An Assessment of Multiple Spacecraft Formation for Asteroid Redirection

Transcription

1 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3, pp. Pk_37-Pk_46, 26 An Assessment of Multiple Spacecraft Formation for Asteroid Redirection By Michael C. F. BAZZOCCHI ) and M. Reza EMAMI,2) ) Institute for Aerospace Studies, University of Toronto, Toronto, Canada 2) Space Technology Division, Luleå University of Technology, Kiruna, Sweden (Received July 3th, 25) 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 a gt : acceleration due to gravity tractor C : risk consequence value C v : coefficient of variation c i : specific heat d : asteroid-spacecraft distance d ast : asteroid diameter E : expected percentage of objectives achieved E sub : enthalpy of sublimation : spacecraft formation factor F i : force (refer to subscript for further detail) G : gravitational constant g : gravity at sea-level H : absolute magnitude I sp : specific impulse k a : thermal conductivity L : risk likelihood value M r : mass-loss ratio m ast : asteroid mass m i : mass (refer to subscript for further detail) Δm : change in mass ṁ : mass flow rate N : number of spacecraft : normalized index P I : absorbed power P T : estimated likelihood of not meeting performance requirements Q rad : heat loss due to radiation Q cond : heat loss due to conduction R i : specific risk event r : asteroid radius : relative importance value T ast : asteroid period of rotation T sub : temperature of sublimation T : initial temperature t i : time (refer to subscript for further detail) Δt : timeframe for redirection v e : ejection velocity v rot : rotational velocity of the asteroid : utility value v : average velocity of ejecta plume : overall weighted utility value ΔV : delta-v δv : finite delta-v : overall criterion weight y : distance α : inverse specific power λ : scatter factor μ ΔV : average delta-v η : thruster efficiency ρ ast : asteroid density φ : half the angle of the exhaust cone σ ΔV : standard deviation of delta-v. Introduction Asteroid manipulation is currently one of the forefront topics of space exploration. Both the private and public sectors have a vested interest in exploring the best methods for manipulating asteroids, and as a result this provides great incentives for such research. In particular, there are two research areas that receive the most attention, i.e., asteroid deflection for planetary protection, and asteroid redirection for resource exploitation. This paper focuses on the latter in order Copyright 26 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved. Pk_37

2 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3 (26) to explore the potential benefits that near-earth asteroids (NEAs) present for economic profit and in situ resource exploitation. To provide greater insight into the viability of the leading asteroid redirection methods, a systematic assessment is discussed in this paper with consideration of the potential benefits obtained from spacecraft formation approaches. The perspective of asteroid redirection for resource exploitation provides considerable constraints on the assessment. In particular, there will be limitations on the target asteroids, the spacecraft systems employed, and the mission specifications. The asteroid redirection timeframe will be restricted to a four-year period from rendezvous with the asteroid to capture in the Earth-Moon system in order to provide a reasonable return on investment. ) Moreover, the target asteroids will be near-earth asteroids with a certain range of diameter. This diameter range is bounded to more than 2m for economic viability and less than 5m to ensure planetary protection. 2) An NEA is considered a potentially hazardous object (PHO) if its minimum orbital intersection distance is less than.5au and its diameter is approximately greater than 5m. 2) As such, to redirect larger asteroids could result in a planetary defense risk as well as considerable political challenges. In addition, the two asteroid types most suitable for resource exploitation are carbonaceous (C-Type) and metallic (M-Type) asteroids. The carbonaceous asteroids are targeted due to their high concentrations of volatile materials that can be used for the development of propellants and life support systems, whereas the metallic type asteroids contain high concentrations of rare-earth metals, platinum group metals, and other materials useful for in situ construction of space structures. The spacecraft systems will be limited with respect to mass, volume, and technology readiness level (TRL). To ensure economic viability and a baseline for comparison between single and multiple spacecraft approaches, the mass and volume of the system will be restricted to the payload capabilities of an Atlas V launch vehicle. As such, each spacecraft system must have a combined payload less than 68kg as well as a stowed configuration less than a payload envelope of 4.572m in diameter and 2.92m in length. 3) 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. tractor, and laser sublimation, require prolonged hovering about the asteroid in order to impart significant delta-v. Moreover, these methods benefit from maintaining a hover distance that targets the asteroid from one particular direction. As such, a halo orbit formation has been selected as an approach that will maximize operation time for each method; as seen in Fig.. In addition to the singular configurations of each redirection method, scenarios with 3 and 5 spacecraft in halo orbits are investigated. The following equations of motion describe a simplified ideal circular halo orbit about an asteroid, where the orbital motion of the asteroid is neglected: 5) () (2) (3) where is the gravitational constant, is the mass of the asteroid, is the spacecraft thrust, is the mass of the spacecraft, and the radial term can be represented by (4) It is important to note that while this assessment utilizes a halo orbit about the target asteroids, in practice this can be difficult to achieve. This simulation focuses on the benefits of an ideal formation without accounting for the affects of solar radiation pressure on the spacecraft orbits. It has been shown that solar radiation pressure is a significant perturbation for small asteroids where the gravitational acceleration is low. 6) However, for the purpose of this assessment, and to ensure similar depth of formation investigation for flying and landed configurations, a simplified halo orbit model in line with the previous works in the literature has been adopted. 5,7) 2. Spacecraft Formation Strategies 2.. Free-flying formation Three of the redirection methods, i.e., ion beam, gravity Fig.. An example of three spacecraft in a halo orbit. Pk_38

3 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). ) 2 (5) (6) Fig. 2. An example of several landers on the asteroid equator Landed configuration The landed redirection methods, i.e., tugboat and mass ejector, are particularly disadvantaged by the rotation rate of the asteroid. Each method s redirection capability is limited by a certain range of thrust angles and rotation periods that allow it to align its thrust vector with the direction of redirection. This thrusting time period can be increased by placing a series of equidistant spacecraft equatorially along the asteroid surface; such that they are placed in a plane perpendicular to the spin vector of the asteroid. 8) This approach will increase the total time that the system of spacecraft is able to provide a thrust on the asteroid. As in the free-flying case, this landed configuration will be assessed with respect to the utilization of, 3 and 5 spacecraft. 3. Redirection Methods The redirection methods considered in this analysis were selected due to their suitability for an asteroid redirection mission, i.e., tugboat, mass ejector, gravity tractor, ion beam, and laser sublimation. They will be discussed in more detail in the subsequent sections. 3.. Tugboat The tugboat method induces redirection through one or more landed spacecraft using thrusters to push the asteroid. The leading single spacecraft configuration requires that the spacecraft land on the spin axis of the asteroid then alter the spin axis such that it aligns with the redirection thrust vector. While this method is fairly inefficient, it can be easily remedied through a spacecraft formation approach that lands multiple spacecraft equatorially. Multiple spacecraft on the equator with thrusters on a gimbal system will allow the 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; however, this would considerably reduce the delta-v imparted to the asteroid. In this particular model, RIT-XT thrusters will be considered which have a nominal power of 5W, nominal specific impulse of 45s, 6% thruster efficiency and inverse specific power of kg/kw. 9) The force of the 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 asteroid diameter. The structural mass of the system includes the mass of the lander, which will be scaled based on the number and size of the spacecraft in the system. The structural mass for the, 3 and 5 spacecraft models are 45kg, 75kg, and 5kg, respectively. The remaining mass is attributed to fuel and power plant. The lander uses the Philae lander as a reference design. ) The volume of the spacecraft is estimated from the combined lander stowed volume and compressed propellant volume; assuming an optimally compressed liquid xenon fuel. 2) 3.2. Mass ejector The mass ejector redirection method utilizes the available asteroid mass as a projectile to induce a delta-v on the main asteroid body. This concept employs one or more mass ejector spacecraft landing on the surface of the asteroid equatorially, drilling into the asteroid surface and launching asteroid mass to generate a thrust. Mass ejector spacecraft are comprised primarily of a rail gun for launching asteroid mass and an extraction device. In this particular model, the Modular Asteroid Deflection Mission Ejector Node or MADMEN concept will provide a baseline for the key attributes. 3) The total mass of each multiple spacecraft scenario will be maximized in order to allocate the greatest amount of mass to the power systems, which comprise approximately 3% of the dry mass for each spacecraft. 3) In each case, the rail gun size, volume, and power requirements will be scaled according to the reduced spacecraft mass for each scenario. The rail gun will still have a deployable length up to 5m for each case, i.e.,, 3, and 5 spacecraft configurations; however, the base Table. Tugboat specifications. Spacecraft 3 Spacecraft 5 Spacecraft System Mass 68kg 68kg 68kg System Volume 8.5m 3.5 m m 3 Average Power 5W 5W 25W TRL Table 2. Mass ejector specifications. Spacecraft 3 Spacecraft 5 Spacecraft System Mass 68kg 68kg 68kg System Volume 2m 3 25m 3 9m 3 Average Power 2W 3W 4W TRL Pk_39

4 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3 (26) diameters will vary at 4.5m, 3.5m, and 2.5m for each case and range in power for each spacecraft accordingly at 2kW, kw, and 8kW. The projectile ejection velocity, ve, will also range according to the available power for each spacecraft, i.e., 3m/s, 2m/s, and 5m/s for the, 3, and 5 spacecraft scenarios, respectively. The mass-to-power ratio will be held constant at 25kg/kW as well as the rail gun efficiency which will be taken as 3%. 4) Each spacecraft will be limited to launching one projectile per minute in an appropriate launch window that aligns with the redirection vector; approximately ±5. However, projectile launches may be much more infrequent depending on the asteroid s spin rate. Lastly, the total delta-v can be determined through a summation of the finite delta-v s for each projectile. The finite delta-v,, can be found for each projectile according to Eq. (7) 4), where is the projectile mass and is the asteroid mass. (7) 3.3. Gravity tractor The gravity tractor approach utilizes the gravitational attraction of one or more spacecraft in order to generate a thrust on the target asteroid. It maintains its position relative to the asteroid using two thrusters that are angled in order to avoid impinging the asteroid surface with their exhaust cone. 5) This method will also employ two RIT-XT thrusters for station-keeping, and as a result each spacecraft s ability to generate thrust changes as it utilizes propellant to maintain formation. Eq. (8) describes the mass of each gravity tractor over time. 4) (8) where mi is the initial mass of the gravity tractor, r is the asteroid radius, d is the asteroid-spacecraft distance, G is the gravitational constant, Isp is the specific impulse, and g is the gravity at sea-level. Each of the gravity tractors produces a net acceleration on the asteroid according to Eq. (9) that can then be integrated to determine the total delta-v induced by each gravity tractor on the asteroid. 4) (9) Lastly, the total structural mass for each of the three cases, i.e.,, 3, and 5 spacecraft, are 3kg, 45kg, and 6kg, respectively to account for the additional redundancy of the multiple spacecraft systems. The volume of the gravity tractor is primarily determined by the compressed propellant volume, similarly to the tugboat method. The total volume only increments minimally, due to additional structural components and added thrusters, as more spacecraft are added to the system Ion beam The ion beam method is very similar to the gravity tractor approach in that it performs its redirection from a hovering Table 3. Gravity tractor specifications. Spacecraft 3 Spacecraft 5 Spacecraft System Mass 68kg 68kg 68kg System Volume 7m 3 8m 3 9m 3 Average Power W 3W 5W TRL Table 4. Ion beam specifications. Spacecraft 3 Spacecraft 5 Spacecraft System Mass 68kg 68kg 68kg System Volume 7m 3 8m 3 9m 3 Average Power W 3W 5W TRL Table 5. Laser sublimation specifications. Spacecraft 3 Spacecraft 5 Spacecraft System Mass 68kg 68Kg 68kg System Volume 5m 3 4m 3 65m 3 Average Power 6W 38W 5W TRL position above the spacecraft surface. By utilizing a directed ion beam on the asteroid surface the method generates a thrust force on the asteroid. 6) The method will also utilize the RIT-XT thrusters for consistency, and will have a total volume and structural mass that scales similarly to the gravity tractor approach, i.e., 7m 3 at 3kg, 8m 3 at 45kg, and 9m 3 at 6kg for the, 3, and 5 spacecraft scenarios, respectively. Since this method must maintain a hovering position, each spacecraft must have an additional thruster which maintains its proximity to the asteroid so it can maintain orbit. It can be seen that the gravitational forces are negligible compared to the forces of the two thrusters, 6) and as such the thruster force can be calculated according to Eq. (5) with a factor of half accounting for the second thruster, and the delta-v from Eq. (6). ) 3.5. Laser sublimation The laser sublimation approach utilizes a focused laser beam to ablate asteroid material and generate a thrust on the asteroid from the ablated ejecta plume. The mass flow rate,, of the ejecta plume can be determined from Eq. (). 7) 2 2 () where is the rotational velocity of the asteroid, [ymin, ymax] is the height of the spot, [tin, tout] is the time for which the spot is illuminated, PI is the absorbed laser power per unit area from the total of all spacecraft, is the heat loss per unit area through radiation, is the heat loss per unit area through conduction, is the latent heat of sublimation, is the ejecta velocity, and are the heat capacities, is the sublimation temperature, and is the temperature of the material prior to sublimation. From the mass flow rate, the force of sublimation, Fsub, can be found and the change in asteroid mass can be determined. The delta-v can then be found using Eq. (). 7) Pk_4

5 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection () For more details on how to determine the force of sublimation, absorbed power, heat loss, and average ejecta velocity, refer to Ref. 7. The utilized laser power systems will range in size and mass with each of the multiple spacecraft scenarios, using the AdAM/Light-Touch2 model as a reference. 8) In particular, the average required power for the, 3, and 5 spacecraft models will be 6kW, 3.8kW, and.5kw, respectively. Note that the total mass was held constant in order to maximize the size of the laser power system for each option. The size of each spacecraft will decrease across the three scenarios due to the reduced power requirements for each individual spacecraft. However, the volume of the stowed configuration for each individual spacecraft will not be greatly affected. 4. Assessment Criteria In order to assess the viability of the asteroid redirection methods a set of mission criteria have been established. The assessment criteria, i.e., mass, volume, TRL, delta-v, mission risk, cost, power, robustness, asteroid alteration, and long-term value, have been defined in the following subsections and the methodology for assigning values to each criterion is discussed. The criteria presented are adopted from a previous work on singular spacecraft approaches and are adjusted to accommodate evaluation of multiple spacecraft formations. 9) 4.. System mass, volume, power, and TRL Since each redirection method is greater than TRL 2, the mass, volume, power, and TRL can be extracted or easily extrapolated from the relevant literature. It should be noted that the system mass and volume represent the cumulative mass and volume of the system of spacecraft, where less mass and volume are preferred and are constrained by the maximum payload of an Atlas V. Moreover, the power criterion represents the average electrical power required for operation of the system of spacecraft for each redirection method. Since the additional spacecraft are unlikely to modify the overall system TRL, the assigned TRL will remain constant regardless of the selected spacecraft formation approach and in accordance with Table System cost The cost of each spacecraft system will be determined using the conservative NASA QuickCost model, as seen in Eq. (2). 2) This model estimates the total cost of the mission including development costs in calendar year 2 US Dollars. Additionally, $25M was added to each estimated cost to account for the launch of an Atlas V and 5% for each year of mission operations. 2) Ref. 2 further defines the parameters in Eq. (2), the standard error, and the assumptions used in the development of the model. Table 6. Standard technology readiness level definitions. 4) Level Definition TRL Basic principles observed and reported TRL 2 Technology concept and/or application formulated TRL 3 Analytical and experimental critical function and/or characteristic proof-of-concept TRL 4 Component and/or breadboard validation in laboratory environment TRL 5 Component and/or breadboard validation in relevant environment TRL 6 System/subsystem model or prototype demonstration in a relevant environment (ground or space) TRL 7 System prototype demonstration in a space environment TRL 8 Actual system completed and flight qualified through test and demonstration (ground or space) TRL 9 Actual system flight proven through successful mission operations Cost 2.82 Dry Mass. Power (2) The parameters used for the dry mass and power for each spacecraft mission model can be found in Tables -5. Moreover, several of the parameters in the QuickCost model can be held constant across each of the scenarios. In particular, the mission life parameter is taken at 8 years for all scenarios to account for rendezvous with and transfer of the asteroid. Other parameters held constant include the planetary parameter ( for an interplanetary mission), the data rate percentile ( for average data rate), the authority to proceed year (24), and the team experience level (3 for normal level of experience). For each scenario the instrument complexity percentile and percentage new parameters are varied. In particular, the percentage new parameter varied between redirection methods and between scenarios with different number of spacecraft to account for new information learned through developing multiple identical spacecraft. Similarly, the instrument complexity percentile varied with respect to the redirection method being assessed, though it was constant across multiple spacecraft scenarios. The instrument complexity percentile values for each method, i.e., TB, ME, GT, IB, and LS, were assigned values of,.9,,.3, and.8, respectively; where is considered median complexity Mission risk The mission risk assessment focuses on the technical risks of each redirection method, and is assessed by utilizing a standard likelihood/consequence evaluation. 2) Each technical risk is assessed to determine the likelihood of not meeting performance requirements and the consequence on mission objectives. Tables 7 and 8 have been adapted from Ref. 2 (Table 24-), and represent the technical likelihood scale, PT, Pk_4

6 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3 (26) of a risk occurring and the consequence scale for such a risk. Each risk is assigned a likelihood and consequence value, and then the overall expected percentage of objectives returned at the end of mission is quantified through Eq. (3), % (3) where E is the expected percentage of objectives achieved, C is the consequence value, and L is the likelihood value for each risk event Ri. The risks for each redirection method were obtained through modification of the singular spacecraft risk assessment for each model in Ref. 9. The consequence and likelihood values are summarized in Table 9. Since the likelihood of a technical failure can be reduced in the event of multiple spacecraft, a modifier to the singular results was introduced. The probability of the technical failure occurring for all independent spacecraft, N, can be calculated by Eq. (4): 22) (4) This formula was applied to all technical mission risks that can be compensated for by multiple spacecraft redundancy, such as thruster gimbal system or lander failures. It is important to consider that not all spacecraft benefit equally from this type of redundancy. Also, it is important to note that in practice there is considerable risk of a lander spacecraft failing to properly orient and secure itself to the asteroid surface. 23) In general, for the mass ejector and tugboat methods, the mission can be completed with a single functioning spacecraft; albeit with reduced thrusting capabilities. As a result, increasing the number of spacecraft provides a greater opportunity for successful landing on the asteroid surface and reduces the overall risk of mission failure. Table 7. Technical likelihood scale. Very Low 2 Low 3 Moderate 4 High 5Very High P T 2% P T 5% P T 25% P T 5% P T > 5% Table 8. Technical consequence scale. Very Low 2 Low 3 Moderate 4 High Minimal (%) loss of mission objectives Small (%) loss of mission objectives Moderate (5%) loss of mission objectives Significant (9%) loss of mission objectives 4.4. Delta-V, robustness, and asteroid alteration The delta-v, performance robustness, and asteroid alteration for each redirection method were determined through the use of a Monte Carlo simulation. The Monte Carlo analysis generated values for the physical asteroid parameters that the redirection methods may encounter from both theoretical models and available asteroid data. 24) The parameters were generated for an even distribution of M-Type and C-Type asteroids, and, trials were performed. The asteroid diameter was estimated from a power distribution law, 25) and the period of rotation was selected according to a dependent distribution. 9,24) The asteroid densities were taken to follow a Gaussian distribution. 26) The thermal conductivity, specific heat, temperature of sublimation, and enthalpy of sublimation were distributed according to cumulative distribution functions defined in Ref 27. The settings for the Monte Carlo parameters can be found in Table. By utilizing the calculated delta-v the standard deviation of the delta-v,, and the average delta-v,, can be determined (see Table ). From these results a coefficient of variation,, can be determined according to Eq. (5) as a measure of the performance robustness of redirection methods. 9) (5) Table 9. Mission risk consequence and likelihood values for single spacecraft scenarios. 9) Tugboat C(Ri) L(Ri). Operating lifetime of ion thruster currently tested up to 5hrs (shorter than mission length) Landing and attachment to the asteroid surface is unsuccessful Asteroid geometry causes a decrease in the available time intervals for providing thrust in the proper direction through the centre of gravity Thruster gimbal system failure. 4 Mass ejector C(Ri) L(Ri). Landing and attachment to the asteroid surface is unsuccessful Asteroid geometry causes a decrease in the available time intervals for providing thrust in the proper direction through the centre of gravity Drill unable to mine sufficient mass to eject Dust deposits collecting on lander disabling operation. 5 3 Gravity Tractor C(Ri) L(Ri). Operating lifetime of ion thruster currently tested up to 5hrs (shorter than mission length) Thruster angle insufficient to ensure exhaust plume does not impinge the surface of the asteroid Additional fuel required for position-keeping due to uncertainty in the gravitational field 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). Operating lifetime of ion thruster currently tested up to 5hrs (shorter than mission length) Reduced ion beam force on asteroid due to elevated debris interfering with ion beam surface force Reduced fuel directed towards thrusting due to uncertainty in the gravitational field 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. 3 Inconsistent hover distance from asteroid due to uncertainty in the gravitational field effecting net acceleration induced on the asteroid Very High Mission failure (% loss of mission objectives) Pk_42

7 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection Table. Settings of Monte Carlo parameters. Category Range* Average Diameter 2-5m Asteroid Density 38±2 kg/m 3 (C-Type) 532±7 kg/m 3 (M-Type) Enthalpy of Sublimation 2.75x x 7 J/kg Temp. of Sublimation 7-82 K Specific Heat J/KgK Thermal Conductivity -2 W/mK *Each variable follows the distributions discussed in 4.4. Table. Delta-v results of Monte Carlo analysis. Delta-v (km/s) Std. Deviation TB TB TB ME.4.64 ME ME GT GT GT IB IB IB LS LS LS Lastly, the asteroid alteration for those redirection methods that directly change the mass of the asteroid can be determined by measuring the average mass removed from the asteroid relative to its initial mass. A mass-loss ratio, Mr, normalizes the change in mass,, and expresses it as a percentage of the original mass,. 9) (6) 4.5. Long-term value The long-term value of each multiple spacecraft scenario, comprised of a redirection method and selected spacecraft formation, will be assessed with regard to system extensibility and reusability according to the scales provided in Tables 2 and 3. The values were obtained from Ref. 9 for the 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 three formation scenarios Attribute summary Table 4 summarizes the risk and cost attributes, while Table 5 summarizes the attributes allocated for each redirection method and its respective three formation scenarios. These values will be aggregated through a pairwise weighted utility-based method discussed in Section 5, with results from the aggregation in section Aggregation Technique The aggregation of the assessment criteria follows a pairwise weighted utility-based approach. This method will Table 2. System extensibility assessment scale. Value Description Very Low No extensibility of system 2 Low Minor extensibility of redirection system 3 Moderate Moderate extensibility of redirection system. Extended mission achievable with major modification 4 High Major extensibility of redirection system. Extended mission achievable with minor modification 5 Very High Major extensibility of redirection system. Extended mission achievable with no modification Table 3. Reusability assessment scale. Value Description Very Low Secondary mission not achievable 2 Low Secondary mission achievable with major modification 3 Moderate Secondary mission achievable with moderate modification 4 High Secondary mission achievable with minor modification 5 Very High Secondary mission achievable with no modification Table 4. Summary of risk and cost attributes. Criteria TB TB 3 TB 5 Mission risk (%) System cost ($) 795M 773M 744M ME ME 3 ME 5 Mission risk (%) System cost ($) 2.39B.97B.6B GT GT 3 GT 5 Mission risk (%) System cost ($) 545M 54M 568M IB IB 3 IB 5 Mission risk (%) System cost ($) 62M 579M 592M LS LS 3 LS 5 Mission risk (%) System cost ($).55B.2B 969M weigh the criteria through a pairwise comparison approach that assesses the relative importance of each criterion. The values in pairwise comparison range from to 9, where signifies equal importance and 9 signifies extreme importance of one criterion over another. Once each pairwise comparison has been completed, column normalization is achieved using Eq. (7). (7) where is the particular relative importance value at the column index i and the row index j, n is the normalized value at that index, and N is the total number of values in the column. The overall weight of each criterion is then determined using Eq. (8) by taking the mean value of the row after column normalization. (8) where represents the overall criterion weight, and N represents the total number of values in the row. Pk_43

8 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3 (26) Table 5. Summary of attributes. Criteria* TB TB 3 TB 5 ME ME 3 ME 5 GT GT 3 GT 5 IB IB 3 IB 5 LS LS 3 LS 5 System mass (kg) Volume (m 3 ) TRL Delta-v (km/s) Mission risk (%) System cost ($) 795M 773M 744M 2.39B.97B.6B 545M 54M 568M 62M 579M 592M.55B.2B 969M Power (kw) Robustness Alteration (%) Long-Term Value *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 6 depicts the pairwise comparison of the assessment criteria. Since the system mass was increased to the maximum in each redirection method case, this criterion is omitted from our comparison. Moreover, the importance weightings assigned in Table 6 indicate an economic exploitation bias, such that mission risk and cost are particularly overemphasized, followed by delta-v, performance robustness and asteroid alteration. The volume, power, long-term value, and TRL are given a low importance, since it is likely that an investor would be willing to tolerate lower values for these criteria if the aforementioned criteria are well satisfied. Additionally, the utility value of each criterion will be assessed using utility functions, as shown in Figs. 3-. For each redirection method and spacecraft formation scenario, the attributes for each criterion will be assigned a utility value between and according to their utility function. These utility values will then be weighted according to Table 6 and summed to determine the overall utility of each method. The utility functions have been defined to represent the preference of an early investor interested in asteroid exploitation. As such, the utility value of each criterion increases as it provides greater opportunity for profit. For example, the TRL, long-term value, and mission risk utility functions show a direct-s trend, whereas the performance robustness and asteroid alteration follow a reverse-s trend. Further, the slope of the utility function indicates how the criterion is affected by its range of attributes. The asteroid alteration criterion follows a reverse-s trend to show the preference of the user towards less loss of mass during the Table 6. Criteria relative importance values. * C C2 C3 C4 C5 C6 C7 C8 C9 C /3 /8 /9 /9 /5 /5 /2.222 C2 3 /2 /5 /5 3 /2 /2.562 C3 8 2 /2 / C C C6 /3 /8 /9 /9 /5 /4 /3.28 C7 5 2 /2 /3 / C8 5 2 /2 /3 /3 4 / C9 2 /3 /5 /5 3 /2 /2.5 *Each criterion has been assigned a letter identifier in the table, i.e., C-Volume, C2-TRL, C3-Delta-V, C4-Mission Risk, C5- Cost, C6-Average Required Power, C7- Performance Robustness, C8-Asteroid Alteration, and C9-Long-Term Value Volume (m 3 ) Mission Risk (E(%)) TRL Scale Cost (Millions of USD) Delta-V (km/s) Power (kw) Robustness (Coefficient of Variation) Asterod Alteration(M r (%)) Long-Term Value Scale Fig. 3-. 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. ), right is LTV (Fig. ). Pk_44

9 M.C.F. BAZZOCCHI and M. R. EMAMI: An Assessment of Multiple Spacecraft Formation for Asteroid Redirection.8 Table 7. Spacecraft formation factors. Method Method TB GT TB-5.72 IB-3.8 ME IB ME LS-3.86 GT LS criterion will be assessed and multiplied by the criterion s weight. The weighted difference in the utility values for the criteria are then summed and added to to create the formation multiplier factor. The following equation outlines how the formation factors were determined, and Table 7 lists the multiplier factors for each spacecraft formation. (9) Overall Utility Overall Utility TB- TB-3 TB-5 ME- ME-3 ME-5 GT- GT-3 GT-5 IB- IB-3 IB-5 LS- LS-3 LS-5 Fig. 2. Overall weighted utility of each method. IB- IB-3 IB-5 Fig. 3. Overall weighted utility of each ion beam formation approach. asteroid orbital transfer; where no mass loss, i.e., %, is assigned the greatest utility, and complete mass loss, i.e., %, has the lowest utility. The utility function for the delta-v has a trend that highlights the advantage of greater redirection capability with respect to more possible target asteroids. The volume utility function shows a preference to smaller systems due to the possibility of reduced launch costs. The utility function for system cost clearly prefers low-cost systems; however, as the cost increases the relative cost differences are not as significant in the utility function. Lastly, the power utility function indicates a preference to lower power systems due to the greater availability. Each utility function spans the expected range of values for the corresponding criterion. In order to assess the potential advantage of spacecraft formation for each redirection method a spacecraft formation multiplier factor has been determined. To assess the multiplier factor for each spacecraft formation, the difference between the singular and multiple spacecraft utility value for each where is the spacecraft formation multiplier factor for each number of spacecraft b, is the utility value for each redirection method for criterion i, N is the total number of criteria, and is the weight for each criterion. The spacecraft formation factors are then applied to the aggregated weighted utility of the singular spacecraft scenario for each redirection method. The overall weighted utility of each method,, with the applied formation factor, can be determined through Eq. (2). 6. Results & Discussion (2) The results from the aggregation are presented in Table 8 and Fig. 2. The highest aggregated values were obtained for the ion beam, gravity tractor, and tugboat methods. The general trend across the methods shows an advantage to methods utilizing multiple spacecraft. As expected, the landed strategies, i.e., tugboat and mass ejector methods, are more advantaged by multiple spacecraft, since a formation approach increases the thrust window available for the methods. The mass ejector s poor overall performance, however, can likely be attributed to the combined effects of high mission risk, system cost, and asteroid alteration, despite its high delta-v capabilities. The laser sublimation approach also benefited from a spacecraft formation approach, but suffered primarily due to the variability intrinsic to the asteroid population and its dependence on favourable conditions. As such, it remains for future work to assess the performance of the laser sublimation method for a range of highly suitable target asteroids compared to other redirection methods. The tugboat, gravity tractor, and ion beam methods have the best performance in the aggregation. It is interesting that the gravity tractor is the only method that shows no improvement from spacecraft formation design. This is likely attributed to the negative impact of increased power and volume requirements, while generating no increase in delta-v capabilities and only minimally decreasing cost and risk. It should also be noted that the delta-v utility value for the gravity tractor method is nearly zero. This indicates that despite its good performance with respect to other criteria, its delta-v capabilities are insufficient for such a mission. Considering the tugboat and ion beam methods, it is shown Pk_45

10 Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists3 (26) Table 8. Overall utility weighted values. Method Method TB- 775 GT-5 52 TB IB- 85 TB-5 53 IB ME- 786 IB ME-3 32 LS-.378 ME-5 66 LS-3 9 GT- 79 LS GT that the tugboat benefits from increases in number of spacecraft, whereas the ion beam method only improves from the single spacecraft to the 3 spacecraft formation scenario (Fig. 3). This suggests that there is likely an optimal number of spacecraft for each method, and where the scaling of the main systems should be further considered. While the three spacecraft halo formation approach for the ion beam method shows the greatest viability across all methods, a more detailed investigation into formation optimization and a more in depth spacecraft design should be completed. Moreover, a consistency analysis and additional systematic aggregation approaches should be applied for further validation. 7. Conclusion This paper investigates five of the leading asteroid redirection techniques and the advantage of spacecraft formation for each. Through a Monte Carlo analysis the methods were analyzed with respect to the expected variation in the asteroid population to determine the average delta-v, performance robustness, and asteroid alteration. The determined system attributes were then aggregated using a pairwise weighted utility-based approach, and spacecraft formation factors were created. The results of the aggregation show a preference towards the ion beam approach for free-flying methods, and the tugboat approach for landed methods. It was also shown that the application of a spacecraft formation strategy can improve the overall system performance for the tugboat, mass ejector, ion beam, and laser sublimation approaches. A more detailed system analysis for each formation, as well as an investigation of various spacecraft formation strategies may increase the viability of these redirection methods considerably. Moreover, future work should seek to establish more rigorous criteria assessment methodologies and explore alternative aggregation approaches to validate these conclusions. 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