Any Yes High High Propulsion

Electric Engine Active Any Any Yes High Low

Electric Tether Active Low Equatorial Yes Moderate Low

Drag Surface Passive Low Any Yes High Low

High, above Solar Sail Either Polar Yes Low Moderate 750 km

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160 Both engines offer quick orbit transfers at minimal mass as both 2 140 engines require less fuel mass than the size of the 150 m sail. Chemical Propulsion This timescale for this orbit transfer is too small to offer the 120 benefits of continuous thrust at a constant mass the solar sail 100 can offer. The other case for disposal of geostationary orbits is for re- 80 Tether entry into Earth’s atmosphere. Simulation was run to calculate 60 the feasibility of completing this orbit transfer using both types

Mass Mass (kg) Atmospheric Drag Surface of engines and a solar sail (Table 3). The sail’s control system 40 used was the same as the previous simulation, however 20 orienting the solar sail as to only provide drag. The sail used Electric Engine solar radiation pressure to provide drag down to the altitude of 0 750 km, where atmospheric drag forces became dominant and 150 650 1150 1650 the sail becomes a drag surface. Orbit Altitude (km)

Figure 5: Mass requirements for deorbiting for re-entry into Earth’s Table 4 atmosphere for 1000 kg 5 m2 satellite initially in circular orbit. Lower Geosynchronous Orbit for Re-entry of Earth’s Atmosphere

Disposal Transfer Time Mass Area-Time Product It is noticeable that at higher altitudes the fuel mass required Method to deorbit using chemical propulsion steadily increases to be Chemical greater than the static masses of the electrodynamic tether and 0.0014 years 1187.2 kg 0.0112 m2-years Propulsion deployable drag surface. However, the electric engine remains Electric the lowest mass required and looks to offer the most efficient 0.776 years 446.2 kg 6.208 m2-years means for orbit transfer in terms of area-time product and mass Engine required. Solar Sail 174.1 years 9 kg 17410 m2-years The data gathered from this simulation offers some insight (100 m2) into the effectiveness of each removal method, but it only Solar Sail 37.0 years 100 kg 37000 m2-years considers one configuration of the electrodynamic tether and (1000 m2) deployable drag surface. The mass and deorbit time will change with altering the parameters such as the tether’s length and the The initial results for GEO re-entry into Earth’s atmosphere drag surface’s area, and these parameters can be optimized show using a hybrid solar sail/drag surface remains unfeasible depending on the design constraints of the satellite. due to the long transfer time and large area-time product. Likewise, using either the chemical or electric engine provide Geosynchronous Orbit low transfer times, however the mass budgets are too large to justify using re-entry over raising the orbit altitude 300 km. For satellites in GEO, two case will be investigated. The first Potential still exists for using this hybrid method if the solar one is to raise the altitude 300 km for a 3000 kg satellite. The sail’s area is increased enough to meet the 25-year requirement solar sail’s will be oriented perpendicular to the incident due the lower mass. However, this would continue to increase radiation vector of the sun when the satellite moves away from the area-time product the probability of collision. the sun and orienting the sail parallel to the sun’s incident radiation vector when the satellite moves toward the sun as to Conclusion only provide a positive ∆푣. Transfer times were calculated for various sail areas and compared to the mass of fuel required for The problem of space debris will only become a greater issue chemical and electric engines (Table 2). Masses for the solar for future generations. It is crucial for cost-effective and sail were used based on JAXA’s IKAROS [19]. efficient disposal methods to be developed to keep the space environment clean and minimize the risk of catastrophic Table 3 Raise Geosynchronous Orbit by 300 km satellite collisions. Current rules require satellites to deorbit within 25-years following the end of the operational lifetime. Disposal Method Transfer Time Mass This timescale allows for more mass efficient low thrust methods to be used for disposal. In LEO, electrodynamic tethers Chemical 0.5013 days 11.07 kg Propulsion and deployable drag surfaces have both shown to be feasible methods for removing satellites at the end of their operational Electric Engine 1.835 days 1.109 kg lifetime. Both methods were able to deorbit the satellite within the 25-year requirement using an acceptable amount of mass. Solar Sail (100 m2) 605.1 days 9 kg While these two methods are feasible, the electric engine looks to offer the best means for disposal at minimal area-time Solar Sail (150 m2) 403.9 days 12.5 kg product and low mass. In GEO, solar sails were not found to be

2 as effective as using an engine but do offer advantages in mass Solar Sail (200 m ) 302.9 days 16 kg for longer orbit transfers.

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