An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30, pp. Pk_137-Pk_146, 2016

By Michael C. F. BAZZOCCHI1) and M. Reza EMAMI1,2)

1) Institute for Aerospace Studies, University of Toronto, Toronto, Canada 2) Space Technology Division, Luleå University of Technology, Kiruna, Sweden

(Received July 30th, 2015)

In this paper, asteroid redirection methods are systematically compared and analyzed to assess their viability for a near-Earth asteroid mission. The intent is to examine the benefits of spacecraft formation for redirecting a near-Earth asteroid to an orbit in the Earth-Moon system in order to exploit asteroid resources. The primary methods of asteroid redirection will be studied in terms of the characteristics of asteroid population, and they will be compared within a resource exploitation framework and with respect to free-flying and landed spacecraft formation strategies. Such methods are investigated based on the major criteria for mission design, and a detailed assessment of each method is discussed. In addition, the uncertainty intrinsic to asteroid characterization is quantified through the use of a Monte Carlo analysis, which provides insight into the robustness of various formation strategies for the targeted population of near-Earth asteroids A comparative analysis of mission parameters for each redirection method will be completed both with and without its associated spacecraft formation strategy in order to demonstrate the potential benefits of spacecraft formation.

Key Words: Asteroid Redirection, Spacecraft Formation, Near-Earth Asteroids, Asteroid Resource Exploitation

Nomenclature : relative importance value Tast : asteroid period of rotation �̃ agt : acceleration due to gravity tractor Tsub : temperature of sublimation C : risk consequence value T0 : initial temperature Cv : coefficient of variation ti : time (refer to subscript for further detail) ci : specific heat Δt : timeframe for redirection d : asteroid-spacecraft distance ve : ejection velocity dast : asteroid diameter vrot : rotational velocity of the asteroid E : expected percentage of objectives achieved : utility value Esub : enthalpy of sublimation v̄ : average velocity of ejecta plume �� : spacecraft formation factor : overall weighted utility value Fi : force (refer to subscript for further detail) ΔV : delta-v �� G : gravitational constant �δv : finite delta-v g : gravity at sea-level : overall criterion weight H : absolute magnitude y : distance �� Isp : specific impulse α : inverse specific power ka : thermal conductivity λ : scatter factor L : risk likelihood value μΔV : average delta-v Mr : mass-loss ratio η : thruster efficiency mast : asteroid mass ρast : asteroid density mi : mass (refer to subscript for further detail) φ : half the angle of the exhaust cone Δm : change in mass σΔV : standard deviation of delta-v ṁ : mass flow rate N : number of spacecraft 1. Introduction : normalized index Asteroid manipulation is currently one of the forefront PI : absorbed power topics of space exploration. Both the private and public �� PT : estimated likelihood of not meeting sectors have a vested interest in exploring the best methods for performance requirements manipulating asteroids, and as a result this provides great incentives for such research. In particular, there are two Qrad : heat loss due to radiation research areas that receive the most attention, i.e., asteroid Qcond : heat loss due to conduction deflection for planetary protection, and asteroid redirection for Ri : specific risk event resource exploitation. This paper focuses on the latter in order r : asteroid radius

Pk_137 Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016)

to explore the potential benefits that near-Earth asteroids tractor, and laser sublimation, require prolonged hovering (NEAs) present for economic profit and in situ resource about the asteroid in order to impart significant delta-v. exploitation. To provide greater insight into the viability of the Moreover, these methods benefit from maintaining a hover leading asteroid redirection methods, a systematic assessment distance that targets the asteroid from one particular direction. is discussed in this paper with consideration of the potential As such, a halo orbit formation has been selected as an benefits obtained from spacecraft formation approaches. approach that will maximize operation time for each method; The perspective of asteroid redirection for resource as seen in Fig. 1. In addition to the singular configurations of exploitation provides considerable constraints on the each redirection method, scenarios with 3 and 5 spacecraft in assessment. In particular, there will be limitations on the target halo orbits are investigated. The following equations of asteroids, the spacecraft systems employed, and the mission motion describe a simplified ideal circular halo orbit about an specifications. The asteroid redirection timeframe will be asteroid, where the orbital motion of the asteroid is restricted to a four-year period from rendezvous with the neglected:5) asteroid to capture in the Earth-Moon system in order to provide a reasonable return on investment.1) Moreover, the (1) target asteroids will be near-Earth asteroids with a certain ݔ௜ ܶ௜ range of diameter. This diameter range is bounded to more ௜ ௔௦௧ ଷ ௜ ൅ ௜ ݉ܩݔሷ ൎ െ than 20m for economic viability and less than 150m to ensure ݎ ݉ 2) (2) planetary protection. An NEA is considered a potentially ௜ ௜ ݕଷ ௜ ܯܩ hazardous object (PHO) if its minimum orbital intersection ݕሷ ൎ െ distance is less than 0.05AU and its diameter is approximately ݎ (3) greater than 150m.2) As such, to redirect larger asteroids could ݖ௜ ௜ ଷ݉ܩ result in a planetary defense risk as well as considerable ݖሷ௜ ൎ െ ݎ௜ political challenges. In addition, the two asteroid types most where is the gravitational constant, is the mass of suitable for resource exploitation are carbonaceous (C-Type) the asteroid, is the spacecraft thrust, ௔௦௧ is the mass of and metallic (M-Type) asteroids. The carbonaceous asteroids ܩ ݉ the spacecraft, and௜ the radial term can be represented௜ by are targeted due to their high concentrations of volatile ܶ ݉ ௜ materials that can be used for the development of propellants ݎ (4) and life support systems, whereas the metallic type asteroids ଷ ଶ ଶ ଶ ௜ ௜ ௜ ௜ toൌ noteඥݔ that൅ݕ while൅ݖ this assessment utilizes a ݎcontain high concentrations of rare-Earth metals, platinum It is important group metals, and other materials useful for in situ halo orbit about the target asteroids, in practice this can be construction of space structures. difficult to achieve. This simulation focuses on the benefits of The spacecraft systems will be limited with respect to mass, an ideal formation without accounting for the affects of solar volume, and technology readiness level (TRL). To ensure radiation pressure on the spacecraft orbits. It has been shown economic viability and a baseline for comparison between that solar radiation pressure is a significant perturbation for single and multiple spacecraft approaches, the mass and small asteroids where the gravitational acceleration is low.6) volume of the system will be restricted to the payload However, for the purpose of this assessment, and to ensure capabilities of an Atlas V launch vehicle. As such, each spacecraft system must have a combined payload less than similar depth of formation investigation for flying and landed 6800kg as well as a stowed configuration less than a payload configurations, a simplified halo orbit model in line with the envelope of 4.572m in diameter and 12.192m in length.3) previous works in the literature has been adopted. 5,7) Lastly, the TRL for each redirection method must be greater than 2, i.e., “Technology concept and/or application formulated”.4) As such, the following redirection methods have been selected as proper candidates for a resource exploitation mission: tugboat, mass ejector, gravity tractor, ion beam, and laser sublimation, as they will be explained in Section 3. Sections 2 to 5 outline the spacecraft formation approaches, the primary redirection methods, the mission assessment criteria, as well as the selected multi-criteria decision making process, respectively. Section 6 provides results and a detailed discussion on the viability of various redirection methods and formation approaches. Some concluding remarks are made in Section 7.

2. Spacecraft Formation Strategies

2.1. Free-flying formation Fig. 1. An example of three spacecraft in a halo orbit. Three of the redirection methods, i.e., ion beam, gravity

2 Pk_138 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

thruster can be calculated using Eq. (5) and the delta-v can be found from Eq. (6). 10)

(5) �� 2� � (6) �� where is the force of � the � thrusters, is the mass of

the tugboat�� system, is the structural�� mass, is the timeframe� for redirection, is the inverse� specific power, �� is the ejection velocity of the thruster, is the thruster� efficiency, is the density� of the asteroid, and is the� � Fig. 2. An example of several landers on the asteroid equator. asteroid diameter. The structural mass of the system includes �� the mass of the lander, which will be scaled based on the 2.2. Landed configuration number and size of the spacecraft in the system. The structural The landed redirection methods, i.e., tugboat and mass mass for the 1, 3 and 5 spacecraft models are 450kg, 750kg, ejector, are particularly disadvantaged by the rotation rate of and 1050kg, respectively. The remaining mass is attributed to the asteroid. Each method’s redirection capability is limited by fuel and power plant. The lander uses the Philae lander as a a certain range of thrust angles and rotation periods that allow reference design.11) The volume of the spacecraft is estimated it to align its thrust vector with the direction of redirection. from the combined lander stowed volume and compressed This thrusting time period can be increased by placing a series propellant volume; assuming an optimally compressed liquid of equidistant spacecraft equatorially along the asteroid xenon fuel.12) surface; such that they are placed in a plane perpendicular to 3.2. Mass ejector the spin vector of the asteroid. 8) This approach will increase The mass ejector redirection method utilizes the available the total time that the system of spacecraft is able to provide a asteroid mass as a projectile to induce a delta-v on the main thrust on the asteroid. As in the free-flying case, this landed asteroid body. This concept employs one or more mass ejector configuration will be assessed with respect to the utilization of spacecraft landing on the surface of the asteroid equatorially, 1, 3 and 5 spacecraft. drilling into the asteroid surface and launching asteroid mass to generate a thrust. Mass ejector spacecraft are comprised 3. Redirection Methods primarily of a rail gun for launching asteroid mass and an extraction device. In this particular model, the Modular The redirection methods considered in this analysis were Asteroid Deflection Mission Ejector Node or ‘MADMEN’ selected due to their suitability for an asteroid redirection concept will provide a baseline for the key attributes.13) The mission, i.e., tugboat, mass ejector, gravity tractor, ion beam, total mass of each multiple spacecraft scenario will be and laser sublimation. They will be discussed in more detail in maximized in order to allocate the greatest amount of mass to the subsequent sections. the power systems, which comprise approximately 30% of the dry mass for each spacecraft. 13) In each case, the rail gun size, 3.1. Tugboat volume, and power requirements will be scaled according to The tugboat method induces redirection through one or the reduced spacecraft mass for each scenario. The rail gun more landed spacecraft using thrusters to ‘push’ the asteroid. will still have a deployable length up to 15m for each case, i.e., The leading single spacecraft configuration requires that the 1, 3, and 5 spacecraft configurations; however, the base spacecraft land on the spin axis of the asteroid then alter the Table 1. Tugboat specifications. spin axis such that it aligns with the redirection thrust vector. 1 Spacecraft 3 Spacecraft 5 Spacecraft While this method is fairly inefficient, it can be easily System Mass 6800kg 6800kg 6800kg remedied through a spacecraft formation approach that lands System Volume 8.5m3 11.5 m3 14.5 m3 multiple spacecraft equatorially. Multiple spacecraft on the Average Power 5000W 15000W 25000W equator with thrusters on a gimbal system will allow the TRL 4-6 4-6 4-6 method to provide continuous thrust on the asteroid in the

appropriate direction. A single spacecraft on the equator could still provide thrust to the asteroid within a rotational window; Table 2. Mass ejector specifications. however, this would considerably reduce the delta-v imparted 1 Spacecraft 3 Spacecraft 5 Spacecraft to the asteroid. In this particular model, RIT-XT thrusters will System Mass 6800kg 6800kg 6800kg 3 3 3 be considered which have a nominal power of 5000W, System Volume 120m 215m 190m nominal specific impulse of 4500s, 60% thruster efficiency Average Power 20000W 30000W 40000W and inverse specific power of 10kg/kW.9) The force of the TRL 3 3 3

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diameters will vary at 4.5m, 3.5m, and 2.5m for each case and Table 3. Gravity tractor specifications. range in power for each spacecraft accordingly at 20kW, 1 Spacecraft 3 Spacecraft 5 Spacecraft 10kW, and 8kW. The projectile ejection velocity, ve, will also System Mass 6800kg 6800kg 6800kg range according to the available power for each spacecraft, i.e., System Volume 7m3 8m3 9m3 300m/s, 200m/s, and 150m/s for the 1, 3, and 5 spacecraft Average Power 10000W 30000W 50000W scenarios, respectively. The mass-to-power ratio will be held TRL 3-5 3-5 3-5 constant at 25kg/kW as well as the rail gun efficiency which 14) will be taken as 30%. Each spacecraft will be limited to Table 4. Ion beam specifications. launching one projectile per minute in an appropriate launch 1 Spacecraft 3 Spacecraft 5 Spacecraft window that aligns with the redirection vector; approximately System Mass 6800kg 6800kg 6800kg ±5°. However, projectile launches may be much more System Volume 7m3 8m3 9m3 infrequent depending on the asteroid’s spin rate. Lastly, the Average Power 10000W 30000W 50000W total delta-v can be determined through a summation of the TRL 4-6 4-6 4-6 finite delta-v’s for each projectile. The finite delta-v, , can be found for each projectile according to Eq. (7) 14) , where Table 5. Laser sublimation specifications. is the projectile mass and is the asteroid�� mass. 1 Spacecraft 3 Spacecraft 5 Spacecraft

�� System Mass 6800kg 6800Kg 6800kg (7) System Volume 15m3 40m3 65m3 �� Average Power 16000W 13800W 11500W 3.3. Gravity tractor�� The gravity tractor approach� �� utilizes the gravitational TRL 2-3 2-3 2-3 attraction of one or more spacecraft in order to generate a position above the spacecraft surface. By utilizing a directed thrust on the target asteroid. It maintains its position relative to ion beam on the asteroid surface the method generates a thrust the asteroid using two thrusters that are angled in order to force on the asteroid.16) The method will also utilize the avoid impinging the asteroid surface with their exhaust RIT-XT thrusters for consistency, and will have a total 15) cone. This method will also employ two RIT-XT thrusters volume and structural mass that scales similarly to the gravity for station-keeping, and as a result each spacecraft’s ability to tractor approach, i.e., 7m3 at 300kg, 8m3 at 450kg, and 9m3 at generate thrust changes as it utilizes propellant to maintain 600kg for the 1, 3, and 5 spacecraft scenarios, respectively. formation. Eq. (8) describes the mass of each gravity tractor Since this method must maintain a hovering position, each 14) over time. spacecraft must have an additional thruster which maintains its proximity to the asteroid so it can maintain orbit. It can be (8) seen that the gravitational forces are negligible compared to 16) �� the forces of the two thrusters, and as such the thruster force �� can be calculated according to Eq. (5) with a factor of half �� where mi is the initial mass of the gravity tractor, r is the accounting for the second thruster, and the delta-v from Eq. 10) asteroid radius, d is the asteroid-spacecraft distance, G is the (6).

gravitational constant, Isp is the specific impulse, and g is the 3.5. Laser sublimation gravity at sea-level. Each of the gravity tractors produces a net The laser sublimation approach utilizes a focused laser beam to ablate asteroid material and generate a thrust on the acceleration on the asteroid according to Eq. (9) that can then asteroid from the ablated ejecta plume. The mass flow rate, , be integrated to determine the total delta-v induced by each of the ejecta plume can be determined from Eq. (10).17) gravity tractor on the asteroid. 14) ��

(9) �� (10) �� 2� �� 1 � � �� ̅ �� Lastly, the total structural mass �for each of the three cases, i.e., 2 1, 3, and 5 spacecraft, are 300kg, 450kg, and 600kg, where is the rotational velocity of the asteroid, [ymin, max in out respectively to account for the additional redundancy of the y ] is the�� height of the spot, [t , t ] is the time for which the � multiple spacecraft systems. The volume of the gravity tractor spot is illuminated, PI is the absorbed laser power per unit area is primarily determined by the compressed propellant volume, from the total of all spacecraft, is the heat loss per unit similarly to the tugboat method. The total volume only area through radiation, is �� the heat loss per unit area � increments minimally, due to additional structural components through conduction, �� is the latent heat of sublimation, � and added thrusters, as more spacecraft are added to the is the ejecta velocity, �� and are the heat capacities, � �̅ system. is the sublimation temperature,� � and is the temperature�� of the material prior to sublimation.� � From the mass flow rate,� the 3.4. Ion beam � � The ion beam method is very similar to the gravity tractor force of sublimation, Fsub, can be found and the change in approach in that it performs its redirection from a hovering asteroid mass can be determined. The delta-v can then be found using Eq. (11).17)

4 Pk_140 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

Table 6. Standard technology readiness level definitions.4) Level Definition � (11) � TRL 1 Basic principles observed and reported �� TRL 2 Technology concept and/or application formulated �� For more details on how to determine the force of sublimation, TRL 3 Analytical and experimental critical function and/or absorbed power, heat loss, and average ejecta velocity, refer to characteristic proof-of-concept Ref. 17. TRL 4 Component and/or breadboard validation in laboratory The utilized laser power systems will range in size and environment mass with each of the multiple spacecraft scenarios, using the TRL 5 Component and/or breadboard validation in relevant environment AdAM/Light-Touch2 model as a reference.18) In particular, the TRL 6 System/subsystem model or prototype demonstration in average required power for the 1, 3, and 5 spacecraft models a relevant environment (ground or space) will be 16kW, 13.8kW, and 11.5kW, respectively. Note that TRL 7 System prototype demonstration in a space environment the total mass was held constant in order to maximize the size TRL 8 Actual system completed and “flight qualified” through of the laser power system for each option. The size of each test and demonstration (ground or space) spacecraft will decrease across the three scenarios due to the TRL 9 Actual system “flight proven” through successful mission reduced power requirements for each individual spacecraft. operations However, the volume of the stowed configuration for each individual spacecraft will not be greatly affected. (12) �.�� .�� 4. Assessment Criteria Cost � 2.82� � �Dry Mass��.�� Power� � � �2.718��.�� In order to assess the viability of the asteroid redirection � �2.718��.�� methods a set of mission criteria have been established. The � �2.718��.�� assessment criteria, i.e., mass, volume, TRL, delta-v, mission � �2.718 ��.�� risk, cost, power, robustness, asteroid alteration, and � 1⁄ �2.718��.�� long-term value, have been defined in the following � �2.718 ��.�� subsections and the methodology for assigning values to each The parameters used� 1for⁄ �2.718 the dry mass and� power for each criterion is discussed. The criteria presented are adopted from spacecraft mission model can be found in Tables 1-5. a previous work on singular spacecraft approaches and are Moreover, several of the parameters in the QuickCost model adjusted to accommodate evaluation of multiple spacecraft can be held constant across each of the scenarios. In particular, 19) formations. the mission life parameter is taken at 8 years for all scenarios to account for rendezvous with and transfer of the asteroid. 4.1. System mass, volume, power, and TRL Other parameters held constant include the planetary Since each redirection method is greater than TRL 2, the parameter (1 for an interplanetary mission), the data rate mass, volume, power, and TRL can be extracted or easily percentile (0.5 for average data rate), the authority to proceed extrapolated from the relevant literature. It should be noted year (2014), and the team experience level (3 for normal level that the system mass and volume represent the cumulative mass and volume of the system of spacecraft, where less mass of experience). For each scenario the instrument complexity and volume are preferred and are constrained by the maximum percentile and percentage new parameters are varied. In payload of an Atlas V. Moreover, the power criterion particular, the percentage new parameter varied between represents the average electrical power required for operation redirection methods and between scenarios with different of the system of spacecraft for each redirection method. Since number of spacecraft to account for new information learned the additional spacecraft are unlikely to modify the overall through developing multiple identical spacecraft. Similarly, system TRL, the assigned TRL will remain constant the instrument complexity percentile varied with respect to the regardless of the selected spacecraft formation approach and redirection method being assessed, though it was constant in accordance with Table 6. across multiple spacecraft scenarios. The instrument 4.2. System cost complexity percentile values for each method, i.e., TB, ME, The cost of each spacecraft system will be determined using GT, IB, and LS, were assigned values of 0.7, 0.9, 0.4, 0.3, and the conservative NASA QuickCost model, as seen in Eq. 0.8, respectively; where 0.5 is considered median complexity. 20) (12). This model estimates the total cost of the mission 4.3. Mission risk including development costs in calendar year 2010 US Dollars. The mission risk assessment focuses on the technical risks Additionally, $250M was added to each estimated cost to of each redirection method, and is assessed by utilizing a account for the launch of an Atlas V and 5% for each year of standard likelihood/consequence evaluation.21) Each technical mission operations.20) Ref. 20 further defines the parameters in risk is assessed to determine the likelihood of not meeting Eq. (12), the standard error, and the assumptions used in the development of the model. performance requirements and the consequence on mission objectives. Tables 7 and 8 have been adapted from Ref. 20 (Table 24-11), and represent the technical likelihood scale, PT,

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of a risk occurring and the consequence scale for such a risk. Table 7. Technical likelihood scale. 5Very Each risk is assigned a likelihood and consequence value, 1Very Low 2 Low 3 Moderate 4 High High and then the overall expected percentage of objectives PT ≤ 2% PT ≤ 15% PT ≤ 25% PT ≤ 50% PT> 50% returned at the end of mission is quantified through Eq. (13), Table 8. Technical consequence scale. 5Very 1Very Low 2 Low 3 Moderate 4 High � (13) High Mission Minimal Small Moderate Significant � � failure ��%� � �� (1%) loss (10%) loss (50%) loss (90%) loss �� (100% loss of mission of mission of mission of mission where E is the expected percentage of objectives achieved, C of mission objectives objectives objectives objectives is the consequence value, and L is the likelihood value for objectives) each risk event Ri. 4.4. Delta-V, robustness, and asteroid alteration The risks for each redirection method were obtained The delta-v, performance robustness, and asteroid alteration through modification of the singular spacecraft risk for each redirection method were determined through the use assessment for each model in Ref. 19. The consequence and of a Monte Carlo simulation. The Monte Carlo analysis likelihood values are summarized in Table 9. Since the generated values for the physical asteroid parameters that the likelihood of a technical failure can be reduced in the event of redirection methods may encounter from both theoretical multiple spacecraft, a modifier to the singular results was models and available asteroid data.24) The parameters were introduced. The probability of the technical failure occurring generated for an even distribution of M-Type and C-Type for all independent spacecraft, N, can be calculated by Eq. asteroids, and 10,000 trials were performed. The asteroid 22) (14): diameter was estimated from a power distribution law,25) and the period of rotation was selected according to a dependent (14) distribution.19,24) The asteroid densities were taken to follow a � 26) �� Gaussian distribution. The thermal conductivity, specific This formula was applied to all technical mission risks that heat, temperature of sublimation, and enthalpy of sublimation can be compensated for by multiple spacecraft redundancy, were distributed according to cumulative distribution such as thruster gimbal system or lander failures. It is functions defined in Ref 27. The settings for the Monte Carlo important to consider that not all spacecraft benefit equally parameters can be found in Table 10. By utilizing the from this type of redundancy. calculated delta-v the standard deviation of the delta-v, , Also, it is important to note that in practice there is and the average delta-v, , can be determined (see Table�� considerable risk of a lander spacecraft failing to properly 11). From these results a coefficient of variation, , can� be orient and secure itself to the asteroid surface.23) In general, �� determined according to Eq. (15) as a measure� of the for the mass ejector and tugboat methods, the mission can be performance robustness of redirection methods.19) � completed with a single functioning spacecraft; albeit with reduced thrusting capabilities. As a result, increasing the number of spacecraft provides a greater opportunity for (15) �� successful landing on the asteroid surface and reduces the � � � �� overall risk of mission failure. � Table 9. Mission risk consequence and likelihood values for single spacecraft scenarios.19)

Tugboat C(Ri) L(Ri) 1. Operating lifetime of ion thruster currently tested up to 15000hrs (shorter than mission length). 4 1 2. Landing and attachment to the asteroid surface is unsuccessful. 5 3 3. Asteroid geometry causes a decrease in the available time intervals for providing thrust in the proper direction through the centre of gravity. 3 2 4. Thruster gimbal system failure. 4 1 Mass ejector C(Ri) L(Ri) 1. Landing and attachment to the asteroid surface is unsuccessful. 5 3 2. Asteroid geometry causes a decrease in the available time intervals for providing thrust in the proper direction through the centre of gravity. 3 1 3. Drill unable to mine sufficient mass to eject. 4 3 4. Dust deposits collecting on lander disabling operation. 5 3 Gravity Tractor C(Ri) L(Ri) 1. Operating lifetime of ion thruster currently tested up to 15000hrs (shorter than mission length). 4 1 2. Thruster angle insufficient to ensure exhaust plume does not impinge the surface of the asteroid. 3 1 3. Additional fuel required for position-keeping due to uncertainty in the gravitational field. 1 3 4. Inconsistent hover distance from asteroid due to uncertainty in the gravitational field effecting net acceleration induced on the asteroid. 3 3 Ion Beam C(Ri) L(Ri) 1. Operating lifetime of ion thruster currently tested up to 15000hrs (shorter than mission length). 4 1 2. Reduced ion beam force on asteroid due to elevated debris interfering with ion beam surface force. 2 4 3. Reduced fuel directed towards thrusting due to uncertainty in the gravitational field. 1 3 4. Inconsistent hover distance from asteroid due to uncertainty in the gravitational field effecting net thrust on the asteroid. 2 2

Laser Sublimation C(Ri) L(Ri) Thrust degradation due to deposited re-condensed ejecta material. 3 5 Additional fuel required for position-keeping due to uncertainty in the gravitational field. 1 3 Inconsistent hover distance from asteroid due to uncertainty in the gravitational field effecting net acceleration induced on the asteroid. 3 3

6 Pk_142 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

Table 10. Settings of Monte Carlo parameters. Table 12. System extensibility assessment scale. Category Range* Value Description Average Diameter 20-150m 1 Very Low No extensibility of system Asteroid Density 1380±20 kg/m3 (C-Type) 3 Minor extensibility of redirection system 5320±70 kg/m (M-Type) 2 Low Enthalpy of Sublimation 2.75x105-1.9686x107 J/kg 3 Moderate Moderate extensibility of redirection system. Extended Temp. of Sublimation 1700-1812 K mission achievable with major modification Specific Heat 375-750 J/KgK 4 High Major extensibility of redirection system. Extended Thermal Conductivity 0.2-2 W/mK mission achievable with minor modification Major extensibility of redirection system. Extended *Each variable follows the distributions discussed in 4.4. 5 Very High mission achievable with no modification

Table 11. Delta-v results of Monte Carlo analysis. Table 13. Reusability assessment scale. Delta-v (km/s) Std. Deviation Value Description TB 1 1.210-7 1.210-6 TB 3 0.015 0.017 1 Very Low Secondary mission not achievable TB 5 0.014 0.017 2 Low Secondary mission achievable with major modification ME 1 0.041 0.064 3 Moderate Secondary mission achievable with moderate ME 3 0.123 0.191 modification ME 5 0.205 0.318 4 High Secondary mission achievable with minor modification GT 1 6.110-8 4.610-8 5 Very High Secondary mission achievable with no modification GT 3 6.110-8 4.610-8 GT 5 6.110-8 4.610-8 IB 1 0.0078 0.0093 Table 14. Summary of risk and cost attributes. IB 3 0.0076 0.0091 Criteria TB 1 TB 3 TB 5 IB 5 0.0075 0.0089 Mission risk (%) 63.9 86.9 86.9 LS 1 7.210-5 1.810-4 System cost ($) 795M 773M 744M LS 3 6.010-5 1.510-4 ME 1 ME 3 ME 5 LS 5 4.810-5 1.310-4 Mission risk (%) 26.5 70.2 70.2 System cost ($) 2.39B 1.97B 1.61B Lastly, the asteroid alteration for those redirection methods GT 1 GT 3 GT 5 that directly change the mass of the asteroid can be Mission risk (%) 84.45 84.45 84.45 determined by measuring the average mass removed from the System cost ($) 545M 540M 568M IB 1 IB 3 IB 5 asteroid relative to its initial mass. A mass-loss ratio, Mr, Mission risk (%) 91.45 94.95 96.25 normalizes the change in mass, , and expresses it as a System cost ($) 602M 579M 592M percentage of the original mass, .19) LS 1 LS 3 LS 5 �� Mission risk (%) 37.25 62.25 74.75 �� System cost ($) 1.55B 1.21B 969M (16) weigh the criteria through a pairwise comparison approach � �� 4.5. Long-term value� �� that assesses the relative importance of each criterion. The The long-term value of each� multiple spacecraft scenario, values in pairwise comparison range from 1 to 9, where 1 comprised of a redirection method and selected spacecraft signifies equal importance and 9 signifies extreme importance formation, will be assessed with regard to system extensibility of one criterion over another. Once each pairwise comparison and reusability according to the scales provided in Tables 12 has been completed, column normalization is achieved using and 13. The values were obtained from Ref. 19 for the Eq. (17). singular systems, and since the addition of a spacecraft formation approach minimally affects long-term value, the

values are held constant for each redirection method across all (17) ��̃ three formation scenarios. �� ∑�� ̃ 4.6. Attribute summary where is the particular relative importance value at the Table 14 summarizes the risk and cost attributes, while column index i and the row index j, n is the normalized value �̃ Table 15 summarizes the attributes allocated for each at that index, and N is the total number of values in the redirection method and its respective three formation column. The overall weight of each criterion is then scenarios. These values will be aggregated through a pairwise determined using Eq. (18) by taking the mean value of the row weighted utility-based method discussed in Section 5, with after column normalization. results from the aggregation in section 6.

� (18) 5. Aggregation Technique � 1 �� The aggregation of the assessment criteria follows a � �� where represents the overall criterion weight, and N pairwise weighted utility-based approach. This method will represents the total number of values in the row. ��

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Table 15. Summary of attributes. Criteria* TB 1 TB 3 TB 5 ME 1 ME 3 ME 5 GT 1 GT 3 GT 5 IB 1 IB 3 IB 5 LS 1 LS 3 LS 5 System mass (kg) 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 6800 Volume (m3) 8.5 11.5 14.5 120 215 190 7 8 9 7 8 9 15 40 65 TRL 4-6 4-6 4-6 3 3 3 3-5 3-5 3-5 4-6 4-6 4-6 2-3 2-3 2-3 Delta-v (km/s) 1.210-7 0.015 0.014 0.041 0.123 0.205 6.110-8 6.110-8 6.110-8 0.0078 0.0076 0.0075 7.210-5 6.010-5 4.810-5 Mission risk (%) 63.9 86.9 86.9 26.5 70.2 70.2 84.45 84.45 84.45 91.45 94.95 96.25 37.25 62.25 74.75 System cost ($) 795M 773M 744M 2.39B 1.97B 1.61B 545M 540M 568M 602M 579M 592M 1.55B 1.21B 969M Power (kW) 5 15 25 20 30 40 10 30 50 10 30 50 16 13.8 11.5 Robustness 10.3 1.19 1.19 1.55 1.55 1.55 0.753 0.753 0.753 1.19 1.19 1.19 2.51 2.56 2.61 Alteration (%) 0 0 0 15.2 45.7 76.2 0 0 0 0 0 0 0.022 0.018 0.015 Long-Term Value 1.5 1.5 1.5 1 1 1 4 4 4 4 4 4 2.5 2.5 2.5 *Note: TB -Tugboat, ME - Mass Ejector, GT - Gravity Tractor, IB - Ion Beam, and LS - Laser Sublimation; the subsequent number is the number of spacecraft.

Table 16 depicts the pairwise comparison of the assessment exploitation. As such, the utility value of each criterion criteria. Since the system mass was increased to the maximum increases as it provides greater opportunity for profit. For in each redirection method case, this criterion is omitted from example, the TRL, long-term value, and mission risk utility our comparison. Moreover, the importance weightings functions show a “direct-S” trend, whereas the performance assigned in Table 16 indicate an economic exploitation bias, robustness and asteroid alteration follow a “reverse-S” trend. such that mission risk and cost are particularly Further, the slope of the utility function indicates how the overemphasized, followed by delta-v, performance robustness criterion is affected by its range of attributes. The asteroid and asteroid alteration. The volume, power, long-term value, alteration criterion follows a reverse-S trend to show the and TRL are given a low importance, since it is likely that an preference of the user towards less loss of mass during the investor would be willing to tolerate lower values for these criteria if the aforementioned criteria are well satisfied. Table 16. Criteria relative importance values. * C1 C2 C3 C4 C5 C6 C7 C8 C9 Additionally, the utility value of each criterion will be C1 1 1/3 1/8 1/9 1/9 1 1/5 1/5 1/2 0.0222 assessed using utility functions, as shown in Figs. 3-11. For C2 3 1 1/2 1/5 1/5 3 1/2 1/2 1 0.0562ݓ෥ C3 8 2 1 1/2 1/2 8 2 2 3 0.1533 each redirection method and spacecraft formation scenario, C4 9 5 2 1 1 9 3 3 5 0.2517 the attributes for each criterion will be assigned a utility value C5 9 5 2 1 1 9 3 3 5 0.2517 between 0 and 1 according to their utility function. These C6 1 1/3 1/8 1/9 1/9 1 1/5 1/4 1/3 0.0218 C7 5 2 1/2 1/3 1/3 5 1 2 2 0.1044 utility values will then be weighted according to Table 16 and C8 5 2 1/2 1/3 1/3 4 1/2 1 2 0.0878 summed to determine the overall utility of each method. C9 2 1 1/3 1/5 1/5 3 1/2 1/2 1 0.0510 The utility functions have been defined to represent the *Each criterion has been assigned a letter identifier in the table, i.e., C1-Volume, C2-TRL, C3-Delta-V, C4-Mission Risk, C5- Cost, C6-Average Required Power, preference of an early investor interested in asteroid C7- Performance Robustness, C8-Asteroid Alteration, and C9-Long-Term Value.

1 1 1

0.9 0.9 0.9

0.8 0.8 0.8

0.7 0.7 0.7

0.6 0.6 0.6

0.5 0.5 0.5

0.4 0.4 0.4

0.3 0.3 0.3

0.2 0.2 0.2

0.1 0.1 0.1

0 0 0 0 50 100 150 200 1 2 3 4 5 6 7 8 9 0 0.1 0.2 0.3 0.4 0.5 3 Volume (m ) TRL Scale Delta-V (km/s) 1 1 1

0.9 0.9 0.9

0.8 0.8 0.8

0.7 0.7 0.7

0.6 0.6 0.6

0.5 0.5 0.5

0.4 0.4 0.4

0.3 0.3 0.3

0.2 0.2 0.2

0.1 0.1 0.1

0 0 500 1000 1500 2000 2500 0 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 Cost (Millions of USD) Mission Risk (E(%)) Power (kW) 1 1 1

0.9 0.9 0.9

0.8 0.8 0.8

0.7 0.7 0.7

0.6 0.6 0.6

0.5 0.5 0.5

0.4 0.4 0.4

0.3 0.3 0.3

0.2 0.2 0.2

0.1 0.1 0.1

0 0 0 0 2 4 6 8 10 12 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 Robustness (Coefficient of Variation) Asterod Alteration(M (%)) r Long-Term Value Scale Fig. 3-11. Utility functions for each criterion; top: left is volume (Fig. 3), center is TRL (Fig. 4), right is delta-v (Fig. 5), middle: left is risk (Fig. 6), center is system cost (Fig. 7), right is power (Fig. 8), bottom: left is robustness (Fig. 9), center is asteroid alteration (Fig. 10), right is LTV (Fig. 11).

Pk_18 44 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

Table 17. Spacecraft formation factors. criterion will be assessed and multiplied by the criterion’s Method Method weight. The weighted difference in the utility values for the TB-3 1.1644 GT-5 0.9823 criteria are then summed and added to 1 to create the �� TB-5 1.1720 IB-3 1.0018 formation multiplier factor. The following equation outlines ME-3 1.1536 IB-5 0.9967 how the formation factors were determined, and Table 17 lists ME-5 1.1833 LS-3 1.1186 the multiplier factors for each spacecraft formation. GT-3 0.9924 LS-5 1.1826

0.8 � (19)

� �� 0.7 ��

0.6 where is the spacecraft formation multiplier factor for each number of spacecraft b, is the utility value for each �� 0.5 redirection method for criterion i, N is the total number of criteria, and is the weight for�� each criterion. 0.4 The spacecraft� formation factors are then applied to the Overall Utility Overall aggregated weighted�� utility of the singular spacecraft scenario 0.3 for each redirection method. The overall weighted utility of

0.2 each method, , with the applied formation factor, can be determined through Eq. (20). �� 0.1 �

0 TB-1 TB-3 TB-5 ME-1 ME-3 ME-5 GT-1 GT-3 GT-5 IB-1 IB-3 IB-5 LS-1 LS-3 LS-5 � (20) Fig. 12. Overall weighted utility of each method. � � �� 0.785 �� ∙ �� 0.784 6. Results & Discussion

0.783 The results from the aggregation are presented in Table 18 0.782 and Fig. 12. The highest aggregated values were obtained for 0.781 the ion beam, gravity tractor, and tugboat methods. The

0.78 general trend across the methods shows an advantage to methods utilizing multiple spacecraft. As expected, the landed Overall Utility Overall 0.779 strategies, i.e., tugboat and mass ejector methods, are more 0.778 advantaged by multiple spacecraft, since a formation approach 0.777 increases the thrust window available for the methods. The 0.776 mass ejector’s poor overall performance, however, can likely

0.775 be attributed to the combined effects of high mission risk, IB-1 IB-3 IB-5 Fig. 13. Overall weighted utility of each ion beam formation approach. system cost, and asteroid alteration, despite its high delta-v capabilities. The laser sublimation approach also benefited asteroid orbital transfer; where no mass loss, i.e., 0%, is from a spacecraft formation approach, but suffered primarily assigned the greatest utility, and complete mass loss, i.e., due to the variability intrinsic to the asteroid population and 100%, has the lowest utility. The utility function for the its dependence on favourable conditions. As such, it remains delta-v has a trend that highlights the advantage of greater for future work to assess the performance of the laser redirection capability with respect to more possible target sublimation method for a range of highly suitable target asteroids. The volume utility function shows a preference to asteroids compared to other redirection methods. The tugboat, smaller systems due to the possibility of reduced launch costs. gravity tractor, and ion beam methods have the best The utility function for system cost clearly prefers low-cost performance in the aggregation. systems; however, as the cost increases the relative cost It is interesting that the gravity tractor is the only method differences are not as significant in the utility function. Lastly, the power utility function indicates a preference to lower that shows no improvement from spacecraft formation design. power systems due to the greater availability. Each utility This is likely attributed to the negative impact of increased function spans the expected range of values for the power and volume requirements, while generating no increase corresponding criterion. in delta-v capabilities and only minimally decreasing cost and In order to assess the potential advantage of spacecraft risk. It should also be noted that the delta-v utility value for formation for each redirection method a spacecraft formation the gravity tractor method is nearly zero. This indicates that multiplier factor has been determined. To assess the multiplier despite its good performance with respect to other criteria, its factor for each spacecraft formation, the difference between delta-v capabilities are insufficient for such a mission. the singular and multiple spacecraft utility value for each Considering the tugboat and ion beam methods, it is shown

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Lockheed Martin Commercial Launch Services, 2010. Table 18. Overall utility weighted values. 4) Mankins, J.: SPS-ALPHA: Example of an Integrated Technology Method Method Readiness and Risk Assessment, IAC-14-D3.4.2-27288, 2014. TB-1 0.4775 GT-5 0.7521 5) Wie, B.: Dynamics and Control of Gravity Tractor Spacecraft for ෨௕ ෨௕ Asteroid Deflection, Journal of Guidance, Control and Dynamics, TB-3 0.6459ܸ IB-1 0.7815ܸ 31 (2008), pp. 1413-1423. TB-5 0.6531 IB-3 0.7826 6) Yu, S., Hou, X. and Liu, L.: On Two Kinds of Intermediate Orbits ME-1 0.2786 IB-5 0.7772 for Asteroid Explorations, Advances in Space Research, 52 (2013), pp. 125-135. ME-3 0.4320 LS-1 0.3718 7) McInnes, C.: Near Earth Object Orbit Modification Using ME-5 0.4606 LS-3 0.4911 Gravitational Coupling, Journal of Guidance, Control, and GT-1 0.7709 LS-5 0.5554 Dynamics, 30 (2007), pp. 870-873. 8) Sanchez, J. P. and McInnes, C.R.: Synergistic Approach to GT-3 0.7625 - - Asteroid Exploitation and Planetary Protection, Advances in Space Research, 49 (2012), pp. 667-685. 9) EADS Astrium: Ion Propulsion Systems, Available from that the tugboat benefits from increases in number of http://cs.astrium.eads.net/sp/spacecraft-propulsion/ion-propulsion/, spacecraft, whereas the ion beam method only improves from 2014. the single spacecraft to the 3 spacecraft formation scenario 10) Bombardelli, C. and Pelaez, J.: Ion Beam Shepherd for Asteroid Deflection, Journal of Guidance, Control, and Dynamics, (Fig. 13). This suggests that there is likely an optimal number 34(2011), pp.1270-1272. of spacecraft for each method, and where the scaling of the 11) National Space Science Data Center: Philae, NASA, available from http://nssdc.gsfc.nasa.gov/nmc/spacecraftDisplay.do?id=2004-006 main systems should be further considered. While the three C, 2014. spacecraft halo formation approach for the ion beam method 12) Welle, R.: Propellant Storage Considerations for Electric nd shows the greatest viability across all methods, a more Propulsion, 22 International Electric Propulsion Conference, AIAA-91-2589, (1991), pp. 1-10. detailed investigation into formation optimization and a more 13) Olds, J., Charania, A. and Schaffer, M.: Multiple Mass Drivers as in depth spacecraft design should be completed. Moreover, a an Option for Asteroid Deflection Missions, AIAA Planetary Defense Conference, 2007. consistency analysis and additional systematic aggregation 14) Sanchez, J. P., Colombo, C., Vasile, M. and Radice, G.: approaches should be applied for further validation. Multicriteria Comparison among Several Mitigation Strategies for Dangerous Near-Earth Objects, Journal of Guidance, Control, and Dynamics, 32 (2009), pp. 121-141. 7. Conclusion 15) Lu, E. T. and Love, S. G.: Gravitational Tractor for Towing Asteroids, Nature, 438(2005), pp. 177-178. This paper investigates five of the leading asteroid 16) Bombardelli, C., Urrutxua, H,. Merino, M., Pelaez, J. and Ahedo, E.: The Ion Beam Shepherd: A New Concept for Asteroid redirection techniques and the advantage of spacecraft Deflection, Acta Astronautica, 90 (2013), pp. 98-102. formation for each. Through a Monte Carlo analysis the 17) Gibbings, A., Vasile, M., Watson, I., Hopkins, J-M. and Burns, D.: methods were analyzed with respect to the expected variation Experimental Analysis of Laser Ablated Plumes for Asteroid Deflection and Exploitation, Asta Astronautica, 90(2013), pp. in the asteroid population to determine the average delta-v, 85-97. performance robustness, and asteroid alteration. The 18) Vasile, M,, Vetrisano, M., Gibbings, A., Yarnoz, D., Sanchez, J. P., determined system attributes were then aggregated using a Hopkins, J-M., Burns, D., McInnes, C., Colombo, C., Branco, J., Wayman, A. and Eckersley, S.: Light-touch2: a Laser-based pairwise weighted utility-based approach, and spacecraft Solution for the Deflection, Manipulation and Exploitation of formation factors were created. The results of the aggregation Small Asteroids, IAA Planetary Defence Confernce, Flagstaff, show a preference towards the ion beam approach for 2013. 19) Bazzocchi, M. C. F. and Emami, M. R.: A Systematic Assessment free-flying methods, and the tugboat approach for landed of Asteroid Redirection Methods for Resource Exploitation, AIAA methods. It was also shown that the application of a spacecraft SciTech 8th Symposium on Space Resource Utilization, 2015. formation strategy can improve the overall system 20) Wertz, J. R., Everett, D. F. and Puschell, J. J.: Space Mission performance for the tugboat, mass ejector, ion beam, and laser Engineering: The New SMAD, Microcosm Press, Hawthorne, CA, 2011, Chaps. 11, 24. sublimation approaches. A more detailed system analysis for 21) NASA: Risk Management Reporting, GSFC-STD-0002, 2009. each formation, as well as an investigation of various 22) Zadeh, L. A.: Probability Measures of Fuzzy Events, Journal of spacecraft formation strategies may increase the viability of Mathematical Analysis and Applications, 23(1968), pp.421-427. 23) European Space Agency: Three Touchdowns for Rosetta’s Lander, these redirection methods considerably. Moreover, future available at www.esa.int/Our_Activities/Space_Science/Rosetta/Th work should seek to establish more rigorous criteria ree_touchdowns_for_Rosetta_s_lander, 2014. assessment methodologies and explore alternative aggregation 24) NASA: Planetary Data System: Small Bodies Node, available from pdssbn.astro.umd.edu/index.shtml, 2014. approaches to validate these conclusions. 25) Sanchez, J.P. and McInnes, C.: Asteroid Resource Map for Near-Earth Space, Journal of Spacecraft and Rockets, 48(2011), References pp. 153-165. 26) Krasinsky, G., Pitjeva, E., Vasilyev, M. and Yagudina, E.: Hidden Mass in the Asteroid belt, Icarus, 158 (2002), pp. 98-105. 1) Sonter, M.: The technical and Economic Feasibility of Mining the 27) Zuani, F., Vasile, M. and Gibbings, A.: Evidence-based Robust Near-earth Asteroids, Acta Astronautica, 41 (1997), pp. 637-647. Design of Deflection Actions, Celestial Mechanics and Dynamical 2) Yeomans, D.: NASA Near Earth Object Program, NASA Astronomy, 114 (2012), pp. 107-136. Headquarters, Available from: http://www.nasa.gov, 2014. 3) United Launch Alliance: Atlas V Launch Services User’s Guide,

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