Design and Evaluation of an Orbital Debris Remediation System

SYST 495 Technical Report

Benjamin Noble Yahya Almanee Abdulelah Shakir Sungmin Park

George Mason University Systems Engineering Senior Design Project, 2015-2016

Table of Contents

1 Introduction ...... 5

2 Context Analysis ...... 7 2.1 Current Investments ...... 7 2.2 Types of Orbits ...... 8 2.3 Orbital Debris Threat ...... 9

3 Stakeholder Analysis ...... 11 3.1 National Governments ...... 11 3.1.1 United States of America ...... 12 3.1.2 Europe ...... 12 3.1.3 Russia ...... 13 3.1.4 China ...... 13 3.2 Commercial Industry ...... 14 3.2.1 Transport Companies ...... 14 3.2.2 System Manufacturers ...... 14 3.2.3 Insurance Companies ...... 14 3.3 Civil Organizations ...... 14 3.3.1 Inter-Agency Space Debris Coordination Committee (IADC) ...... 14 3.3.2 National Aeronautics and Space Administration (NASA) ...... 15 3.3.3 National Oceanic and Atmospheric Administration (NOAA) ...... 15 3.3.4 European Space Agency (ESA) ...... 15 3.3.5 Russian Federal Space Agency ...... 15 3.3.6 China National Space Administration (CNSA) ...... 16 3.4 Stakeholder Interactions and Tensions ...... 16 3.5 Process for Implementing ADR ...... 19

4 Problem Statement ...... 21 4.1 Overview ...... 21 4.2 Problem Analysis ...... 21 4.3 Gap Analysis ...... 21 4.4 Need Statement ...... 22

5 Requirements ...... 23 5.1 Scope and Assumptions ...... 23 5.2 Mission Requirements ...... 23 5.3 Functional Requirements ...... 23

6 Concept of Operations ...... 24 6.1 Competing Approaches ...... 24 6.1.1 Active Debris Removal (ADR) ...... 24 6.1.2 Just-in-time Collision Avoidance (JCA) ...... 25 6.1.3 Property Rights ...... 26 6.2 Design Alternatives ...... 26 6.2.1 Launch and Rendezvous Designs ...... 27 6.2.2 Grapple Designs ...... 28 6.2.3 De-tumble Designs ...... 30 6.2.4 De-orbit Designs ...... 30 6.3 Method of Analysis ...... 31 6.3.1 Launch and Rendezvous ...... 32 6.3.2 Grapple ...... 36 6.3.3 De-tumble ...... 40 6.3.4 De-orbit ...... 42 6.3.5 Political Viability ...... 44 6.4 Utility Analysis ...... 49 6.4.1 Value Hierarchy ...... 49 6.4.2 Attribute Descriptions ...... 50 6.4.3 Attributes and ADR Designs ...... 52 6.4.4 Weight Elicitation ...... 52 6.4.5 Analytic Hierarchy Process (AHP) ...... 54

7 Results ...... 55 7.1 Launch and Rendezvous ...... 55 7.2 Grapple ...... 55 7.3 De-orbit ...... 56 7.4 Overall Debris Remediation System ...... 58

8 Business Case ...... 59

8.1 Potential Market Size ...... 59 8.2 Business Model ...... 59 8.3 Sales Profile ...... 60

9 Project Plan ...... 62 9.1 Statement of Work ...... 62 9.1.1 Objective ...... 62 9.1.2 Project Scope ...... 62 9.2 Work Breakdown Structure ...... 63 9.3 Schedule ...... 64 9.4 Critical Path ...... 66 9.5 Project Risks ...... 67 9.6 Earned Value ...... 68

10 References ...... 71

11 Models, Data and Code ...... 75

Table of Figures Figure 1 - History of Orbital Debris ...... 6 Figure 2 - Satellite Population, Sep. 2015 ...... 7 Figure 3 - Stakeholder Relationships ...... 19 Figure 4 - Process for Implementing ADR ...... 20 Figure 5 - ADR CONOPS ...... 25 Figure 6 - Network Analysis Simulation Flowchart ...... 36 Figure 7 - Object Categorization Simulation Flowchart ...... 38 Figure 8 - Value Hierarchy ...... 49 Figure 9 - Work Breakdown Structure ...... 63 Figure 10 - Critical Path ...... 66 Figure 11 - CPI, SPI ...... 69 Figure 12 - Earned Value ...... 70

Table of Tables Table 1 - Stakeholder Tensions ...... 17 Table 2 - ADR CONOPS to Attributes ...... 52 Table 3 - Project Risks ...... 67

1 Introduction Over the past 60 years, spaceflight has evolved and expanded tremendously. What was once the realm only of national governments has now become a prime economic feeding ground for corporations and industries around the world [1]. Threatening this fledgling environment is the hazard of orbital debris. The speeds required to reach and maintain orbital velocity are such that terrific amounts of energy are contained in even the smallest of orbital particles. Should these objects impact an operational satellite, the consequences can be dire, ripping straight through fragile aluminum and silicon bodies. In addition, each collision produces even more debris, which itself becomes a new threat. This leads to a chain reaction effect, referred to as the Kessler Syndrome. Should a critical mass and number of objects trigger the Kessler Syndrome, the result would be an impenetrable sphere of trash orbiting our planet, severely impeding any future development or use of space [2]. The probability of collisions has increased 7-fold over the past 10 years [3, 4]. This increase is attributed to the overall rise in orbital populations, driven by expansion of the commercial space industry [1] and by recent collision events. In 2007 the Chinese launched an anti-satellite missile against their own Fengyun satellite, producing 2841 pieces of debris, and in 2009 there was a random collision between the Cosmos 2251 and Iridium 33 satellites, producing a further 1788 pieces of debris, together doubling the number of objects in orbit below 1000 kilometers [3, 5]. These factors led to an increase in conjunction events, which are directly proportional to collision probability [3]. The international space community has made strides to mitigate the propagation of further debris, mostly focusing on total life-cycle planning for new satellite launches [6]. While this reduces further worsening of the problem, it does not directly deal with the issue at hand, that of the current debris population. Thus, it is imperative that a remediation design be chosen and implemented.

Figure 1 - History of Orbital Debris

There have been dozens of design solutions posited, but there is a need for a rigorous, comprehensive analysis of alternatives. As a part of this effort, a metric for evaluating the effectiveness of designs is necessary.

2 Context Analysis

2.1 Current Investments There are currently over 1261 operational satellites in orbit. Of these, 52% are communications satellites, with the remaining 48% being spread between meteorological, military, navigational, and scientific purposes [1]. These satellites range in size from 1 kilogram to 18,000 kilograms [7]. Launch costs are generally proportional to the mass of the payload, with a current price of anywhere from $4500 to $22,000 per kilogram [8]. A relative newcomer to the launch services community, SpaceX, claims to be able to provide launches for $1700 per kilogram [9], though this capability has yet to be proven. There are also the direct development costs of each satellite to consider. This information is more difficult to ascertain, as many factors play into each satellite, including fixed costs, learning curves, evolution of technology and miniaturization, and economy of scale. However, estimates can be found to determine the feasible range of development costs, which goes from $7,500 for a Cubesat to $2.2 billion for the ESA’s Envisat [10, 11].

Figure 2 - Satellite Population, Sep. 2015

All told, the global space industry is worth approximately $203 billion. These investments generate revenue from a variety of sources, including the manufacture and launch of orbital 7 systems. The main drivers of revenue come from satellite services as a whole, such as television and meteorology, comprising over 60% of revenue in 2014. Ground equipment, used to interface with orbiting space assets, constitutes a further 28% of revenue [1].

2.2 Types of Orbits Orbits are defined in terms of six major elements: semi-major axis, eccentricity, inclination, argument of periapsis, time of periapsis passage, and longitude of ascending node. The semi- major axis is the distance from the center of the orbit (for most satellites, this is the Earth itself) to the farthest point on the ellipse, in essence the altitude of the object. Eccentricity varies from 0 to 1, 0 being a perfectly circular orbit and 1 being a parabola (and technically not truly an orbit at all, but an escape trajectory). Inclination is the angular distance between the orbital plane of the object and the equator of the body being orbited (or primary body), measured in degrees. The argument of periapsis, periapsis being the point in the orbit where the object is closest to the primary body, is the angular distance between the ascending node and the periapsis itself. The time of periapsis passage is self-explanatory; it is the time when the object passes through its periapsis. Lastly, the ascending node is the point on the orbit where the orbit crosses the equator of the primary body from south to north [12]. Orbits are chosen depending on the use desired for the given satellite. For example, a geostationary (GEO) orbit, with an altitude of 35,786 kilometers, an eccentricity of 0, and an inclination of 0 degrees, is used to “hover” over a given latitude. This is useful for weather monitoring, allowing long-term tracking of changes. However, this is only usable near the equator. A Molniya orbit has an altitude ranging from 500 to 39,873 kilometers, an eccentricity of 0.7, and an inclination of 63.4 degrees. This leads to a large loiter time over a single hemisphere, allowing for similar effectiveness as a geostationary orbit. Finally, there are many orbits in Low Earth Orbit (LEO) below 2000 kilometers altitude, with various inclinations. A polar orbit, with inclination near 90 degrees, can be used to quickly survey the entire planet. As the satellite flies pole-to-pole, the earth spins underneath it, allowing total coverage of the planet [13]. The orbital populations, both of operational satellites and debris, vary widely with altitude, inclination, and eccentricity. Some of the most highly populated regions are around 800 kilometers and 1500 kilometers [14]. 8

2.3 Orbital Debris Threat There are presently over 22,000 objects larger than 10 centimeters in orbit, and approximately 21,000 of those are debris [1, 15]. In addition, there are over 100 million pieces of debris that are too small to track and are estimated based on a variety of factors, including known collision events, simulations, and historical trends [15]. This debris takes many forms, from loose screws or flaky particles to entire obsolete or retired satellites. In addition, some of the largest objects are expended rocket bodies, comprising 97% of the total mass [5]. These derelicts can contain leftover propellant or faulty batteries, and can thus prove to be a serious risk for explosion and further propagation of debris [16]. The energy contained in a given object, a good measure for the potential for damage, is given by the following equation: �� = 2 When velocity is large, as it is for every orbital object, � increases dramatically very quickly. In addition, while not as intense of an effect as velocity, increases in mass also have a serious impact on energy. Ever since the launch of Sputnik in 1957, Earth’s orbits have been getting more and more crowded. In particular, the last 10 years have seen a sharp rise of the number and mass of objects in orbit. Advances in technology, especially in communications, have led to larger numbers of satellites launched, increasing the operational population [1]. In addition, there have been several collision events, notably the 2007 Chinese anti-satellite missile test and the 2009 collision between the Iridium 33 and Cosmos 2251 satellites, which have drastically increased the debris population [5]. The combination of these two factors has led to an increase in conjunction events, which itself leads to an increased collision probability. Currently, the composite collision rate for an object in low earth orbit is 0.005 per year [16]. This calculation includes collisions ranging from tiny micro-meteor impacts to massive, explosive collisions with other space assets. This risk is projected to continue to climb, even in the face of post-mission disposal (PMD) efforts [14]. Scientists have recognized the potential threat of un-remediated space debris ever since the 1960’s and the first orbital flights. As soon as it was clear that atmospheric drag would not 9 capture all objects above a certain altitude (around 600 kilometers [17]), it also became clear that anything that gets into orbit above that height will tend to stay in orbit. In 1978, Dr. Donald Kessler made the first prediction of what would become known as the Kessler Syndrome. The Kessler Syndrome refers to a chain reaction of collisions, where each collision produce enough debris to further collide with other objects, resulting in a domino effect that would eventually obliterate all satellites in orbit [18]. Acknowledging this threat, the international space community has made strides to prevent further worsening of the danger. To do so, the United Nations Office of Outer Space Affairs (UNOOSA) has published guidelines for all newly launched satellites, essentially requiring total lifecycle planning before a launch [6]. Every satellite that goes up into space should have a plan for when it is coming back down. However, this effort alone is not sufficient to prevent the Kessler Syndrome; some form of remediation will be required [5], and this is where this project comes in.

3 Stakeholder Analysis Top-level stakeholders consist of three groups: National government, commercial industry, and civil organizations. Each top level stakeholder consists of sub-level stakeholders. National governments that is considered are: the United States of America, Europe, Russia, and China. For commercial industry, three sub-level stakeholders are considered: Transport companies, systems manufacturers, and insurance companies. For civil organizations, six organizations are taken into account: Inter-Agency Space Debris Coordination Committee, National Aeronautics and Space Administration, National Oceanic and Atmospheric Administration, European Space Agency, Russian Federal Space Agency, and China National Space Administration.

3.1 National Governments All of national government follow the same process regarding space programs, however, each national government distributes responsibilities in space programs differently. The following is the process that each national government follow in space-related activities: In the United States of America, the President’s office is responsible for creating a space policy based on proposals of space activities by NASA; the US Congress has the authority of determining whether or not to approve funding for the proposed space policy. Then, the White House offices is responsible for execution of findings that will be available to NASA to perform the space policy [19, 20]. In Europe, the European Space Agency is considered as a main stakeholder; the European Space Agency is an intergovernmental agency that is not a body of the European Union, however, the European Union is the largest financial contributor to the ESA space programs [21]. The space policies of the European Space Agency are proposed to its member states for agreement; Each member state has one vote, regardless of its size or financial contribution [22]. the European Space Agency is responsible for implementing space activities that are determined [23]. In Russia, the Federal Space Agency is an executive governmental body that has the authority of determining the policies in aerospace industry [24] and implementing government policy and legal regulation [25]. In China, The State Administration on Science, Technology, and Industry for National Defense (SASTIND) is responsible for executing space-related regulations [26]. China Space Agency sets

11 overall guidance and policy [27]. Afterward, the Chinese State Council is the government body that has the authority of approving funds, and issuing a five-year space plan [28]. Funds execution and operating space activities is the responsibility of the People’s Liberation Army [29].

3.1.1 United States of America In the United States of America, four main departments that has interactions related to space debris remediation programs are considered: The President’s office, the Congress, the Department of Defense, and the White House offices which includes the Office of Science and Technology Policy, the National Security Council, the Office of Management and Budget. The overall objective is to create a space policy that has been advised by NASA, afterward, space policies that has been created would either get approved for funding or rejected by the Congress. If a space policy gets approved, it will be funded by one of the White House offices, the Office of Management and Budget [30]. The Department of Defense main objective is to maintain and protect the security of the United States of America. it uses different types of operational satellites, such as communications and monitoring satellites to achieve its goals [31].

3.1.2 Europe In Europe, two top-level stakeholders are considered: the European Union, which is the largest financial contributor to the European Space Agency (ESA), and Non-European Union state members, which are members of European Space Agency that are not a part of European Union. the European Union consists of three main departments: the European Commission, the European Parliament, and the Council of the European Union [21]. The European Commission is an independent governmental body of national governments of the European Union state members that represents the European Union interests as a whole. Its main objectives are to propose new European laws to both the European Parliament and the Council, and to implement decisions that are made by the European Parliament and Council. The European Parliament is elected by citizens of the European Union to represent their interests [32]. It has three main objectives: approval of European laws, democratic supervision, and

12 authority over European Union’s budget. the Parliament shares the approval of European laws and authority over European Union’s budget with the Council [33]. The Council of the European Union is the main decision-making body in the European Union that represents the interests of the European Union member states. It has two main objectives: approval of European laws, jointly with the Parliament, and approval of the European Union’s budget, jointly with the Parliament [34].

3.1.3 Russia In Russia, two main stakeholders are considered: Aerospace Forces of the Ministry of Defense of the Russian Federation, and the Prime Minister of Russian Federation offices. Aerospace Forces objectives are to provide reliable information of any warning about missile attacks, observe and detect space threats against Russia, launch spacecraft, and control military and dual-purpose satellite systems [35]. The Prime Minister of Russian Federation offices are responsible for implementing governmental policies regarding the development of defense, rockets, and spacecraft [36].

3.1.4 China In China, three stakeholders have been considered: Chinese State Council, the State Administration on Science, Technology, and Industry for National Defense (SASTIND), and People’s Liberation Army (PLA), which is a component of China’s Ministry of Defense. The Chinese State Council is the highest ranking government body of China; It holds the responsibility for both funding decisions for space activities and issuing a five-year space plan as a form of government White Paper [28]. SASTIND is the main civilian regulatory authority in China [37]. SASTIND objectives are to coordinate and manages China’s space activities, and execute space regulations. People’s Liberation Army’s objective is to operate the manned spaceflight program, and execute funding for space activities [29].

3.2 Commercial Industry

3.2.1 Transport Companies Commercial space transport companies including SpaceX, United Launch Alliance (ULA) and Federal Aviation Administration are the main transport companies that has interactions related to space debris remediation programs [38]. Their overall objectives are to enable people to live on other planets, provide spacecraft launch services to the government of the United States and provide safety, efficiency and environmental responsible to the stakeholders [38].

3.2.2 System Manufacturers The commercial space systems manufacturers including Lockheed Martin, Boeing and Orbital Sciences, are companies that manufacture and design space systems and has interactions related to space debris remediation programs. Their objectives is to solve complex problems, advance scientific discovery, deliver innovative solutions, design, build and support aircrafts, spacecraft, rockets and satellites and build and deliver defense, space and aviation to the whole world [40].

3.2.3 Insurance Companies XL Catlin, AGCS space coverage and STARR are a global insurance companies and considered part of stakeholders. All of them provides space and satellites insurance including, AIT, pre- launch, launch, commissioning and in-orbit life, in-orbit incentives, service interruption/loss of revenue, third party liability, captive risk management launch plus in-orbit risks, In-orbit coverage, satellite incentive coverage, launch risk guarantee, and space third-party legal liability.

3.3 Civil Organizations

3.3.1 Inter-Agency Space Debris Coordination Committee (IADC) The Inter-Agency Space Debris Coordination Committee is an international governmental meeting for the worldwide coordination of activities to deal with space debris of manmade and natural debris. The overall objective of the IADC is to allow the member agencies to exchange information on space debris research activities and identify debris mitigation options [41].

3.3.2 National Aeronautics and Space Administration (NASA) The National Aeronautics and space Administration is the United States government space agency program. NASA headquarters are located in Washington, D.C., and there are ten NASA research centers like Johnson Space Center and Kennedy Space Center and their objectives is to provides overall guidance and direction [42]. NASA main objectives are to develop the future in space exploration, explore the the earth and solar system and aeronautics research [43].

3.3.3 National Oceanic and Atmospheric Administration (NOAA) The National Oceanic and Atmospheric Administration is a federal agency focused on the conditions of the oceans and atmosphere. Their main objectives are to provide information about oceans and atmosphere including environmental monitoring and severe weather prediction, as well as providing sea surface height measurements, that is used to determine ocean circulation, climate change, and sea level rise [44].

3.3.4 European Space Agency (ESA) The European Space Agency is an international organization with 22 member states. ESA headquarters are located in Paris, French and there are five ESA centers like the European Space Operations Center (ESOC) and The European Space Astronomy Center (ESAC) and their objectives is to provides overall guidance and direction. ESA main objectives is to find more about earth, space environment, solar system and the universe, as well as developing satellite technologies and services [45].

3.3.5 Russian Federal Space Agency The Russian Federal Space Agency (which is also commonly called Roscosmos) is the Russian government space agency program. RFSA headquarters are located in Moscow and their main objectives is to provide state services and administration of the state space assets and manage the international cooperation in joint space programs and projects. RFSA is also responsible for overall regulation of the activities at the Baikonur spaceport [46]. The Cosmonauts Training Centre (GCTC) is a Russian training center and it is to responsible for training cosmonauts (Astronauts) for their space missions [47]. The Baikonur Cosmodrome and the Plesetsk

Cosmodrome are an operational space launch facility. All space station flights using launch vehicles is launched from these facilities [48].

3.3.6 China National Space Administration (CNSA) The China National Space Administration is the national space agency of the People’s Republic of China. CNSA headquarters are located in Beijing and the overall objectives of CNSA is to plan and develop space activities, sign governmental agreements in the space area on behalf of organizations, intergovernmental scientific and technical exchanges, enforcement of national space policies and sets overall guidance and policy for the entire space program. CNSA includes the Department of General Planning, Department of System Engineering, Department of Science, Technology and Quality Control and Department of Foreign Affairs [37].

3.4 Stakeholder Interactions and Tensions As mentioned that top-level stakeholders includes national governments, which is broken down into United States, European Union, China ,and Russia. For Civil Organizations, space agencies of each national government is considered which includes NASA, ESA, CNSA, and RFSA. Finally, Commercial Industry is divided to system manufactures companies, transport companies, and insurance companies. Each national government approve and fund their own space agency, while each space agency research, collect data and provide overall guidance to their national governments. NASA, ESA, CNSA and RFSA exchange information on space debris research activities and identify debris mitigation options [41]. Finally, Commercial Industry provide space services and insurances to both National governments and Civil Organizations. There are four main tensions among stakeholders that are considered: International political tensions, insurance companies, time of occurrence of large debris collisions, and regulations. For the political tensions, Russia owns most of satellites and debris in space [53], and doesn't want anyone to touch their objects which will lead to a roadblock with other national governments. Also, some of the methodologies may be construed to have the potential dual use as a weapon to either disable or de-orbit. When a country launches a rocket for space activities, it is possible that other countries will suspect the purpose of the launch [54].

Another political tensions is that some of the removed objects using removal alternatives might be an international issue due to inaccuracy of dropping locations. For the insurance companies there are two type of tensions. The first type is the tension between the commercial companies and the insurance companies, where insurance companies’ objective is to manage risks, while commercial companies’ objective is to minimize cost. The second type is the Competitiveness between insurance companies, whether they consider collision risk in their policies. Time of occurrence of large debris collision is how frequent does a large debris getting hit by another object which will cause debris population to grow. According to XL Catlin Vice President and Global Underwriting Manager, Christopher Kunstadter, the current risk of collisions of large objects in space is not covered as a separate policy option, and competition between insurance companies (along with slim profit margins) guarantees that no excess costs will be incurred to cover space debris unless absolutely necessary. Similarly, commercial companies would not pay attention to the issue since they are fully insured. On the other hand, growing risk of collision of large debris is a vital issue to all government space agencies since one of their objectives is to remediate space debris until it reaches stable condition. Another tension is between regulations issuing organizations and satellite launchers. Organizations such as, IADC requires launchers to have an end-of-life plan; however, not all satellite launchers follow their guidelines and regulations [55].

Table 1 - Stakeholder Tensions

Type Tension ● Russia owns most of satellites/debris in space, and doesn't want anyone to remove their debris objects. ● Some of the methodologies may be construed Political to have the potential dual use a weapon to either disable or de-orbit (China and Russia). ● Removing objects using ADR alternatives could be an international conflict due to inaccuracy of dropping locations.

● Insurance companies’ objective is to manage risks. While commercial companies’ objective is to minimize cost. Commercial ● Competitiveness between insurance companies if considers collision risk in their policies ● for insurance companies: Problem doesn't matter that much (make profit in present time) Time of occurrence of larger effects ● for commercial: They are insured, it wouldn’t (large debris) matter ● military/national government: ● for government agencies: concerned Time of occurrence of smaller effects ● Not considered (small debris/fragments) ● Policy that requires owner of satellite to have a United Nations – Satellite re-entry controlled plan manufacturers – Organizations ● Not all owners/satellites manufacturers would involves/owns satellites agree/register. ● IADC & COPUOS regulations. ● Space agencies (NASA) would like more funds for their research and projects. Financial ● Government wants to reduce budgets as much as possible (US)

Figure 3 below summarizes the various stakeholder interactions and tensions:

Figure 3 - Stakeholder Relationships

3.5 Process for Implementing ADR As mentioned earlier, space debris population is increases; which causes to decrease the space safety for both current and future spacecraft. In other words, increase of space debris population has a positive correlation with risk of collision of operating spacecraft in space. Moreover, satellite demand has been increasing in the last decade. Implementation of Active Debris Removal is driven by such changes that are considered the triggers for considering Active Debris Removal efforts. Process of implementing Active Debris Removal consists of three major phases: Pre-launch, launch, and in-orbit life phase. Each phase consists of objectives of top level stakeholders. For the pre-launch phase, all top level stakeholders are involved; furthermore, it is the phase where most of processes and objectives are done. It starts with civil organizations, such as NASA that conduct research, collect data, and provide proposals to national government such as the United States government. National government's objectives are to approve the proposed space policy and to provide funding for the proposed space policy. After national approval of a space policy, it needs to politically viable for all countries. In other words, space policy should be approved internationally to avoid any political conflicts and tensions. Both national and

19 international approval of a space policy are very important processes because governments are potential executive bodies that considered a main decision making body in implementing Active Debris Removal. Afterwards, commercial industry is responsible for designing and building the specified Active Debris Removal design(s) based on the proposed space policy. At the end of the pre-launch phase, insurance companies will evaluate the spacecraft and then determine pre- launch insurance costs. At the beginning of the second (launch) phase, Active Debris Removal design(s) would be built and ready for launching. Civil organizations will be responsible for both determining launching type and site; Selection of launching type and site would be heavily dependent on targeted debris object(s) that is planned to be removed from space. After selection of launching type and site, insurance companies appear once again to cover launching risks. Eventually, commercial industry is responsible for providing launching services for the spacecraft. In the last phase, in-orbit life phase, all stakeholders are involved in the beginning. Civil organizations are responsible for monitor the progress of capturing targeted debris object(s) from space, while national governments and commercial industry are working simultaneously in providing space surveillance and detection of movements of objects in space to avoid any collision. Figure 4 describes the processes and objectives of stakeholders in implementing Active Debris Removal design(s):

Figure 4 - Process for Implementing ADR 20

4 Problem Statement

4.1 Overview Probability of collision can be assumed to be directly proportional to conjunction rates. Conjunction rates, and thus collision probability, between objects in Low Earth Orbit has increased from 1419 conjunctions per day in 2006 to 10,704 conjunctions per day in 2010 [3, 4]. Much of this expansion stems from new low-cost, high-volume satellite designs, particularly Cubesats [1]. In addition, there have been two major events in the past 10 years that contributed to the debris population. In 2007 the Chinese launched a SC-19 anti-satellite missile against the defunct Chinese Fengyun satellite. The test was a success for the missile, and a tragedy for the rest of the satellite community, producing 2841 pieces of debris [3]. In 2009 there was a collision event between the Iridium 33 and Cosmos 2251 satellites. The Cosmos 2251 was a defunct Russian communications satellite whose orbit happened to intersect the Iridium communications satellite’s orbit. They collided, producing 1788 pieces of debris [3]. The combination of these two events, along with continued and expanded launches, has increased the overall population from 0 manmade objects in 1956 to over 100 million objects today [15].

4.2 Problem Analysis It has been shown that Post Mission Disposal (PMD) alone is not sufficient to control debris environment and that some form of remediation will be necessary. However, the community has not reached any form of consensus as to the best approach with which to achieve this goal. Therefore, in order for advancement to be made on this problem, agreement must be reached on the best remediation strategy for orbital debris remediation.

4.3 Gap Analysis There have been dozens of remediation design solutions posited, but there is a need for a rigorous, comprehensive analysis of alternatives. As a part of this effort, a metric for evaluating the effectiveness of designs is necessary. As it currently stands, differing designs have no universal metric for comparison, leading to ineffective and fruitless evaluations, essentially apples-to-oranges assessments. Without a common sounding board, there is no way to successfully rank or equate designs. 21

4.4 Need Statement Without remediation, the number of objects and the number and frequency of collisions are expected to climb, even with complete cessation of future launches [5]. Thus, it is imperative that a remediation design be chosen and implemented. In order to facilitate this, a method and strategy are needed for measuring the quality and value of designs, along with an initial trade- space analysis and positing the recommended solution (or solutions). Remediation of 5 high-risk objects per year for 10 years.

5 Requirements

5.1 Scope and Assumptions In order to scope the problem properly, some assumptions were made. First and foremost, it can be shown that delta-V costs for orbital plane changes are far greater than similar altitude changes. At the same time, as was stated in the context, there are certain altitudes and inclinations with high-than-average density of objects. In addition, it can be shown that SL-16 rocket bodies are some of the highest mass objects in LEO, and they also happen to inhabit those densely populated orbits. Thus, as a stated goal is to reduce the overall collision risk, measured by probability and mass, it is clear that those high density orbits will certainly be targeted. Thus, rather than include an exhaustive query of all possible space debris objects, the scope can be reduced to only examining the high-density populations of SL-16’s at 71, 74 and 81 degrees inclination and between 600 and 800 kilometers altitude.

5.2 Mission Requirements MR.1 The ADR solution shall focus remediation efforts in LEO (below 2000 km). MR.2 The ADR solution shall select high-risk objects as a function of mass and collision probability. Risk for a given object i at time t is defined as a function of collision probability (P(t)) and mass (m) [5]:

� � = � � ∗ � MR.3 The ADR solution shall de-orbit at least 5 high-risk debris objects per year for 10 years. MR.4 The ADR solution shall release no more objects or vehicles than it recovers. MR.5 The ADR solution shall execute de-orbit maneuver within 2 months of end-of-life.

5.3 Functional Requirements FR.1 The ADR solution shall be able to maneuver throughout LEO (up to 2000 km). FR.2 The ADR solution shall be able to engage with debris up to 8300 kg (dry mass of SL-16). FR.3 The ADR solution shall be able to remove debris objects from orbit.

6 Concept of Operations In order to address the lack of a rigorous examination of remediation designs, a thorough analysis of design alternatives will be performed. To do so, a value hierarchy and utility function with which to compare and contrast designs will be constructed.

6.1 Competing Approaches There have been various attempts to resolve the debris problem, but the most widely acknowledged is Active Debris Removal (ADR). Just-in-time Collision Avoidance (JCA) has been posited as a potential alternative, and some of the pros and cons are listed below. ADR JCA Traits Stochastic, long-term Deterministic, short-term Number of Objects Removed 30-50 5-3000 Cost per Collision Avoided $100 million to $100 billion $10 million to $10 billion

As this project is essentially concerned with long-term stability of the space environment and JCA is a short-term solution, ADR was chosen as the primary focus of this study.

6.1.1 Active Debris Removal (ADR) ADR uses mechanism to remove debris object completely from orbit. The general concept of those studies is shown in Figure 5: 1. Identify the target object 2. Maneuver to and rendezvous with the target 3. Grapple with the target 4. De-tumble the target (if necessary) 5. Remove the object from orbit There are many different types of mechanism for each step. Some mechanisms are implementable in to more than one step. The mechanisms will be explained in section 6.2. Depends on mechanism implemented, overall ADR performance and total cost will be changed.

Figure 5 - ADR CONOPS

6.1.2 Just-in-time Collision Avoidance (JCA) Beside the ADR, there is another strategy for prevention of collisions involving space debris, called just-in-time collision avoidance (JCA). The JCA system is to deflect a debris object’s trajectory to avoid a collision. For the concept of the JCA, the first step is to identify an imminent collision object from ground and orbital systems, then an air-launch system is used to deploy the JCA system on board. After deploying the JCA, cloud of high density gas is deployed in path of one of the potentially-colliding objects. If the object’s orbit is altered enough, then the collision will be prevented. The total time for intervention is 10’s of minutes to hours, and the air-launch system takes less than 30 min [52]. The effect on a debris object is dependent on the density and size of the JCA gaseous cloud in addition to the area to mass ratio of the object. The higher the area to mass ratio of the object is, the greater the change in the object’s orbit from the gaseous impulse will be. Compared to ADR, JCA has advantages. JCA has better cost efficiency. Since JCA uses the air- launch system instead of a rocket launch system, it costs about 10 times less. Using the gas cloud enables a JCA system to skip the process of capturing and de-tumbling which reduce operational time and increase safety for other unexpected collision by non-trackable objects. 25

There is also disadvantage which is that the debris object is still on the Earth orbit. Even if an imminent collision is prevented, since the object is left on orbit, it can cause future collision. There is no decrease in overall collision probability.

6.1.3 Property Rights An alternative to a traditional, direct remediation would be to explore political strategies. The root of the orbital debris problem stems from the tragedy of the commons. As no one truly owns outer space, and orbits are rarely policed, there is little to no incentive to mitigate or remediate your own space waste. Therefore, it is possible that the best solution would involve a long-term solution of this problem. The classic approach to the tragedy of the commons is property rights. Thus, a potential remediation design would be an expansion and allocation of property rights in outer space. There are several assumptions involved, along with many complex issues with implementation, but this is a promising, enduring solution that would have ramifications and ripple effects far beyond the immediacy of this project.

6.2 Design Alternatives The goal of ADR is to remove debris object from orbit above and beyond the currently-adopted mitigation measures [5]. Since 2006 studies for removal of derelict spacecraft or satellites have been conducted by researchers across the world. The general concept of those studies is that: 1. Identify and launch towards the target object 2. Maneuver to and rendezvous with the target 3. Grapple with the target 4. De-tumble the target (if necessary) 5. De-orbit the object Each of these steps is implemented by a different type of design, enumerated in detail below. Those considered for launch vehicles are Delta IV, Atlas V, and Falcon 9. Among the grapplers evaluated are the robotic arm, throw net, harpoons, COBRA IRIDES, and three-coordinated electromagnetic spacecraft. De-orbiters include inflatables and propulsion systems. Combining elements of each of these provides an overall debris remediation system.

6.2.1 Launch and Rendezvous Designs In order to get a payload into orbit, an initial launch is required. To analyze these, there are three launch vehicles presented below, the Delta IV, the Atlas V, and the Falcon 9. These are all currently commercially available for launches to low Earth orbit. The designs for rendezvous are considered as the second stages for the launch vehicles. For all designs considered, the first stage of the rocket brings the payload into orbit after which those fuel tanks and motors are discarded and fall back to Earth. After that, the second stage engines kick in and can be used to place the payload, in this case the ADR grapple and de-orbit mechanisms, into position near the derelict objects. After launching the vehicle, an orbital maneuver in which the spacecraft will change its orbit to approach the targeted debris object at a very close distance is required. Both launch and rendezvous processes can be performed using any of these design alternatives. Since the system’s goal in these two processes is to minimize “Delta-V Cost”, the system will pre-select the most cost efficient design. Since the cost of Falcon 9 is the lowest, therefore the system will pre-select it as the best design alternative in both launch and rendezvous.

6.2.1.1 Delta IV The United Launch Alliance (ULA) manufacturers the Delta IV, which is available in multiple configurations, mostly varying by the number of solid rocket motors added. The main engine for the first stage is the RS-68A and provides over 700,000 pounds of thrust at sea level. The second stage utilizes the RL10 propulsion system and can be used to precisely place payloads. The variant used is the RL10B-2, which is slightly more massive and more powerful than other RL10 variants. Max Payload to LEO: 28,370 kg Cost per kg to LEO: $13,072

6.2.1.2 Atlas V The Atlas V family of rockets are produced by the United Launch Alliance (ULA). They are also heavily modifiable by the addition or removal of solid rocket boosters. The first stage is powered by an RD-180 engine, with 860,000 pounds of thrust. The second stage utilizes the same

27 propulsion system as the Delta IV, the RL10, specifically the RL10A variant, which slightly smaller than the RL10B-2 used in the Delta IV. Max Payload to LEO: 18,850 kg Cost per kg to LEO: $13,182

6.2.1.3 Falcon 9 The Falcon 9, produced by commercial spaceflight company SpaceX, is powered by 9 Merlin engines producing 1,530,000 pounds of thrust at sea level. The second stage is powered by a single Merlin engine with 210,000 pounds of thrust and can be used to accurately place payloads and maneuver in orbit. Max Payload to LEO: 13,150 kg Cost per kg to LEO: $4,109

6.2.2 Grapple Designs Grappling designs can be categorized as one of two types: contact and contactless. The contactless mechanisms, such as eddy current and three-coordinated electromagnetic spacecraft, are almost solely electromagnetic in nature, as well as some of the contact methods, fail to meet mission requirements and thus are removed from further analysis.

6.2.2.1 Robotic Arm A robotic arm is used to physically grab the debris and perform a maneuver to change its orbit. In one instantiation, it has a deployed length of 3.7 m and a mass of 80 kg, and it has an estimated peak power demand of 360 W. Single debris that the robotic arm can catch at a time is up to 7,000 kg, which would include RADARSAT-1, ERS 1, SPOT 4, MIDORI II, and MIDORI satellites. The robotic arm allows a rigid and controlled connection to the target and allows repeated capture attempts, but it cannot offer a safe removal of debris target via controlled entry. International Astronautical Congress (IAC) stated a limitation of the robotic arm, “since a number of high priority debris do not disintegrate during an entry, this would cause an on-ground casualty risk not compliant with regulations.” [49]

6.2.2.2 Throw Net In this method, the system throws a net towards a debris object and pulls the object along a tether. The total area of the net is 3,600 m2 connected to a tether with a length of 70 m. The net entangles the objects due to masses or a closing mechanism. It is a single-shot mechanism, thus in case of a miss, there is a second net for capture attempt. This mechanism can capture a debris with a mass up to 10,000 kg which covers all the derelict objects in LEO.

6.2.2.3 Harpoon Harpoon method has a similar concept with the net method. The system shoots a harpoon towards a debris object and pulls the object along a tether, and in case of a miss shooting, the system consists two harpoons in each launch. The system consists of a barbed tip to prevent pull- out after impact, and consists of a crushable cartridge and on-ground test stabilizer. The mass of each harpoon is only 8 kg and the tether weights 1.3 kg, and it can handle up to 9,000 kg. The firing distance should be greater than 10 m [59].

6.2.2.4 COBRA IRIDES COBRA was proposed as a solution to one of the challenges issued by ESA within the framework of the SysNova competition and it was eventually declared the winner. According to the paper, “The COBRA IRIDES Experiment” [50] the COBRA IRIDES experiment is to be performed after the completion of the IRIDES experiment, the goal of which is to perform close rendezvous with a non-cooperative satellite (Picard, dry mass = 144.72 kg). After the IRIDES experiment ends, Mango satellite (dry mass = 137.815 kg) will be in close proximity of Picard. The objective of the COBRA experiment is to use plume impingement of Mango’s thrusters on the surface of Picard to induce torque on the Picard and impart a new rotational state. The rotational state before and after the thruster firing will be determined by means of observations with Mango’s on-board camera. Basically, the COBRA is a contactless ADR method using plume impingement from a hydrazine monopropellant propulsion system to impart momentum on a target debris either to change its orbit or its attitude.

The main feasibility of the experiment depends on the observability of the torque effect of the plume impingement during post-processing of the experiment data. Mango satellite observes the target, rotates the thruster towards the target, performs the push, rotates back and continues observing. The main concern during the experiment is to ensure that the plume impingement occurs in a favorable configuration with the thruster plume impacting on the solar panel to maximize the torque imparted on Picard. Thales Alenia Italy evaluated the possible damaging effects on it. Considerable effects are paschen discharges, chemical contamination, thermal loading, erosion, and force loading.

6.2.2.5 ElectroDynamic Debris Eliminator (EDDE) The ElectroDynamic Debris Eliminator (EDDE) is a unique design alternative in one particular manner: it is a system that performs both the grapple and de-orbit stages of remediation. Designed for long-term, on-orbit removal of debris, EDDE is powered by a propellantless electric motor that reacts against the Earth’s magnetic field in order to facilitate movement. Grapple and de-orbiting of debris is achieved by a combination of long extendable tethers an lightweight expendable nets. By performing multiple remediations over a long period of time, EDDE reduces the costs associated with repetitive launches [60].

6.2.3 De-tumble Designs De-tumbling is only required when coupled with some of the other designs, specifically the robotic arm. It is performed by the same vehicle that performs the rendezvous and is accomplished by thrusting to counter angular velocity.

6.2.4 De-orbit Designs To de-orbit a debris object it is necessary to move the debris object close enough to the atmosphere that it will experience drag and eventually fall to Earth. Within approximately 600 km this will be true for most debris objects, but this can be modified by manipulation of the force of drag.

Method: Description: TRL: Inflatables Modify surface area 3 EDDE Modify altitude 2 Propulsion Modify altitude 9

6.3 Method of Analysis This method of analysis revolves around the ADR CONOPS: 1. Identify and launch towards the target object 2. Maneuver to and rendezvous with the target 3. Grapple with the target 4. De-tumble the target (if necessary) 5. De-orbit the object Each of these steps can be run as a model and further de-composed into attributes that can be analyzed in a value hierarchy. It is important to note that an overall debris remediation system will incorporate several design elements needed to fulfill all the stages of ADR. In the following sections are listed descriptions of the analysis associated with each stage of the ADR CONOPS, including the inputs and outputs of each. At a high level, this can be described via the flow chart below.

Some designs are also removed from analysis due to failure to meet requirements or significantly low TRL’s and therefore unrealistic expectation of implementation within the near future.

6.3.1 Launch and Rendezvous The stages of launch and rendezvous can be handled via a network analysis tool. Built in MATLAB, this network analysis takes in TLE data as inputs and outputs a series of maneuvers and delta-v costs. A series of functions take in Two-Line Elements (TLE) data, the standard for the US Space Surveillance Network, and converts it to more accessible Classic Orbital Element (COE) and State Vectors (SV). Once these elements are obtained, they are run through a calculation to determine delta-v, or the change in velocity, required to maneuver between two orbits. These delta-v calculations are used as the “distances”, or arc lengths, in the network analysis. The goal is to minimize the distance traveled, as delta-v can be effectively used as a proxy for fuel costs, a significant portion of total launch costs. A design with similar effectiveness but a lower overall delta-v will be preferred over a higher delta-v approach.

6.3.1.1 Classic Orbital Elements There are six COE’s that together provide a comprehensive description of where an object is in orbit. They are as follows: Semi-major axis: the size of the orbit, specifically the length from the center of the orbit to the longest edge of the ellipse. In other words, the semi-major axis is half the distance of the long axis of an ellipse. Eccentricity: the shape of the orbit, where eccentricity of zero is a circular orbit and eccentricity of greater than or equal to one is a parabolic or hyperbolic orbit (and thus no longer truly in orbit around the original body). Inclination: the tilt of the orbital plane with respect to a fundamental plane, in this case the equatorial plane. Inclination of 90 degrees is a polar orbit, that is it passes directly over the poles, and inclination of 0 or 180 degrees is an equatorial orbit. Longitude of the ascending node: where exactly the orbit intersects with the equatorial orbit (and thus is undefined with inclination is 0). A “node” is the point at which two orbits intersect, and from simple geometry it can be shown that two intersecting circles will have two points of 32 intersection. The longitude of the ascending node, or the point of intersection where the satellite is going from south to north, is used to define the swivel of the orbit. Argument of perigee: the perigee is the point in an orbit that is closest to the body being orbited. The argument of perigee is measured as the angle from the ascending node to the perigee, giving an orientation of the orbit within the orbital plane (used to determine northern or southern hemisphere, for example). True anomaly: the final COE tells exactly where within the orbit an object is at a specific time, measured as the angle from the perigee to the exact position of the spacecraft at a given time.

6.3.1.2 State Vectors State vectors are a more traditional, familiar format for position and velocity, using vectors. These are convenient in the calculations, as the mathematics of vector multiplication, vector calculus, etc. are far more well-known to us than the esoteric orbital elements.

6.3.1.3 Model As we will be analyzing pairs of orbits, we are faced with an initial hurdle for object selection. Looking at the formula for combinations: � �! = � �! � − � ! And plugging in values the total population (n) and the sets to be combined (k), we see that we will quickly reach a factorial explosion. For n=500, k=2: 500 500! = = 124,750 2 2! 500 − 2 ! As the orbital population consists of 500,000+ objects, it is easy to see how an exhaustive analysis is prohibitively costly, at least without much larger computational capabilities. Thus, we begin by reducing the population to be analyzed by selecting high-mass objects. Once we have our target population, we begin our object categorization and network analysis steps concurrently. In the network analysis, we much first take in TLE data, convert and store it as COE data for ease of future use. This COE data is then fed into the main driver of our model, our maneuver selection. We have two nested loops, one for interceptor selection and one for target selections, ensuring that we check each target for each interceptor. As long as targets exist

33 for a given interceptor, we convert the COE data to SV data, then send the SV data through a Lambert problem solver to calculate delta-v. All targets are looped over and combined with calculations from the object categorization to determine the overall value for a given target. This best target is chosen for the actual maneuver, which is then “performed”, advancing the internal clock by the Time Of Flight (TOF) of the maneuver. This time change, or delta-T, is fed back through the system, as this time delay affects the position vectors of all objects. The target that was chosen is removed from the catalog, and the process is repeated until some constraint is broken (maximum payload or delta-v, minimum scores reached, etc.). These constraints will be varied and modified as experiments are performed and knowledge of the performance of the model is better understood. Aside from conversion between COE’s and SV’s and TLE’s, the main network analysis function is performed by Lambert. Essentially, this is a method for taking two position vectors and a time of flight and calculating velocity vectors. This allows us to do a variety of things, including constructing our network of delta-v costs. This can be computationally intensive, and there are still some kinks to work out (namely, the finding the minimum point in a non-linear system of equations), but there have been similar efforts utilizing the Lambert problem in a similar method before [57]. The steps to solve Lambert’s problem are as follows [58]:

Calculate � and � using � = �� ∙ �� and � = �� ∙ �� Choose prograde or retrograde trajectory and find ∆�:

�� ∙ �� cos , �� ×�� < 0 �� ∙ � 360° − cos � � , �� ×� ≥ 0 �� ∆� = �� ∙ �� cos , �� ×�� ≥ 0 �� ° �� ∙ �� 360 − cos , �� ×�� < 0 �� Find �: � � � = sin ∆� 1 − cos ∆� Iterate through the following equations to find �:

�(�) � = � − �′(�) � � � � = � � + � �(�) − �∆� � � 1 �′(�) = 2� � � � − 3� � � � � � 2 � � �(�) + ��(�)/ + 3� � � � �(�) �′(�) � � � = �(�) 4 � � � = (−1) 2� + 3 ! � � � = (−1) 2� + 2 ! Find �(�): �� − 1 �(�) = � + � + � �(�) Find �, �, �� : �(�) � = 1 − �

� �(�) � = �� − 1 �� (�)

�(�) � = � �

�(�) � = 1 − �

Calculate �� : 1 � = (� − �� ) � � � � � �� − �� = � − � � � � � �

In section 9. Preliminary Model Code you can see the actual MATLAB functions that are used in the model. In Figure 14 the functions used are labeled below the title of the block.

Figure 6 - Network Analysis Simulation Flowchart

6.3.2 Grapple Prior to this CONOPS stage, the DRS will launch, approach and rendezvous with targeted debris. During the grappling stage, DRS will grab the targeted object using one of the following methods: (1) Robotic arm, (2) throw net, (3) harpoon and (4) COBRA IRIDES. One of the disadvantages of autonomous methods to capture is that it is still in development phase; It is only verified in simulation and not yet proved in practical use [61]. In addition, grappling stage considered one of the most complex stages since a lot of uncertainties in position, velocity, rotation, and mass, which will be the parameters considered in this section of the analysis [62]. It is important to highlight that "the system” is focused on removal of bigger debris since they yield more potential risk on operational satellites in Low Earth Orbit.

�� = �� + �� + �� − � �� = 1 − �� − �� = � �� = � There are 4 Active Debris Removal grappling alternatives robotic arm, throw net, harpoon and COBRA. Each ADR will be tested on a targeted object based on mass, rotation and altitude. Each ADR have strengths and weaknesses based on mass, rotation and altitude. For example, a high rotation object would be better to be grappled if a net is used and worse for a robotic arm to be used. Also, high mass object would be better to be grappled by a throw net instead of the COBRA. The targeted debris object will be a minimum of 50 objects in 10 years. The targeted objects will be the highest risk object among the other. Since most of the targeted objects will have a high mass, the COBRA alternative will be eliminated since it cannot handle high mass objects. Grappling model will start off by collecting data for all ADR designs. Each grappler has a score for mass, rotation and altitude for each objects. The model will continue operating the same procedure for the next 49 objects. Then, scores for mass, rotation and altitude for each grappler

37 will be summed. Finally, the total score for each ADR will be compared and the highest score will recommended for grappling.

Figure 7 - Object Categorization Simulation Flowchart

Robotic Arm: Max Mass: 7000 kg Min Mass: 1 kg Mean Velocity: 2.8 km/s Mean Angular Rotation: 2.5 Debris Control: 9 Weaponization: 10 TRL: 6

Countries Involved: USA, EU, Japan (3 total) Cost: $67.62M

Throw Net: Max Mass: 10,000 kg Min Mass: 0.1 kg Mean Velocity: 3 km/s Mean Angular Rotation: 1 Debris Control: 7 Weaponization: 5 TRL: 5 Number of Countries Involved: USA, EU, Japan (3 total) Cost: $84.18M

Harpoon: Max Mass: 9000 kg Min Mass: 4 kg Mean Velocity: 3 km/s Mean Angular Rotation: 2 Debris Control: 5 Weaponization: 0 TRL: 4 Number of Countries Involved: USA, EU, Japan, UK (4 total) Cost: $7.96M

COBRA IRIDES: Max Mass: 150 kg Min Mass: 1 kg Mean Velocity: 3 km/s Mean Angular Rotation: 3.5

Debris Control: 2 Weaponization: 5 TRL: 3 Number of Countries Involved: EU (1 total) Cost: $302.15M

ElectroDynamic Debris Eliminator (EDDE): Max Mass: 8300 kg Min Mass: 2 kg Mean Velocity: 4 km/s Mean Angular Rotation: 2.5 Debris Control: 6 Weaponization: 10 TRL: 2 Number of Countries Involved: USA (1 total) Cost: $314.35M

6.3.3 De-tumble De-tumbling is required in order to bring the derelict debris objects under control, particularly when being grappled by a robotic arm.

When an object has an angular velocity, sometimes this needs to be countered before the object can be maneuvered out of orbit. In order to do so, torque must be applied to counter the pre- existing angular velocity.

� = 0

� − � � = �

�(�) = ��

�(�) = �(� − �)

If � is set to 0, the equation can be re-written as:

�(�) = −��

Design: Traits: Electric Propulsion Slow, low thrust, low TRL Chemical Propulsion Quick, high thrust, high TRL

6.3.4 De-orbit For analyzing the de-orbit capabilities of different designs, a first-order estimation for de-orbit time and delta-V cost is developed. The major assumption inherent to this model is that the force of drag is directly proportional to the time to de-orbit. Second, time to de-orbit

�� = 2 Atmospheric density at a given altitude can be found by: � = ��

Where � is calculated from a standard table: Atmospheric Scale Height & Density, to 35,786 km Atmospheric Density Altitude Scale Height Mean Maximum (km) (km) (kg/m3) (kg/m3) 0 8.4 1.225 1.225 100 5.9 5.25E-07 5.75E-07 150 25.5 1.73E-09 1.99E-09

200 37.5 2.41E-10 3.65E-10 250 44.8 5.97E-11 1.20E-10 300 50.3 1.87E-11 4.84E-11 350 54.8 6.66E-12 2.18E-11 400 58.2 2.62E-12 1.05E-11 450 61.3 1.09E-12 5.35E-12 500 64.5 4.76E-13 2.82E-12 550 68.7 2.14E-13 1.53E-12 600 74.8 9.89E-14 8.46E-13 650 84.4 4.73E-14 4.77E-13 700 99.3 2.36E-14 2.73E-13 750 121 1.24E-14 1.59E-13 800 151 6.95E-15 9.41E-14 850 188 4.22E-15 5.67E-14 900 226 2.78E-15 3.49E-14 950 263 1.98E-15 2.21E-14 1,000 296 1.49E-15 1.43E-14 1,250 408 5.70E-16 2.82E-15 1,500 516 2.79E-16 1.16E-15 2,000 829 9.09E-17 3.80E-16 2,500 1220 4.23E-17 1.54E-16

The coefficient of drag for a long cylindrical object, such as an SL-16 rocket body, can be estimated as:

� = 0.82 Time to de-orbit is found by the following: �� − � � = �� => � = = = 2� �� − �

�� = � − � + � 2�

Iterate numerically until �(�) ≤ �, where:

�� 398,600 � � = 6378 �� + �

�� 398,600 − 6378 �� ∗ � � � = �

And find � at that point, �� = � − �.

Method: Description: TRL: Inflatables Modify surface area 3 EDDE Modify altitude 2 Propulsion Modify altitude 9

6.3.5 Political Viability For each design there is also the question of political viability. This viability can be decomposed into “Agreeability” and “Verifiability”, which are further described below. This viability applies to all stages of all design alternatives, and the methods of analysis for each type are described below.

6.3.5.1 Agreeability Agreeability measures how agreeable each grappling designs among entities (nations) involved. It will convert qualitative measures to quantitative ones in terms of weaponization and legal framework of each design.

6.3.5.1.1 Weaponization Purposes for any selected ADR design should be maintained in a peaceful context. The possibility of using a certain ADR design for military or other non-peaceful uses would violate

Outer Space Treaty and international space law. Hence, it is important to consider it to reach a better international agreement. In this criteria, the higher the score for weaponization, the safer, more secured, less weaponized the ADR design is. Therefore, ADR designs with high tendency of being used as a weapon shall be given a low score. A discrete scale (0, 5, 10) will be used; 0 being completely non weaponized, 5 being moderately weaponized, and 10 being highly weaponized. • Robotic Arm: This technology considered the least weaponized alternative since it is transparent. Additionally, it does not require any kind of shooting during operational phase. Thus, it receives a score of 10 • Throw Net: This technology/alternative considered moderately weaponized because it has a compartment that holds the net (not very transparent publicly). Also, it requires shooting of a projectile that releases the net in order to catch a debris object. Therefore, it gets a score of 5 • Harpoon: Appearance of Harpoon technology/alternative looks more like a weapon. In addition, it has a similar capability of ASAT in destroying active satellites, therefore, it gets score of 0

6.3.5.1.2 Legal Framework Legal framework is easiness of implementing an ADR design within the current international space law. It is important to overcome legal roadblock and make sure not to trespass the current legal law. In this criteria, the higher the score for legal framework, the better ADR design is. High Technology Readiness Level (TRL) for any ADR would be worthless if it cannot be implemented with current framework. Thus, an analysis of current legal framework is necessary. Current Legal Framework: • The Outer Space Treaty: There are three articles that have connection with the issue of space debris: Article VI, VII, and IX. Article VI states, ''States party to this treaty shall bear international responsibility for national activities in outer space." Article VII stated that each party of the treaty is internationally liable for damages of another state party that is caused by objects (and components or fragments of objects) that they launched

into space. Lastly, Article IX encourages and allows state parties to explore outer space while preserving the Earth and space environment. • The Liability Convention: makes state liable for damages "caused elsewhere than on the surface of the Earth to a space object of one launching state or to persons or property on board such a space object of another launching state … only if the damage is due to its fault or the fault of persons for whom it is responsible." • The Registration Convention: is useful because it seeks for determining liability since all launching states should notify the UN of any objects they launch and provide the UN with objects’' orbital parameters [64]. Issues to address within the international law: • Unclear definition distinction between “space debris” and “space object” • There is no legal provision that imposes any obligation to state parties to prevent creating more space debris or to remediate/remove their current space debris • Since the launching state “(i) A state which launches or procures the launching of a space object. (ii) A state from whose territory or facility a space object is launched” [64] is held liable and responsible for any damages or failures, which discourage co-operation of countries in remediation effort [65]. In addition, removal of space debris objects requires permission from owner(s) of space debris objects, which is another obstacle that needs to be overcome. • Ownership of debris: Even though a satellite might be dysfunctional, that doesn’t imply that the launching state has abandoned it. Thus, there is no right for other state/nation to remove it from orbit [65]. In other words, in order to remove space debris from space, an authorization from the launching state is required.

6.3.5.2 Verifiability Verifiability measures how each grappling design is justified among nations. Unlike Agreeability, Verifiability values does not change for each grappling design. However, changes in values are made based on (1) nationality of country(s) involved in developing each grappling design, and (2) number of nations involved in developing each grappling design.

6.3.5.2.1 Nationality The nationality of both space debris and the initiative country to (apply) the space policy could affect the political verifiability of a space policy. Nationality influences many aspects of a given space policy such as, the technology used, the available economic resources, and the objects that can be deorbited. In “Nationality” criteria, a value will be given depends on (1) the countries/nations that will implement the effort of mitigating orbital debris and (2) the nationality of the targeted objects that are planned to be removed from space. The values in this sub-attribute will not be dependent on the type of ADR design that will be used for the mitigation plan. Scores will be given on a 1- 10 scale. Further explanation will be provided in each section.

6.3.5.2.1.1 Initiative Nations that will start a mitigation effort will affect willingness of cooperation of other nations. Only few nations are expected to initialize a mission of space debris mitigation due to their effort and concern in space debris issue. Furthermore, economic resources plays an important role in initializing such a project. A score will be given for a country/nation based on its economic stand. As mentioned, countries that have interest in space debris mitigation will be considered.

Country: GDP (US$ Trillion): Percent of Total: Score: European Union 18.64 0.33 9 USA 17.97 0.32 9 Russia 1.24 0.02 2 China 11.39 0.20 7 Japan 4.12 0.07 4 France 2.42 0.04 2 Total: 55.78 0.98

6.3.5.2.1.2 Objects Nationality of objects in space is also important to consider and could affect political viability. USA, Russia, and China have most debris objects in space. Therefore, it is reasonable to assign American, Russian, and Chinese debris a higher score than other nations.

Country: Number of Objects: Percent of Total: Score: USA 5162 0.30 7 Russia 6288 0.37 9 Europe (ESA) 107 0.01 1 China 3773 0.22 7 Japan 209 0.01 1 France 517 0.03 3 India 169 0.01 2 Other 838 0.05 1 Total: 17,063 1.00

6.3.5.2.2 Type of Cooperation Cooperation in space debris remediation effort is crucial because it influence the economic nature of remediation projects by reducing development and operational cost. The larger number of participants reflects verifiability. multilateral cooperation of countries is definitely more effective than bilateral cooperation. In “Type of Cooperation” criteria, a value will be given depends of the cooperation to be made. In other words, values in this criteria will not be dependent on ADR design used for mitigation. Scores will be given on a 1-10 scale, the larger number of participants indicates a higher value and vice versa.

Number of Nations Involved: Score: 1 1 2-3 3 4-5 5

6-7 7 8-10 10

6.4 Utility Analysis To bring all the elements of the disparate design alternatives together, a utility function is defined. This utility includes components from all the stages of the ADR CONOPS, from launch to de-orbit.

6.4.1 Value Hierarchy The value hierarchy for this utility function is found below. The top level attributes are performance, risk, TRL, and political viability. Each of those are further decomposed, and details can be found in the following sections.

Figure 8 - Value Hierarchy

6.4.2 Attribute Descriptions Performance: The overall quality of the remediation system, as further defined via “Object Scores” and “Delta-V Cost”. Risk: Any danger including accident, failure, or delay in a process to remediate space debris, further defined by “Safety”, “Reliability”, and “TRL”. Political Viability: The viability of a solution in the international sphere, as further defined by “Agreeability” and “Verifiability”. Object Scores: The appropriateness of the given ADR design for the types of debris that are being remediated. For instance, an object with a large rotation will have a higher score when remediated by a net than a robotic arm, and an object with high mass will have a higher score when remediated by the arm. Delta-V Cost: The delta-v cost incurred by the deployment of the given Debris Remediation System, according to the network optimization model. Safety: It considers any damages caused by failures or problems during the project. Further decomposed by “Accidents”, “Debris Control”, and “Landing”. Reliability: The quality of ADR system to remediate or remove debris object. Further decomposed by “Approach”, “Maneuver”, “Grapple”, “De-tumble”, and “De-orbit”. TRL: The Technology Readiness Level of each ADR system, as defined by NASA: • TRL 1: Basic principles are observed and reported upon. • TRL 2: Concept has been developed or a purpose and function has been identified. • TRL 3: Either mathematical or experimental proof has been provided for the concept. • TRL 4: Prototypes have been built and successfully tested in a laboratory setting. • TRL 5: Testing of prototypes in a relevant environment (though not in a full implementation). • TRL 6: Prototypes have been built and successfully tested in an environment representative of an operating environment (partial integration).

• TRL 7: Prototypes have been built and successfully tested in a live operating environment at or near full-scale. • TRL 8: Actual completion and implementation, full integration, full and finalized testing and validation. • TRL 9: System has successfully completed mission operations in fully realistic environment. Accidents: Accidental collisions and failures/problems in system that can alter the system itself to new debris object. For launch systems, calculated by (failures/attempts), using historical data. Debris Control: Risk of failure in processes of grabbing and de-tumbling debris object. Landing: Damage by debris object in case of that debris object does not fully burn upon the atmosphere. Approach: A process for DRS (carrying ADR system) to reach debris object in a certain distance. Includes probabilistic risk assessment ratings for loss of mission from [63]. Maneuver: A process for ADR system to operate and propel itself throughout the LEO environment. Grapple: A process for ADR system to catch debris object. It is only applied to certain ADR systems which require the physical contact with debris object. De-tumble: A process for ADR system to stop the rotation of debris object. De-orbit: A process for ADR system to change an orbit of debris object. Agreeability: The ability for multiple sides to have same views and opinions. Further decomposed by “Weaponization”, “Legal Framework”, and “Strategy”. Verifiability: The ability to confirm that requirements/policy/laws are met correctly. Further decomposed by “Type of Cooperation” and “Nationality”. Weaponization: The possibility of using a certain ADR design for military or other non-peaceful uses would violate Outer Space Treaty and international space law. Legal Framework: Ease of implementing an ADR design within the current international space law. It is important to overcome legal roadblock and make sure not to trespass the current legal law. Type of Cooperation: Cooperation of two or more countries in effort of remediation (single country vs. multiple countries).

Nationality: The nationality of both space debris and the initiative country to (apply) the space policy could affect the political verifiability of a space policy. Further defined by “Initiative” and “Objects”. Initiative: Nationality of the country that is associated with applying the space policy, in other words, the country that plan and deploy ADR. Objects: Nationality of objects in space is also important to consider and could affect political viability. For example, Russia has most space debris and doesn’t want any other country to remove their debris from space.

6.4.3 Attributes and ADR Designs Each stage of the ADR CONOPS corresponds to a certain set of the attributes in the value hierarchy. Thus, when an overall remediation system is constructed, every attribute has a value. Table 2 delineates the relationships between low-level attributes and the associated stages. Table 2 - ADR CONOPS to Attributes

6.4.4 Weight Elicitation Weights were elicited via a pairwise comparison and AHP analysis with the stakeholders. Is this… More Important Equal Less Important …than this? 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 Performance X TRL Risk X Performance

Political Viability X Risk Political TRL X Viability Political Performance X Viability Risk X TRL Object Scores X Delta-V Cost Safety X Reliability Accidents X Debris Control Debris Control X Landing Landing X Accidents Approach X Maneuver Maneuver X Grapple Grapple X De-tumble De-tumble X De-orbit De-orbit X Approach Approach X Grapple Maneuver X De-tumble Grapple X De-orbit De-tumble X Approach De-orbit X Maneuver Agreeability X Verifiability Legal Weaponization X Framework Legal Framework X Strategy Strategy X Weaponization

Type of Nationality X Cooperation Initiative X Objects

6.4.5 Analytic Hierarchy Process (AHP) To convert the simple pairwise comparisons into usable weights, an Analytic Hierarchy Process (AHP) was used. The inputs from the weight elicitation process are put into the matrix below: Performance Risk Political TRL Viability Performance 1.00 2.00 5.00 4.00 Risk 0.50 1.00 1.00 2.00 Political Viability 0.20 1.00 1.00 0.25 TRL 0.25 0.50 4.00 1.00 Total 1.95 4.50 11.00 7.25 These values are then normalized and averaged to determine the final weight value for each attribute. This process is repeated for each level in the value hierarchy, see “Models, Data and Code” to see the calculations for all attributes. Performance Risk Political TRL Average Consistency Viability Measure Performance 0.51 0.44 0.45 0.55 0.47 3.27903137 Risk 0.26 0.22 0.09 0.28 0.19 2.969304229 Political Viability 0.10 0.22 0.09 0.03 0.14 3.049345794 TRL 0.13 0.11 0.36 0.14 0.20 3.815399485 Total 0.87 0.89 0.64 0.86 CI: -0.240576593 RI 0.9 (n=4): Ratio: -0.267307326

7 Results Late in development it was realized that the large number of all possible combinations of all possible stages of the ADR CONOPS, close to 150, was prohibitively exhaustive. Rather, promising results could be derived by simplifying the models to focus on a single stage of the ADR CONOPS at a time. Costs for designs were calculated using NASA’s Advanced Missions Cost Model (AMCM) to include development and production costs.

7.1 Launch and Rendezvous The designs used in the launch and rendezvous stages are relatively agnostic to the overall utility of the remediation system. All the designs considered have attribute values within XX% of each other. As such, a simplified approach can be taken: rather than an exhaustive analysis, the design with the lowest cost per kg to LEO can be chosen. Design: Cost per kg to LEO: Delta IV $13,072 Atlas V $13,182 Falcon 9 $4,109 As can be seen, the Falcon 9 is the clear winner and as such is chosen as the desired launch vehicle. Similarly, the rendezvous vehicles are associated with the second stages of the launch vehicles and thus could be reduced to the same evaluation and consideration method as the launch vehicles themselves.

7.2 Grapple The harpoon grappler had a utility of 4.9, the throw net had a utility of 4.8, and EDDE had a utility of 1.4. In addition, some designs such as COBRA IRIDES and the robotic arm were eliminated due to failure to meet requirements for mass capability.

When utility per dollar cost is analyzed, the harpoon’s efficacy becomes even more starkly clear, and thus it is chosen as the preferred grappling design alternative. Design: Utility: Cost: Utility/Cost:

Throw Net 4.9 $7.96 million 5.74

Harpoon 4.8 $84.18 million 61.79

EDDE 1.4 $314.35 million 0.45

7.3 De-orbit The de-orbiters all had relatively low utilities, 1.2 for inflatables, 1.9 for propulsion systems, and 1.4 for EDDE. If the inflatables are combined with a propulsion system, then their utility jumps to 3.0, however the cost does as well.

Similarly, the de-orbiting designs were heavily influenced by cost differences. The propulsion system, largely due to its cost being one fifth the price of the next cheapest alternative, is chosen as the preferred de-orbiting design. If a high-utility design is preferred at any cost, then the inflatables and propulsion combination may become the recommended design. Design: Utility: Cost: Utility/Cost:

Inflatables 1.2 $212.53 million 0.55

Propulsion 1.9 $40 million 4.66

EDDE 1.4 $314.35 million 0.45

Inflatables+Propulsion 3.0 $252.53 million 1.20

7.4 Overall Debris Remediation System A combination of the most promising designs for each stage of the ADR CONOPS will allow for an overall remediation system that will have comparably encouraging utility. Thus for the purposes of this analysis, the highest utility designs are aggregated into an overall “best” debris remediation system recommendation. Design: Recommended: Cost:

Launch and Rendezvous Falcon 9 $61.2M

Grapple Harpoon $7.96M

De-orbit Propulsion $40M

Total: $109.16M

8 Business Case SafeSpace is the name of a hypothetical private venture that specializes on closing the gap between theory and practice regarding orbital debris remediation.

8.1 Potential Market Size Currently, there are 385 satellite owners operating over 1200 satellites. SafeSpace’s goal is to capture 36% of the market over the course of 20 years. SafeSpace’s customer base is projected to increase 5% annually in an optimistic scenario causing to capture 99% of the market share, 2% annually in an expected scenario, and 1% annually in an pessimistic scenario causing to capture 13% of the market share.

8.2 Business Model As addressed earlier, there are 385 satellite owners who provide satellite services ,such as GPS and weather forecast. Users of satellite services generate revenue to satellite owners, satellite operators and launch providers. However, the revenue flow stream might get affected by risk of space debris in case of collisions with operational satellites which will result in a loss of revenue. SafeSpace provide services to reduce space debris population which in turn will create value for satellite owners by (1) operating in a safer space environment, and (2) avoiding loss of revenues. SafeSpace will operate by interacting with ADR manufacturers and launch providers. ADR manufacturers will provide ADR components needed based on an analysis made to determine the best ADR design for specified object(s) to be removed. On the other hand, launch providers will

59 provide launch services to SafeSpace.

8.3 Sales Profile Costs to operate SafeSpace is broken into two categories: (1) Non-recurring costs, and (2) recurring costs. SafeSpace’s non-recurring cost includes design improvement, testing, and finalization cost. On the other hand, recurring costs includes salaries for 5 employees, overhead, ADR design purchase, launch, and maneuvering fuel cost. SafeSpace unit sales is calculated by charging the launch cost * 10% fee , which will result in a total price of $1,487,843. Total Market Value for SafeSpace will be 385 (number of satellite owners) * $1,487,843 = $572.8 Billion. Moreover, the expected annual revenue = $572.8 Billion (Market Share Value)*2% = $4,124,302. The following table specify the return on investment for the next 15 years in pessimistic, expected and optimistic scenarios. As can be seen from the table that expected return of investment will be above stock market in 10 years.

Duration Pessimistic Expected Optimistic Stock Market

5 years -79% 29% 354% 128%

10 years 88% 484% 1675% 163%

15 years 389% 1255% 3852% 208%

Return on investment (ROI)

The following diagram shows revenues generated from SafeSpace in the course of 10 years. It is projected that SafeSpace will breakeven after 2 years in an optimistic scenario, after 4 years in an expected scenario, and after 7 years in a pessimistic scenario.

9 Project Plan

9.1 Statement of Work

9.1.1 Objective Collisions between orbital debris and operational space assets would have significant consequences, rendering those assets inoperative and near space dangerous, increasing the likelihood that others will have their operational lifetimes cut short due to debris impact. Without remediation, the number of objects in low earth orbit and number of collisions will continue to climb, even without additional launches. There is currently no consensus on the optimal strategy for remediation of orbital debris. This lack of agreement stems from the absence of a rigorous, comprehensive analysis of design alternatives. This gap will be closed by performing a traditional risk management investigation, focusing on technical and operational risks, collision hazard evolution, political viability, and costs.

9.1.2 Project Scope Project’s scope will include operational satellites and debris objects in Low Earth Orbit (below 2000 kilometers). A wide range of design alternatives will be explored, but will focus on designs with high feasibility, particularly in terms of timeframe of implementation. In other words, project’s scope will be restricted to designs with implementation schedules that will not be of prohibitive length, with a working goal of less than 50 years. In terms of deliverables, a series of briefs and reports detailing the project status throughout the coming months will be delivered. Also, iterations of models throughout the Spring semester (specific deliverable dates still to be determined) will be delivered as well. Finally, before the 21st of April 2016 a final report detailing project research, a complete description of models and methods, and final recommendations for further work and action will be delivered.

9.2 Work Breakdown Structure

Figure 9 - Work Breakdown Structure

9.3 Schedule

9.4 Critical Path By analyzing project’s schedule, critical path for the project is determined, which leads form problem statement definition (specifically, conducting research), to requirements development, to the actual construction of the model, and finally to the analysis of results.

Figure 10 - Critical Path

9.5 Project Risks The major risks associated with the project all relate the stoppages on the project’s critical path. Attempts have been made to mitigate these risks early on by building a sizeable amount of slack into the project schedule in the first place.

Table 3 - Project Risks

Risk Description Mitigation Strategy Quantitative requirements Stakeholders are not Develop requirements elicitation forthcoming with independently and later ask requirements for verification Political feasibility metrics and Determining a solid, Make contact with political calculations quantifiable metric for insurance underwriters to political feasibility is not gain further knowledge simple Acquiring datasets Datasets can be unreliable, Prepare for a large amount using differing definitions, of data cleaning before use or sometimes wholly contradictory Modeling (coding) Modeling complex orbital Further research into networks may prove feasibility, previous similar technically difficult work, and discussion with experienced SEOR faculty Verification of accuracy The time scale for the Be honest with this project is too long for any weakness in the immediate verification of presentation of data, and results include generous error bounds where appropriate

9.6 Earned Value At the end of the project, around 1275 hours of work is expected. An hourly rate of $30 with 2x overhead modifier for a total hourly cost of $60 is considered. This results in a total budgeted cost of $76,500. Currently, the project approximately 98% complete, with 939 hours worked. Project completion of 95% is scheduled with 1215 hours worked.

Actual Cumulative Hours 939 Actual Percent Complete 98% Scheduled Cumulative Hours 1215 Scheduled Percent Complete 95% Cumulative PV $72,900 Cumulative AC $56,340 Cumulative EV $74,970 CPI 1.33 SPI 1.03 Both the schedule performance index (SPI) and cost performance index (CPI) are hovering around 1.

Figure 11 - CPI, SPI

Figure 12 - Earned Value

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11 Models, Data and Code function [ r, v ] = sv_from_coe( coe ) %sv_from_coe Summary of this function goes here % Detailed explanation goes here global mu h = coe(1); %Angular momentum e = coe(2); %Eccentricity RA = coe(3); %Right ascension of the ascending node incl = coe(4); %Inclination w = coe(5); %Argument of perigee TA = coe(6); %True anomaly rp = (h^2/mu)*(1/(1+e*cos(TA)))*(coe(TA)*[1;0;0]+sin(TA)*[1;0;0]); vp = (mu/h)*(-sin(TA)*[1;0;0]+e+cos(TA))*[0;1;0]);

R3_W = [cos(RA) sin(RA) 0 -sin(RA) cos(RA) 0 0 1]; R1_i = [1 0 0 0 cos(incl) sin(incl) 0 -sin(incl) cos(incl)]; R3_w = [cos(w) sin(w) 0 -sin(w) cos(w) 0 0 0 1]; Q_pX = R3_W'*R1_i'*R3_w'; r = Q_pX*rp; v = Q_pX*vp; r = r'; v = v'; end

75 function [ coe ] = coe_from_sv( R, V ) %coe_from_sv Returns coe = [h e RA incl w TA a] from R and V % Detailed explanation goes here global mu eps = 1e-10; r = norm(R); v = norm(V); vr = dot(R,V)/r;

H = cross(R,V); h = norm(H); incl = acos(H(3)/h); N = cross([0 0 1],H); n = norm(N); if n ~= 0 RA = acos(N(1)/n); if N(2) < 0 RA = 2*pi-RA; end else RA = 0; end

E = 1/mu*((v^2-mu/r)*R-r*vr*V); e = norm(E); if n ~= 0 if e > eps w = acos(dot(N,E)/n/e); if E(3) < 0

w = 2*pi-w; end else w = 0; end else w = 0; end if e > eps TA = acos(dot(E,R)/e/r); if vr < 0 TA = 2*pi-TA; end else cp = cross(N,R); if cp(3) >= 0 TA = acos(dot(N,R)/n/r); else TA = 2*pi-acos(dot(N,R)/n/r); end end a = h^2/mu/(1-e^2); coe = [h e RA incl w TA a]; end

77 function [ V1, V2, dV ] = lambert( R1, R2, t, dir ) %lambert Summary of this function goes here % R1 = initial position vector % R2 = final position vector % t = time of flight between R1 and R2 % dir = direction, 1 if prograde and -1 if retrograde (default prograde) global mu global r1 r2 A r1 = norm(R1); %Magnitudes of R1 and R2 r2 = norm(R2); c12 = cross(R1,R2); theta = acos(dot(R1,R2)/(r1*r2)); %Angle between R1 and R2 if dir > 0 %Prograde if c12(3) <= 0 theta = 2*pi-theta; end elseif dir < 0 %Retrograde if c12(3) >- 0 theta = 2*pi-theta; end else dir = 1; %Default prograde end

A = sin(theta)*sqrt(r1*r2/(1-cos(theta))); z = -100; while F(z,t) < 0 z = z+0.1; end tol = 1e-10; 78 nmax = 5000; ratio = 1; n = 0; while (abs(ratio) > tol) && (n <= nmax) n = n+1; ratio = F(z,t)/dFdz(z); z = z-ratio; end f = 1-y(z)/r1; g = A*sqrt(y(z)/mu); gdot = 1-y(z)/r2;

V1 = 1/g*(R2-f*R1); V2 = 1/g*(gdot*R2-R1); dV = norm(abs(V1-V2)); %Include delta-V calculations

%Subfunctions function dum = y(z) %global r1 r2 A dum = r1 + r2 + A*(z*S(z)-1)/sqrt(C(z)); end

function dum = F(z,t) %global mu A dum = (y(z)/C(z))^1.5*S(z)+A*sqrt(y(z))-sqrt(mu)*t; end function dum = dFdz(z) %global A if z == 0 dum = sqrt(2)/40*y(0)^1.5+A/8*(sqrt(y(0))+A*sqrt(1/2/y(0))); else dum = (y(z)/C(z))^1.5*(1/2/z*(C(z)-3*S(z)/2/C(z))... +3*S(z)^2/4/C(z))... +A/8*(3*S(z)/C(z)*sqrt(y(z))... +A*sqrt(C(z)/y(z)));

end end function dum = C(z) dum = stumpC(z); end function dum = S(z) dum = stumpS(z); end end

%%networkScript.m clear global mu deg = pi/180; mu = 398600;

%Cull TLE data to select high-mass objects %Read in TLE data %Read in object score data %Convert TLE's to COE's %Store database of COE's

%Repeat until no more targets or dV >= maxdV or score >= minScore %Choose/take initial interceptor orbit %Register time

%Repeat for all potential targets %Convert COE's to SV's (including time) %Find dV's from interceptor to target %Store all dV's %Match object scores and dV's

%Choose bestTarget = max{score/dV for all targets} %Set new interceptor orbit to bestTarget %Set time to TOF of bestTarget %Remove bestTarget from database %Record pertinent data (total dV, total time, total score, etc.)

%Read in TLE data %Put TLE file in the same folder as this file fileName = 'tle.txt'; fileID = fopen(fileName,'r'); List1 = fscanf(fileID,'%24c%*s',1); List2 = fscanf(fileID,'%d%6d%*c%5d%*3c%*2f%f%f%5d%*c%*d%5d%*c%*d%d%5d',[1,9]); 81

List3 = fscanf(fileID,'%d%6d%f%f%f%f%f%f%f',[1,8]); fclose(fileID); %Separate the above and put in its own function epoch = L2(1,4)*24*3600; % Epoch Date and Julian Date Fraction in1 = L3(1,3); % Inclination [deg] RAN1 = L3(1,4); % Right Ascension of the Ascending Node [deg] ecc1 = L3(1,5)/1e7; % Eccentricity AoP1 = L3(1,6); % Argument of periapsis [deg] M = L3(1,7); % Mean anomaly [deg] n = L3(1,8); % Mean motion [Revs per day] a1 = (mu/(n*2*pi/(24*3600))^2)^(1/3); % Semi-major axis [km] p = a1*(1-ecc1^2); angMom1 = sqrt(p*mu);

% Calculate the eccentric anomaly using mean anomaly if M < pi E = M + ecc1/2; else E = M - ecc1/2; end tol = 1e-10; %Error tolerance ratio = 1; while abs(ratio) > tol ratio = (E-e*sin(E)-M)/(1-e*cos(E)); E = M + e*sind(E0); end coe1 = [a e inc RAN w E]; coe1 = [angMom1, ecc1, RAN1, in1, AoP1, tAnom1]; %"sv_from_coe" format coe2 = [angMom2, ecc2, RAN2, in2, AoP2, tAnom2];

%Convert to position vectors 82 sv1 = sv_from_coe(coe1); sv2 = sv_from_coe(coe2); r1 = sv1(1); %Interceptor (begining) position vector r2 = sv2(1); %Target (final) position vector dt = 3600; %Time of flight between r1 and r2 dir = 1; %1 for prograde, -1 for retrograde for k=1:500 for n=1:N lambert end end

[v1,v2] = lambert(r1, r2, dt, dir); dV = norm(abs(v1-v2)); coe1 = coe_from_sv(r1,v1); tAnom1 = coe1(6); coe2 = coe_from_sv(r1,v1); tAnom2 = coe2(6);

Debris Population Data: Format: First Line: Field Column Description 1.1 01 Line Number of Element Data 1.2 03-07 Satellite Number 1.3 08 Classification 1.4 10-11 International Designator (Last two digits of launch year) 1.5 12-14 International Designator (Launch number of the year) 1.6 15-17 International Designator (Piece of the launch) 1.7 19-20 Epoch Year (Last two digits of year) 1.8 21-32 Epoch (Day of the year and fractional portion of the day) 1.9 34-43 First Time Derivative of the Mean Motion 1.10 45-52 Second Time Derivative of Mean Motion (decimal point assumed) 1.11 54-61 BSTAR drag term (decimal point assumed) 1.12 63 Ephemeris type 1.13 65-68 Element number 1.14 69 Checksum (Modulo 10) (Letters, blanks, periods, plus signs = 0; minus signs = 1) Second Line: Field Column Description 2.1 01 Line Number of Element Data 2.2 03-07 Satellite Number 2.3 09-16 Inclination [Degrees] 2.4 18-25 Right Ascension of the Ascending Node [Degrees] 2.5 27-33 Eccentricity (decimal point assumed) 2.6 35-42 Argument of Perigee [Degrees] 2.7 44-51 Mean Anomaly [Degrees] 2.8 53-63 Mean Motion [Revs per day] 2.9 64-68 Revolution number at epoch [Revs] 2.10 69 Checksum (Modulo 10)

1 16389U 85097C 16058.55024580 -.00000018 00000-0 21576-4 0 9990 2 16389 71.0039 12.9750 0187521 145.4358 215.9105 13.75991024523607 1 16390U 85097D 16058.52846644 .00000023 00000-0 62735-4 0 9999 2 16390 70.9722 119.1013 0208843 329.7958 29.1231 13.71972487518913 1 16391U 85097E 16057.90440029 .00000014 00000-0 50704-4 0 9991 2 16391 70.9993 354.0748 0190931 167.5447 251.6216 13.76460428524147 1 16392U 85097F 16056.83987473 +.00000003 +00000-0 +43470-4 0 9992 2 16392 070.9701 042.8798 0203513 248.2334 184.8761 13.74284290520883 1 18410U 87041C 16057.49153147 .00000044 00000-0 81164-4 0 9999 2 18410 70.9885 303.9433 0203796 346.3056 62.5434 13.73292961442368 1 18411U 87041D 16056.93923381 +.00000020 +00000-0 +57546-4 0 9994 2 18411 071.0321 270.9201 0190433 194.1540 276.4590 13.75631923444472 1 18412U 87041E 16058.21178740 .00000016 00000-0 53259-4 0 9991 2 18412 71.0270 254.3477 0195714 216.1629 142.6109 13.76055125445147 1 18416U 87027C 16058.20307997 .00000022 00000-0 57103-4 0 9995 2 18416 71.0326 105.6587 0184309 86.9027 330.5019 13.76768890453963 1 18417U 87027D 16058.55329644 .00000098 00000-0 12975-3 0 9997 2 18417 70.9987 168.9014 0204008 221.8908 229.9403 13.73850986450868 1 18476U 87041F 16058.24132218 .00000057 00000-0 94260-4 0 9996 2 18476 70.9932 337.9698 0208777 339.0744 140.4300 13.72432037441502 1 18527U 87027E 16057.21618021 .00000019 00000-0 57164-4 0 9994 2 18527 70.9952 127.1672 0197111 224.3194 134.1984 13.75032518451957 1 18550U 87027F 16057.37940247 .00000061 00000-0 90444-4 0 9990 2 18550 71.0251 42.7165 0180522 81.2963 280.8541 13.78463918455483 1 19125U 88039C 16058.51232003 .00000017 00000-0 52869-4 0 9994 2 19125 71.0302 220.0239 0181958 307.0314 51.4261 13.78870719397651 1 19126U 88039D 16057.32536064 .00000078 00000-0 10874-3 0 9993 2 19126 71.0330 281.0335 0186318 312.5815 155.7617 13.77105753395849 1 19127U 88039E 16058.45753022 .00000000 00000-0 39927-4 0 9990 2 19127 70.9883 44.8643 0207988 152.0909 9.8629 13.71945786390722 1 19128U 88039F 16057.89172796 .00000008 00000-0 47743-4 0 9994 85

2 19128 70.9838 30.5307 0205824 176.8100 210.3311 13.72132485390953 1 19656U 88102C 16056.92047774 +.00000012 +00000-0 +51496-4 0 9996 2 19656 070.9838 352.3275 0209906 116.1374 246.1485 13.71102258363114 1 19657U 88102D 16057.23366350 .00000030 00000-0 68299-4 0 9995 2 19657 70.9852 340.8819 0209279 82.2915 29.4286 13.71443524363782 1 19658U 88102E 16058.31740921 .00000027 00000-0 64558-4 0 9996 2 19658 71.0226 287.8185 0199266 334.1152 142.1714 13.74271122366780 1 19659U 88102F 16056.90055980 +.00000022 +00000-0 +58609-4 0 9999 2 19659 071.0347 225.6295 0189583 244.2265 232.9873 13.76568528368657 1 20626U 90046C 16056.91099375 +.00000024 +00000-0 +62031-4 0 9998 2 20626 071.0191 007.6185 0205082 086.1925 016.8612 13.72141390289635 1 20627U 90046D 16056.88884258 -.00000042 00000-0 48806-6 0 9994 2 20627 70.9753 22.5888 0214953 190.1875 224.2929 13.70235629288194 1 20628U 90046E 16058.21684938 .00000033 00000-0 70862-4 0 9991 2 20628 70.9803 342.2959 0208453 129.3122 232.6667 13.71697756289635 1 20629U 90046F 16058.21979421 .00000116 00000-0 14818-3 0 9996 2 20629 71.0274 332.8162 0198944 19.3923 136.1423 13.73375399291292 1 22221U 92076C 16058.19236064 -.00000034 00000-0 73144-5 0 9996 2 22221 71.0416 78.8133 0182424 138.1752 290.3991 13.76906371169505 1 22222U 92076D 16057.80713939 .00000012 00000-0 52966-4 0 9998 2 22222 70.9971 234.9979 0217336 342.5718 16.7999 13.69890907163496 1 22223U 92076E 16057.55023522 .00000067 00000-0 99645-4 0 9998 2 22223 71.0361 120.2042 0196232 213.0624 255.6445 13.75296202167971 1 22224U 92076F 16058.49315436 .00000058 00000-0 93528-4 0 9995 2 22224 70.9888 100.9628 0198149 287.4784 70.4747 13.74354850167432 1 22289U 92093D 16057.86443466 .00000045 00000-0 35755-4 0 9994 2 22289 70.8303 234.0010 0061345 357.3806 69.6647 14.31313265209487 1 22290U 92093E 16058.17261840 .00000016 00000-0 54494-4 0 9994 2 22290 71.0492 235.9745 0197782 256.7718 222.8750 13.74553879161528 1 22291U 92093F 16057.47412124 .00000005 00000-0 45977-4 0 9994 2 22291 71.0112 281.5443 0209950 338.9904 87.4495 13.71718440159792 86

1 22292U 92093G 16058.15803008 .00000103 00000-0 14081-3 0 9996 2 22292 71.0081 312.4976 0209441 31.9733 80.6053 13.70310245153551 1 22293U 92093H 16056.91944203 -.00000004 +00000-0 +36215-4 0 9997 2 22293 071.0557 258.1422 0199101 235.4568 122.7601 13.73913042155488 1 22294U 92093J 16057.91041397 -.00000262 00000-0 -11701-3 0 9990 2 22294 71.0593 302.3579 0097941 114.4755 327.7084 14.10123382192718 1 22295U 92093K 16058.43187811 .00000174 00000-0 12897-3 0 9998 2 22295 71.0066 33.6364 0100113 307.3620 216.0204 14.06016111188401 1 22296U 92093L 16058.20473789 .00001360 00000-0 48367-3 0 9995 2 22296 70.8474 329.7032 0073261 126.0960 358.3931 14.34657722194188 1 22297U 92093M 16057.42762957 .00000134 00000-0 10737-3 0 9995 2 22297 70.9477 49.8526 0098094 89.0604 272.1750 14.04793566184887 1 22326U 92093P 16057.13891584 .00000276 00000-0 23165-3 0 9991 2 22326 70.6613 299.1226 0149218 161.6287 355.8230 13.91773773170212 1 22327U 92093Q 16058.23749683 .00001086 00000-0 17039-3 0 9999 2 22327 71.1235 47.0076 0099171 261.5644 192.4250 14.71972638227895 1 22329U 92093S 16057.53217815 .00002710 00000-0 43159-3 0 9997 2 22329 70.9036 10.8655 0078402 346.9484 12.9636 14.70959538225938 1 22330U 92093T 16057.88852433 -.00000019 00000-0 19045-4 0 9997 2 22330 70.4186 325.6360 0116951 240.7890 190.9566 14.05681022185050 1 22331U 92093U 16058.49809179 .00000091 00000-0 83983-4 0 9996 2 22331 70.9247 350.3485 0074653 104.5668 8.2604 14.04424710187031 1 22332U 92093V 16058.36601603 .00009273 00000-0 11870-2 0 9990 2 22332 70.5455 18.6956 0021573 188.9597 331.9936 14.81405981207442 1 22333U 92093W 16057.19273043 .00000052 00000-0 29279-4 0 9994 2 22333 71.0038 82.8556 0126185 95.3362 266.2187 14.42971254217268 1 22335U 92093Y 16057.88872968 .00000245 00000-0 20322-3 0 9996 2 22335 71.1633 210.8490 0114577 130.6844 342.6350 13.94956516175480 1 22336U 92093Z 16056.94997627 +.00000254 +00000-0 +21809-3 0 9994 2 22336 071.1300 237.1046 0121688 217.7101 256.7776 13.92378953173199 1 22337U 92093AA 16056.74093142 .00000000 00000-0 33980-4 0 9995 87

2 22337 71.2887 162.1409 0146728 109.1885 252.5169 13.84104770168904 1 22338U 92093AB 16056.69566942 +.00001045 +00000-0 +21745-3 0 9998 2 22338 070.6209 161.4106 0090147 226.1457 254.8010 14.60272229204495 1 22339U 92093AC 16058.53322352 .00000043 00000-0 32063-4 0 9992 2 22339 70.8110 124.6044 0127852 181.6668 178.4057 14.33849844211015 1 22340U 92093AD 16058.00314646 -.00000032 00000-0 95837-5 0 9991 2 22340 70.8727 243.6199 0099640 54.5864 114.2966 13.94111233178179 1 22341U 92093AE 16057.46709444 .00000104 00000-0 10998-3 0 9997 2 22341 70.7453 270.2828 0137487 321.2146 110.0613 13.91888594173939 1 22342U 92093AF 16057.54731166 .00000093 00000-0 10272-3 0 9995 2 22342 70.6981 203.6991 0120474 15.0337 56.8550 13.92337943174075 1 22343U 92093AG 16057.43422454 .00000411 00000-0 25982-3 0 9999 2 22343 70.9583 40.7066 0094488 62.4933 100.7795 14.07678408186280 1 22344U 92093AH 16057.84557082 -.00000024 00000-0 12402-4 0 9996 2 22344 71.0991 359.2771 0109916 122.5986 238.5801 14.04140987180438 1 22347U 92093AL 16057.96793932 .00001125 00000-0 80989-3 0 9994 2 22347 70.8363 248.6745 0179548 68.5950 82.4056 13.91530525165056 1 22348U 92093AM 16058.26685946 .00000206 00000-0 14537-3 0 9999 2 22348 71.2632 343.9714 0106051 68.2545 95.4613 14.05728073184431 1 22349U 92093AN 16056.79882201 +.00000194 +00000-0 +20075-3 0 9999 2 22349 070.8207 285.2095 0182249 056.1455 019.3928 13.80376862163117 1 22350U 92093AP 16058.22789098 .00000169 00000-0 13075-3 0 9995 2 22350 70.9120 322.9366 0071848 256.1351 274.8254 14.05384573187407 1 22351U 92093AQ 16058.52239963 .00000188 00000-0 14788-3 0 9993 2 22351 70.9079 124.6649 0108867 236.5655 244.1803 14.01438726182370 1 22352U 92093AR 16058.19495755 -.00000052 00000-0 -29638-5 0 9994 2 22352 70.8904 74.0009 0078728 249.8741 178.7596 14.00380154182269 1 22353U 92093AS 16056.94141471 +.00000571 +00000-0 +35175-3 0 9994 2 22353 070.9694 146.8037 0116881 120.0111 351.9430 14.06346321181816 1 22354U 92093AT 16057.55211880 .00000001 00000-0 31709-4 0 9993 2 22354 71.1441 188.6928 0142789 37.2150 36.1425 13.92093195174642 88

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2 22376 70.8924 153.8463 0061700 356.9083 166.3334 14.19267711191174 1 22377U 92093BS 16057.40701140 .00000367 00000-0 24514-3 0 9995 2 22377 71.0961 140.6393 0059266 305.6481 53.9127 14.06710570186034 1 22379U 92093BU 16058.50147327 .00000234 00000-0 16989-3 0 9990 2 22379 70.7079 317.8472 0092954 193.0390 166.8322 14.04688398181314 1 22381U 92093BW 16056.92448191 +.00005640 +00000-0 +10563-2 0 9997 2 22381 070.5442 152.1738 0035727 282.8744 076.8411 14.64861879201583 1 22382U 92093BX 16058.47516247 .00000342 00000-0 29611-3 0 9997 2 22382 70.8656 189.5134 0168382 260.4548 215.4626 13.87158879167422 1 22387U 92093CC 16058.13811109 .00000372 00000-0 26027-3 0 9991 2 22387 70.8923 170.3666 0115202 306.8518 118.1161 14.01789654179319 1 22388U 92093CD 16058.23468668 .00000215 00000-0 14534-3 0 9997 2 22388 70.9549 141.9931 0109274 152.0722 240.4507 14.08231704181865 1 22390U 92093CF 16057.19521978 .00000083 00000-0 80872-4 0 9990 2 22390 71.1769 341.8550 0079561 287.9654 71.2803 14.02886475145482 1 22392U 92093CH 16058.51774078 .00000773 00000-0 13079-3 0 9990 2 22392 70.8919 180.5432 0104900 76.7424 0.7360 14.69403770229999 1 22393U 92093CJ 16058.38151543 .00000403 00000-0 27066-3 0 9993 2 22393 71.1248 21.8508 0125871 313.5016 213.1574 14.02736126179968 1 22394U 92093CK 16057.46381271 .00000218 00000-0 15742-3 0 9997 2 22394 71.2794 51.8778 0078037 119.2274 241.6679 14.05205122182108 1 22395U 92093CL 16056.95104914 +.00001493 +00000-0 +67567-3 0 9996 2 22395 071.1496 247.3598 0089804 241.3178 228.5256 14.21479972183383 1 22396U 92093CM 16057.21689625 .00005951 00000-0 10053-2 0 9994 2 22396 70.6557 15.5586 0017971 301.9970 173.5295 14.69724097208469 1 22397U 92093CN 16057.11503957 .00000584 00000-0 28378-3 0 9994 2 22397 70.8053 310.9941 0037588 122.5742 357.8763 14.22166233193887 1 22398U 92093CP 16057.44442461 .00000260 00000-0 18389-3 0 9995 2 22398 70.9547 172.9332 0115373 173.7905 186.4675 14.03601065180638 1 22400U 92093CR 16058.21479450 .00000100 00000-0 11002-3 0 9991 2 22400 71.2384 82.8857 0157258 131.2266 310.3637 13.86920843171299 90

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1 36030U 96051M 16045.18941717 +.00014981 +00000-0 +31674-2 0 9993 2 36030 070.8527 234.9915 0027961 122.8167 239.9260 14.59126634030687 1 36031U 96051N 16056.67580734 +.00004882 +00000-0 +16229-2 0 9996 2 36031 070.8554 269.9351 0016955 137.4991 291.5811 14.38096234330473 1 39300U 92093JR 16057.75326544 .00000106 00000-0 10583-3 0 9990 2 39300 71.1214 101.5082 0104702 152.6132 208.0555 13.95329068665877 1 39301U 92093JS 16029.19245728 .00000111 00000-0 88887-4 0 9991 2 39301 70.8743 220.8314 0034160 179.3639 180.7530 14.10444817690675 1 39302U 92093JT 16048.23680939 .00002036 00000-0 10820-2 0 9993 2 39302 70.9642 359.8170 0162383 270.1836 154.3948 14.08179043573792 1 39303U 92093JU 16055.93953107 +.00000575 +00000-0 +33858-3 0 9992 2 39303 070.9170 255.3724 0062125 037.5183 323.0248 14.11294523120664 1 39304U 92093JV 16057.77728161 .00000188 00000-0 15173-3 0 9997 2 39304 71.2056 77.1139 0093764 312.5134 169.6952 14.00230587707336 1 39305U 92093JW 16057.03545204 .00000103 00000-0 96821-4 0 9999 2 39305 70.9621 181.9717 0093581 176.8330 297.1026 14.00540104730898 1 39707U 92093JX 16046.78271951 .00001923 00000-0 96641-3 0 9990 2 39707 71.1146 186.1568 0109832 221.2896 137.9886 14.14627862110371 1 39708U 92093JY 16056.21913373 .00000997 00000-0 16085-3 0 9995 2 39708 71.2864 249.0620 0085161 42.5519 72.4212 14.71689746690193 1 39709U 92093JZ 16055.06624706 .00000055 00000-0 72480-4 0 9994 2 39709 71.1473 303.4581 0148603 251.8445 106.6438 13.91098477593136 1 39710U 92093KA 16012.60300703 .00000784 00000-0 47952-3 0 9991 2 39710 71.2114 90.3536 0082591 282.0585 77.0343 14.07238754603801 1 39711U 92093KB 16056.57990895 .00000195 00000-0 15808-3 0 9994 2 39711 70.8403 130.3064 0094252 32.5127 328.1743 13.99951614657389 1 39712U 92093KC 15340.45448443 .00000655 00000-0 41471-3 0 9990 2 39712 71.1136 145.1025 0096011 182.0884 177.9848 14.05355868575623 1 39713U 92093KD 16046.41779308 .00000856 00000-0 52097-3 0 9997 2 39713 71.1181 321.5791 0088330 44.0707 316.7408 14.07024901573705 1 39714U 92093KE 16055.38388855 +.00000249 +00000-0 +12866-3 0 9993 103

2 39714 071.0842 079.3598 0099602 238.0191 121.1226 14.21656418096502 1 39715U 92093KF 16056.41026831 .00000370 00000-0 17436-3 0 9995 2 39715 71.0151 313.7945 0004704 182.2527 288.9827 14.26368869117844 1 39716U 92093KG 16002.75106135 .00000645 00000-0 41783-3 0 9997 2 39716 71.1373 142.2522 0104725 131.6275 235.7635 14.03716369588419 1 39717U 92093KH 16055.64762860 .00000284 00000-0 21826-3 0 9992 2 39717 70.6904 54.6406 0107245 293.5673 65.4203 13.99186129606915 1 39718U 92093KJ 16056.57494807 +.00001210 +00000-0 +44013-3 0 9992 2 39718 071.1956 115.0226 0036169 124.1259 236.3315 14.34774761097176 1 39719U 92093KK 16057.14142539 .00000007 00000-0 35604-4 0 9999 2 39719 71.2954 225.3084 0099422 211.9686 268.3192 13.95498292115259 1 39720U 92093KL 16054.77303697 .00000767 00000-0 24086-3 0 9995 2 39720 70.7900 103.0778 0032106 334.7438 25.2126 14.43486088118628 1 39721U 92093KM 16057.11948026 .00000130 00000-0 12307-3 0 9995 2 39721 71.1891 229.6807 0127479 60.6976 300.6805 13.93753343653253 1 39722U 92093KN 16057.07568436 .00000174 00000-0 14577-3 0 9993 2 39722 70.8936 208.3250 0106926 18.8044 96.7967 13.98878808115390 1 39723U 92093KP 16039.61707354 .00001210 00000-0 60906-3 0 9997 2 39723 71.0988 136.0150 0064334 268.4706 158.4249 14.17339754550533 1 39724U 92093KQ 16051.91710221 +.00000199 +00000-0 +16126-3 0 9992 2 39724 070.8522 142.5277 0088814 044.5008 316.3194 14.00125882094280 1 39725U 92093KR 16054.26174182 +.00000326 +00000-0 +20863-3 0 9999 2 39725 071.1781 356.6058 0095929 300.9489 058.2229 14.08277171095407 1 39726U 92093KS 16056.54113993 .00000027 00000-0 53681-4 0 9999 2 39726 71.1549 253.3072 0123266 188.2800 203.2083 13.90386061114736 1 39841U 92093KT 16055.57977061 .00005068 00000-0 66568-3 0 9990 2 39841 70.7579 15.9785 0051134 291.0694 180.9178 14.79863519121700 1 39842U 92093KU 16057.00597518 .00006377 00000-0 11474-2 0 9995 2 39842 70.9617 291.0967 0048201 138.2287 222.2559 14.66220771677607 1 39843U 92093KV 16056.55971140 .00003255 00000-0 75782-3 0 9997 2 39843 70.9260 129.2244 0047957 339.3764 20.5441 14.54926760677970 104

1 39844U 92093KW 16056.91379393 +.00001416 +00000-0 +56943-3 0 9995 2 39844 070.6572 150.8145 0049240 284.3469 075.2195 14.29266748090474 1 39845U 92093KX 16036.52629095 .00000831 00000-0 51828-3 0 9995 2 39845 70.9822 350.1102 0140465 227.0848 131.8412 14.02999043625882 1 39846U 92093KY 16047.83494641 .00003013 00000-0 12594-2 0 9990 2 39846 71.2717 110.6695 0102133 124.9174 237.6943 14.24068307592783 1 39847U 92093KZ 16053.02274460 +.00000818 +00000-0 +31196-3 0 9994 2 39847 071.0343 290.0584 0066785 231.7962 127.7145 14.32538443090824 1 39848U 92093LA 16020.84252350 .00002235 00000-0 81567-3 0 9995 2 39848 71.2341 87.6719 0062924 293.7742 65.4034 14.32994062620041 1 39849U 92093LB 16054.75315200 +.00000351 +00000-0 +25078-3 0 9999 2 39849 070.8661 110.1579 0089120 352.5057 007.4719 14.02310116088669 1 39850U 92093LC 16033.93936115 +.00000378 +00000-0 +26362-3 0 9998 2 39850 071.3276 247.0286 0097471 149.8255 210.6874 14.02242005035673 1 39851U 92093LD 16055.82492469 +.00004059 +00000-0 +17210-2 0 9991 2 39851 071.0943 228.1180 0144891 211.2609 147.9844 14.20443422059773 1 39852U 92093LE 16057.97474918 .00000941 00000-0 31741-3 0 9991 2 39852 71.0104 163.4151 0007351 260.5266 215.3263 14.39535322675069 1 39853U 92093LF 16055.95775282 +.00001316 +00000-0 +18795-3 0 9997 2 39853 071.2824 177.6772 0078705 009.7523 350.5138 14.76673381092826 1 39854U 92093LG 15338.59836456 .00000809 00000-0 46708-3 0 9993 2 39854 71.0235 315.1975 0086263 242.0969 117.6057 14.10219822379003 1 39855U 92093LH 16057.07532072 .00004138 00000-0 14511-2 0 9998 2 39855 70.5284 201.6619 0108443 118.1755 243.0379 14.32371518117935 1 39856U 92093LJ 16016.01238088 .00004500 00000-0 10743-2 0 9994 2 39856 70.8234 147.5236 0039784 223.5475 136.3326 14.53739876571914 1 39857U 92093LK 16048.97168030 .00001069 00000-0 55303-3 0 9993 2 39857 70.9205 255.8356 0066655 181.6321 178.4596 14.16131941392118 1 39858U 92093LL 16057.18308019 .00002220 00000-0 62088-3 0 9998 2 39858 70.9485 240.6081 0051656 44.4776 76.2541 14.46484931576618 1 39859U 92093LM 14033.27483023 .00031030 00000-0 30630-2 0 9998 105

2 39859 70.9775 258.9871 0005248 223.2139 124.1973 14.91829478141682 1 39860U 92093LN 16053.80175158 +.00000610 +00000-0 +28507-3 0 9991 2 39860 070.7855 224.4209 0033845 210.8902 149.0234 14.24160541089264 1 39861U 92093LP 15349.74067240 .01363887 34461-5 91531-3 0 9993 2 39861 71.1859 108.1233 0016769 32.8910 326.9037 16.16333301733066 1 39862U 92093LQ 16054.26541008 .00000703 00000-0 17799-3 0 9999 2 39862 70.8352 270.7985 0088393 322.3103 37.1864 14.52411616560380 1 39863U 92093LR 16056.14481699 +.00001586 +00000-0 +93212-3 0 9992 2 39863 070.9854 231.6543 0162608 071.1579 290.7093 14.03126408088130 1 39864U 92093LS 16058.16819909 .00000060 00000-0 58584-4 0 9996 2 39864 71.1506 359.5629 0129967 245.8838 112.8644 14.07134194116247 1 39865U 92093LT 16052.96370665 +.00000535 +00000-0 +22731-3 0 9991 2 39865 071.0152 273.2927 0002496 130.1897 229.9452 14.29830015089655 1 39866U 92093LU 16057.59865580 .00002115 00000-0 88711-3 0 9997 2 39866 71.2900 114.5072 0096623 134.1981 16.3690 14.24515073117417 1 39867U 92093LV 16053.55104711 .00001180 00000-0 75871-3 0 9996 2 39867 70.9799 11.3783 0183811 198.2894 161.1554 13.97194591586407 1 39868U 93016AS 16033.92250790 +.00003165 +00000-0 +16163-2 0 9994 2 39868 070.9804 130.5512 0155323 250.8669 107.5581 14.10347931065535 1 39869U 93016AT 15134.45870045 .00010423 00000-0 47755-2 0 9991 2 39869 070.9889 171.8267 0125577 181.2004 182.4067 14.17407808562879 1 39870U 93016AU 15035.72429495 .00008590 00000-0 41820-2 0 9991 2 39870 070.9583 059.3213 0138754 005.1571 355.2269 14.13472594606522 1 39871U 93016AV 16057.35519942 .00002485 00000-0 28375-3 0 9991 2 39871 71.0324 47.1704 0073522 246.4395 183.4512 14.85281205694461 1 39872U 93016AW 16057.47214272 .00000583 00000-0 44038-3 0 9994 2 39872 70.9908 87.7045 0150136 212.2464 217.0565 13.93018245682459 1 39873U 93016AX 16055.32019144 .00001665 00000-0 79397-3 0 9996 2 39873 70.4135 175.7072 0113051 178.9097 181.2293 14.17527991116621 1 39874U 93016AY 16057.09420316 .00003213 00000-0 13261-2 0 9998 2 39874 70.9438 204.5191 0112282 69.4460 50.9163 14.24136592690311 106

1 39875U 93016AZ 14200.05863342 .00003955 00000-0 20426-2 0 9997 2 39875 070.9598 097.1391 0139072 304.2127 044.7489 14.10752638505837 1 39876U 93016BA 16056.04538725 .00003047 00000-0 13517-2 0 9997 2 39876 70.9705 287.2218 0127601 120.2569 241.1259 14.19546689116998 1 39877U 93016BB 16008.09264017 +.00002654 +00000-0 +13573-2 0 9995 2 39877 070.9716 168.3156 0149263 287.7011 070.7862 14.10863260084459 1 39878U 93016BC 16043.54647091 .00003932 00000-0 19894-2 0 9994 2 39878 70.9715 100.4077 0153449 240.9879 117.5791 14.10808179115029 1 39879U 93016BD 16058.40562679 .00002901 00000-0 13438-2 0 9997 2 39879 70.9875 317.4183 0129686 133.2134 341.8583 14.17237104622248 1 39880U 93016BE 11289.65973219 +.00003131 +00000-0 +18801-2 0 9998 2 39880 070.9948 036.9454 0155602 357.7717 002.2796 14.01784744371821 1 39881U 93016BF 16037.76724876 .00000913 00000-0 63359-3 0 9994 2 39881 70.9848 74.1234 0137404 198.0914 161.3354 13.97080176567563 1 39882U 93016BG 16057.27099801 .00002983 00000-0 13183-2 0 9994 2 39882 70.9533 280.0213 0125072 123.8976 354.0972 14.19921308662369 1 39883U 93016BH 16005.74396603 .00002825 00000-0 13653-2 0 9997 2 39883 70.9875 149.7193 0145568 277.2996 81.1600 14.14012854652205 1 39884U 93016BJ 15152.44744583 .00006930 00000-0 33612-2 0 9999 2 39884 070.9594 181.9465 0129983 198.2583 173.7449 14.14330569537343 1 39885U 93016BK 16058.29142609 .00004481 00000-0 15578-2 0 9990 2 39885 70.9575 45.7454 0097048 306.1920 53.0265 14.33368800 98336 1 39886U 93016BL 16057.05552198 .00000897 00000-0 20544-3 0 9999 2 39886 71.0151 197.1506 0067468 279.2410 80.1109 14.57149009675148 1 39887U 93016BM 16055.41291285 +.00002568 +00000-0 +12775-2 0 9998 2 39887 070.9781 079.6799 0153342 217.4870 141.5482 14.12016493088814 1 39888U 93016BN 16057.59332679 .00001779 00000-0 92031-3 0 9990 2 39888 70.9654 155.2788 0113060 2.5055 357.6608 14.13056740599800 1 39889U 93016BP 16057.14589876 .00008227 00000-0 19999-2 0 9991 2 39889 70.9267 233.4423 0076952 216.5571 143.0305 14.51280734649782 1 39890U 93016BQ 16041.22289105 .00003614 00000-0 16334-2 0 9992 107

2 39890 70.9722 337.0496 0126862 141.7872 219.2330 14.18509161606463 1 39891U 93016BR 16057.46956901 .00000583 00000-0 23567-3 0 9990 2 39891 70.9998 113.1845 0012315 325.3938 34.6391 14.31937754672108 1 39892U 93016BS 16057.16060099 .00003148 00000-0 12944-2 0 9998 2 39892 70.9846 251.2046 0121601 88.3413 273.1638 14.23760339661916 1 39893U 93016BT 16043.16787398 .00003730 00000-0 17281-2 0 9998 2 39893 70.9724 332.3575 0123984 149.8455 210.9883 14.17401675611324 1 39894U 93016BU 11335.45449335 +.00009964 +00000-0 +55481-2 0 9995 2 39894 070.9726 256.6829 0149417 275.2835 083.0040 14.05657808395930 1 39895U 93016BV 15283.13595160 .00000133 00000-0 12757-3 0 9994 2 39895 70.9819 205.7899 0126294 283.8684 75.4904 13.93509484550323 1 39896U 93016BW 16057.25043088 .00003258 00000-0 13537-2 0 9992 2 39896 70.9682 270.5182 0123932 108.0986 253.3685 14.23063281647724 1 39897U 93016BX 15112.09879868 .00010898 00000-0 51019-2 0 9994 2 39897 070.9542 272.1935 0131187 272.0011 086.6093 14.15930607263704 1 39898U 93016BY 15190.55889597 .00013487 00000-0 29951-2 0 9999 2 39898 070.9596 252.3989 0060115 083.3430 274.7532 14.56010293573834 1 39899U 93016BZ 16056.94195350 .00002614 00000-0 56009-3 0 9997 2 39899 70.9881 155.0470 0004993 134.3010 225.8546 14.59651640626223 1 39900U 93016CA 16046.42635397 .00006224 00000-0 21017-2 0 9993 2 39900 70.9424 77.1738 0089091 343.8969 15.9334 14.35045697666671 1 39901U 93016CB 16056.81795314 .00002216 00000-0 11668-2 0 9992 2 39901 70.9746 120.1429 0160879 251.6209 106.7826 14.07517597510307 1 39902U 93016CC 16058.09233941 -.00000029 00000-0 12230-4 0 9997 2 39902 71.0009 91.0211 0189708 102.2704 291.2419 13.73388898685594 1 39903U 93016CD 16039.98479317 .00000180 00000-0 18111-3 0 9994 2 39903 70.9908 149.1629 0140023 268.6796 207.7456 13.85908539646092 1 39904U 93016CE 11236.01535596 +.00001754 +00000-0 +10234-2 0 9990 2 39904 070.9923 106.8642 0149202 063.1256 299.9771 14.04383882447847 1 39905U 93016CF 16056.92435453 +.00002683 +00000-0 +12902-2 0 9993 2 39905 070.9586 243.2104 0133827 132.8246 299.3802 14.15098398089030 108

1 39906U 93016CG 16056.39839764 +.00002471 +00000-0 +11762-2 0 9996 2 39906 070.9797 325.0844 0133761 142.9010 218.1453 14.15702332088987 1 39907U 93016CH 16056.50064905 +.00000178 +00000-0 +17636-3 0 9996 2 39907 070.9935 101.2102 0135637 235.8016 123.0176 13.87274124089365 1 39908U 93016CJ 16057.83985218 .00000296 00000-0 15454-3 0 9990 2 39908 71.0023 240.1791 0007975 57.3248 3.1283 14.22380914647867 1 39909U 93016CK 11060.90795980 +.00007315 +00000-0 +29176-2 0 9997 2 39909 071.0507 151.1547 0007146 327.4594 039.4449 14.28788563135046 1 39910U 93016CL 16058.29049722 .00008577 00000-0 18453-2 0 9996 2 39910 70.9874 291.1487 0023366 149.4241 210.8272 14.58572008105408 1 39911U 93016CM 16057.87403161 .00000073 00000-0 10999-3 0 9992 2 39911 70.9997 136.8890 0199359 147.1512 214.2167 13.71933273638995

109

Weight Calculations: Political Performance Risk Viability TRL Performance 1.00 2.00 5.00 4.00 Risk 0.50 1.00 1.00 2.00 Political Viability 0.20 1.00 1.00 0.25 TRL 0.25 0.50 4.00 1.00 Total 1.95 4.50 11.00 7.25

Political Consistency Performance Risk Viability TRL Average Measure Performance 0.51 0.44 0.45 0.55 0.47 3.27903137 Risk 0.26 0.22 0.09 0.28 0.19 2.969304229 Political Viability 0.10 0.22 0.09 0.03 0.14 3.049345794 TRL 0.13 0.11 0.36 0.14 0.20 3.815399485 Total 0.87 0.89 0.64 0.86 CI: -0.240576593 RI (n=4): 0.9 Ratio: -0.267307326

Object Scores Delta-V Cost Object Scores 1 6 Delta-V Cost 0.166666667 1 Total 1.166666667 7

Object Consistency Scores Delta-V Cost Average Measure Object Scores 0.857142857 0.857142857 0.857142857 2 Delta-V Cost 0.142857143 0.142857143 0.142857143 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

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Safety Reliability Safety 1 4 Reliability 0.25 1 Total 1.25 5

Consistency Safety Reliability Average Measure Safety 0.8 0.8 0.8 2 Reliability 0.2 0.2 0.2 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

Debris Accidents Control Landing Accidents 1 3 5 Debris Control 0.333333333 1 6 Landing 0.2 0.166666667 1 Total 1.533333333 4.166666667 12

Debris Consistency Accidents Control Landing Average Measure Accidents 0.652173913 0.72 0.416666667 0.596280193 3.314915337 Debris Control 0.217391304 0.24 0.5 0.319130435 3.213190029 Landing 0.130434783 0.04 0.083333333 0.084589372 3.038606511 Total 1 1 1 CI: 0.094451979 RI (n=3): 0.58 Ratio: 0.16284824

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De- Approach Maneuver Grapple tumble De-orbit Approac 0.333333 0.166666 h 1 0.25 333 3 667 Maneuv 0.333333 er 4 1 333 4 0.25 0.333333 Grapple 3 3 1 4 333 De- 0.333333 tumble 333 0.25 0.25 1 0.25 De-orbit 6 4 3 4 1 14.33333 4.916666 Total 333 8.5 667 16 2

De- Consistency Approach Maneuver Grapple tumble De-orbit Average Measure Approac 0.069767 0.029411 0.067796 0.083333 0.087561 h 442 765 61 0.1875 333 83 5.22996458 Maneuv 0.279069 0.117647 0.067796 0.167902 er 767 059 61 0.25 0.125 687 5.611882516 0.209302 0.352941 0.203389 0.166666 Grapple 326 176 831 0.25 667 0.23646 5.859862444 De- 0.023255 0.029411 0.050847 0.058203 tumble 814 765 458 0.0625 0.125 007 5.170679125 0.418604 0.470588 0.610169 0.449872 De-orbit 651 235 492 0.25 0.5 476 5.755066989 Total 1 1 1 1 1 CI: 0.131372783 RI (n=5): 1.12 Ratio: 0.117297127

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Agreeability Verifiability Agreeability 1 6 Verifiability 0.166666667 1 Total 1.166666667 7

Consistency Agreeability Verifiability Average Measure Agreeability 0.857142857 0.857142857 0.857142857 2 Verifiability 0.142857143 0.142857143 0.142857143 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

Legal Weaponization Framework Weaponization 1 0.5 Legal Framework 2 1 Total 3 1.5

Legal Consistency Weaponization Framework Average Measure Weaponization 0.333333333 0.333333333 0.333333333 2 Legal Framework 0.666666667 0.666666667 0.666666667 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

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Type of Nationality Cooperation Nationality 1 0.333333333 Type of Cooperation 3 1 Total 4 1.333333333

Type of Consistency Nationality Cooperation Average Measure Nationality 0.25 0.25 0.25 2 Type of Cooperation 0.75 0.75 0.75 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

Initiative Objects Initiative 1 0.25 Objects 4 1 Total 5 1.25

Consistency Initiative Objects Average Measure Initiative 0.2 0.2 0.2 2 Objects 0.8 0.8 0.8 2 Total 1 1 CI: 0 RI (n=2): 0 Ratio: N/A

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