Manned Missions to Near-Earth Objects

Lehrstuhl für Raumfahrttechnik Prof. Dr. rer. nat. Ulrich Walter

Semesterarbeit RT-SA-2012/26

Manned Missions to Near-Earth Objects Target Selection and Evaluation of Mission Opportunities

Author: Ralf Boden

Advisor:

Dipl.-Ing. Andreas Hein Lehrstuhl für Raumfahrttechnik / Institute of Aeronautics Technische Universität München

Bestätigung der Eigenen Arbeit Ich erkläre hiermit, dass ich diese Arbeit ohne fremde Hilfe angefertigt und nur die in dem Literaturverzeichnis angeführten Quellen und Hilfsmittel benutzt habe. Garching, den

Name:

Ralf Boden

Matrikelnummer

2877060

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Abstract In recent years Near-Earth Objects have received an increased amount of attention as potential targets for future human exploration. These objects offer scientifically interesting targets and at the same time function as a stepping stone towards enabling access to Mars; due to shorter transfer times and ∆v requirements. The aim of this research is to identify NEOs that are likely to be candidates for manned sample-return missions in the near future and to evaluate them based on their value and the effort needed to reach them. In a first step the number of NEOs is reduced to include only targets that are feasible. This process includes eliminating targets that exceed restrictions to mission duration and ∆v. Asteroids that do not fulfill the requirements for sample-return operations are also excluded from the candidate list; hereby NEOs above 21.5 magnitudes are removed. What remains is a list of targets and mission opportunities that need to be evaluated using a baseline mission design. The architecture and spacecraft setup used for this type of mission is explained, and a model for determining the in-LEO mass is provided. A final selection of promising candidates is based on minimum in-LEO mass and the NEO’s accessibility; the latter being indicated by the number of available mission opportunities. It is discovered that very few targets can be accessed with a reasonable spacecraft mass, while at the same time fulfilling all mission requirements. A major factor for this is the restriction to targets that allow sample-return. Removing the restriction on asteroid size causes a great increase in available targets. These can be accessed with lower in-LEO mass; caused by a lower ∆v, as mission duration remains identical. By adapting the spacecraft setup for flyby missions, some targets are accessible with in-LEO masses in the range of the payload capability of a Saturn V. Both missions with small in-LEO masses, and those targeting larger asteroids can be considered as options for future missions; depending on the trade-off between cost and scientific value. As a result, the final target selection includes NEOs for both options. The current lack of an optimal target leads to the conclusion, that more incentive is required to increase the number of accessible targets for future human missions to NEOs. More effort should be made towards the discovery of NEOs, to increase the chances of finding an optimal target. Reducing in-LEO mass through advanced architectures is also an important part in enabling human NEO exploration and should be the subject of future studies.

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Zusammenfassung Asteroiden auf erdnahen Bahnen, sogenannte Near-Earth Objects, erleben ein wachsendes Interesse als Ziel für bemannte Raumfahrtmissionen. Der Grund ist, dass diese Objekte nicht nur aus wissenschaftlicher Sicht von Interesse sind sondern auch die Möglichkeit bieten, Technologien für zukünftige Mars-Missionen zu entwickeln und zu erproben. Die Anforderungen, in Bezug auf Missionsdauer und ∆v, sind hierbei durch die Lage der NEOs niedriger als bei Mars Missionen. Ziel dieser Arbeit ist es, potentielle Kandidaten für eine bemannte Mission aus der bisher bekannten NEO population zu identifizieren. Hierbei werden in einem ersten Schritt alle Asteroiden ausgeschlossen, die wegen der Missionsdauer und der ∆vKosten als unrealistisch gelten. Asteroiden, bei denen das Einsammeln von Proben zu gefährlich ist, werden ebenfalls aussortiert. Betroffen sind alle NEOs, deren absolute Helligkeit H den Wert 21.5 überschreitet. Es bleibt eine Auswahl an potentiellen Zielen übrig, die mit Hilfe eines ersten Missionsdesigns ausgewertet werden können. Eine detaillierte Beschreibung dieses Designs erlaubt es, die für eine NEO Mission benötigte in-LEO Masse zu bestimmen. Eine Liste mit vielversprechenden Kandidaten wird erstellt, aufgrund von geringem Massenbedarf und der Erreichbarkeit der NEOs. Die Ergebnisse zeigen, dass nur eine geringe Anzahl an NEOs mit einer realistischen in-LEO Masse erreicht werden können und dabei alle Anforderungen erfüllen. Eine Ursache hierfür ist die Begrenzung der NEO Größe, ohne die wesentlich mehr NEOs als Ziele zur Verfügung stehen. Da diese NEOs jedoch weniger von Interesse sind, wird eine alternative Mission vorgestellt um ihre Attraktivität durch geringere in-LEO Masse zu erhöhen. Hierbei handelt es sich um eine Flyby-Mission. Da beide Typen von Missionen ihre Vorzüge haben, erfolgt die Auswahl eines Ziels anhand einer Abwägung zwischen wissenschaftlichem Interesse und benötigtem Aufwand. Aus diesem Grund sind NEOs für beide Missionen in der Kandidaten-Liste enthalten. Das Fehlen von Asteroiden, die alle Anforderungen gleichzeitig erfüllen, lässt die Schlussfolgerung zu, dass Anstrengungen hinsichtlich der Entdeckung neuer, noch unbekannter Asteroiden verstärkt werden müssen. Dadurch können die Chancen, ein ideales Ziel für bemannte NEO Missionen zu finden, stark erhöht werden. Auch das Entwickeln von fortschrittlichen Missionsarchitekturen kann die Anzahl an erreichbaren NEOs erhöhen und den in-LEO Massenbedarf senken. Dies könnte die Grundlage für weitere Forschung auf dem Gebiet bemannter NEO Missionen sein.

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Contents 1. Introduction 1.1. Increase of Interest in NEOs as Targets for Manned Missions 1.2. Research Goals . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Requirements and Constraints . . . . . . . . . . . . . . . . 1.4. Research Outline . . . . . . . . . . . . . . . . . . . . . . . 2. NEOs as Targets for Manned Missions 2.1. Origin of NEOs . . . . . . . . . . . . . . . . . . . . . . 2.2. The NEO Population . . . . . . . . . . . . . . . . . . . 2.2.1. Types and Classes . . . . . . . . . . . . . . . . 2.2.2. Absolute Magnitude H of NEOs . . . . . . . . . 2.2.3. NEO Rotation Rates . . . . . . . . . . . . . . . 2.3. Past and Present NEO Research . . . . . . . . . . . . . 2.3.1. Remote NEO Research . . . . . . . . . . . . . . 2.3.2. Robotic Missions . . . . . . . . . . . . . . . . . 2.3.3. Manned Mission Studies . . . . . . . . . . . . . 2.4. Reasons for Exploration of NEOs . . . . . . . . . . . . 2.4.1. Scientific Research . . . . . . . . . . . . . . . . 2.4.2. PHA Mitigation . . . . . . . . . . . . . . . . . 2.4.3. In-Situ Resource Utilization . . . . . . . . . . . 2.5. Reasons for Manned Missions . . . . . . . . . . . . . . 2.5.1. Increased Public Interest . . . . . . . . . . . . . 2.5.2. NEOs as a Stepping Stone toward Mars . . . . . 2.5.3. Development of Human Spaceflight Capabilities 2.5.4. Increase of Flexibility and Yield . . . . . . . . . 3. Astrodynamics for NEO Trajectories 3.1. The Two-Body-Problem . . . . . . . . . . . . . . 3.2. Specific Orbital Energy and the Vis-Viva Equation 3.3. Orbital Elements . . . . . . . . . . . . . . . . . . 3.4. The Sphere of Influence . . . . . . . . . . . . . . 3.5. Patched Conics . . . . . . . . . . . . . . . . . . . 3.6. The Lambert Problem . . . . . . . . . . . . . . .

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Contents 3.7. Earth Departure and Return Trajectories . . . . . . . . . . . . . . . 4. Baseline Design 4.1. Overview . . . . . . . . . . . . . . 4.2. Trajectory Design . . . . . . . . . 4.3. Spacecraft Configuration . . . . . . 4.3.1. Spacecraft Systems . . . . 4.3.2. Main Spacecraft Modules . 4.3.3. Propulsion Systems . . . . 4.4. Safety Considerations . . . . . . . 4.4.1. Spacecraft Systems failure . 4.4.2. Propulsive Systems Failure .

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8. Future Work 8.1. Use of Advanced Architectures for NEO Missions . . . . . . . . . . . 8.2. Implementation of Advanced Technologies . . . . . . . . . . . . . .

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A. Multilevel Mission Architecture Concept A.1. Advanced Astromechanics . . . . . . . . . . . . . . . . . . . . . . . A.1.1. ED-VEGA Maneuvers . . . . . . . . . . . . . . . . . . . . . A.1.2. The Restricted Three-Body-Problem . . . . . . . . . . . . .

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5. Results 5.1. Target availability and Mission Opportunities 5.2. Delta-v Requirements . . . . . . . . . . . . 5.3. In-LEO Mass Requirements . . . . . . . . . 5.4. Example Mission to Apophis (99942) . . . .

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6. Discussion 6.1. Increasing the Number of Mission Opportunities . 6.1.1. A Selection of Promising Targets . . . . . 6.1.2. Example Mission to 2000 SG344 . . . . . . 6.2. Alternative Reduced Mass Flyby Mission . . . . . 6.2.1. Example Flyby Missions . . . . . . . . . . 6.3. Comparison with Data from Similar Studies . . . . 6.3.1. Target Selection and Delta-v Requirements 6.3.2. Spacecraft Mass Estimation . . . . . . . . 7. Conclusion 7.1. Limited Number of Suitable Targets . . . . 7.2. Increasing the Number of Accessible NEOs 7.2.1. Identifying the Properties of Known 7.2.2. Identification of New NEOs . . . .

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Contents

A.2. A.3. A.4.

A.5.

A.1.3. The Earth Rotating Frame . . . . . . . . . . . . . . . Concept Outline . . . . . . . . . . . . . . . . . . . . . . . . Level 1 – Single Launch Mission . . . . . . . . . . . . . . . . Level 2 – Pre-launch Vehicle Utilization . . . . . . . . . . . . A.4.1. Outline and Goals . . . . . . . . . . . . . . . . . . . A.4.2. Considerations regarding Pre-launch Cargo Options . . A.4.3. Current Conclusions . . . . . . . . . . . . . . . . . . Level 3 – Deep Space Port (DSP) and Spacecraft Reusability A.5.1. Outline and Goals . . . . . . . . . . . . . . . . . . . A.5.2. Available Staging Points for a DSP . . . . . . . . . . A.5.3. NEO mission departures/arrivals from a DSP . . . . . A.5.4. Current Conclusion . . . . . . . . . . . . . . . . . . .

B. Level 1 Design – Tools and Considerations B.1. Trajectory Calculation Program . . . . . . . . . . . . . . B.1.1. Overview . . . . . . . . . . . . . . . . . . . . . . B.1.2. Verification . . . . . . . . . . . . . . . . . . . . . B.1.3. Program Limitations . . . . . . . . . . . . . . . . B.2. Anytime-Return Option . . . . . . . . . . . . . . . . . . B.3. Spacecraft Mass-estimation . . . . . . . . . . . . . . . . B.3.1. Baseline Mission Mass estimation Program . . . . B.3.2. Variations of Parameters in the Spacecraft Design B.4. Propulsion Systems Data and Calculation . . . . . . . . . B.5. PM Redundancy instead of Free-Return Option . . . . . . C. Data and Graphs C.1. Planetary Data . . . . . . . . . . . C.1.1. Bulk Parameters . . . . . . C.1.2. Orbital Parameters . . . . . C.2. NEO Search Programs . . . . . . . C.3. Target Selection Orbital Data . . . C.4. List of Available Launch Windows . C.5. Target Specific Requirements . . . C.5.1. Delta-v Requirements . . . C.5.2. In-LEO Mass Requirements

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List of Figures 2.1. View of all known objects in the Solar System. Visible accumulations of objects are the Main Belt (a), the Jupiter Trojans (a) and the Trans-Neptunian Objects (TNO) (b). . . . . . . . . . . . . . . . . . 6 2.2. NEO population within Earth proximity as of May 2011. . . . . . . . 6 2.3. Magnitude – Diameter relation for the albedo range from 0.05 to 0.25. 8 2.4. Size distribution of known NEOs. It shows that the majority of NEOs have diameters below 1 km (H ≤ 19). . . . . . . . . . . . . . . . . . 9 2.5. Simple model of forces acting on a particle on the NEO surface. . . . 9 2.6. Sum of grav. and rot. acceleration over H for different periods T . . . 11 2.7. Distribution of magnitudes and available rotation rates for known NEOs (a) and the entire population of Solar System objects (b). . . . 12 2.8. Overview of NEO discoveries, as seen in [JPL11e] . . . . . . . . . . 13 3.1. Model of the Two Body Problem. . . . . . . . . . . . . . . . . . . . 3.2. Kepler Elements describing the position of an object in space around a central Body. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. View of the orbital plane showing the in-plane Kepler elements, as well as the apsis distances rapoapsis and rperiapsis . . . . . . . . . . . . . . 3.4. Transfer Trajectories between Earth and a NEA, calculated from the Lambert Problem, with increasing transfer times dt. . . . . . . . . . 3.5. Departure trajectory passing through the SOI, showing both ∆v∞ and the actually required velocity change ∆v from the parking orbit. . . . 3.6. ∆v for departure from a 400 km parking-orbit and the resulting ∆v∞ calculated from the Oberth Maneuver 3.27. . . . . . . . . . . . . . . 3.7. Speeds at the Entry Interface (EI) resulting from a given SOI reentry speed ∆v∞ . Reentry speeds of manned and robotic missions are also shown as a reference. . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. General overview of the baseline architecture, utilizing a single spacecraft for the transfers between Earth and the target asteroid. . . . . . 4.2. Trajectory profile for a standard NEO mission with in- and outbound trajectories, including the short stay at the target asteroid. . . . . . . 4.3. Simplified flowchart of the NEO trajectory profile calculation process for a single NEO. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures 4.4. Models for habitational volume Vhab requirements over mission duration. 4.5. Basic model for determining the shielding surface for the NEO spacecraft, used to calculate the required radiation shield mass. . . . . . . 4.6. Overview of the modular spacecraft setup used in the baseline NEO mission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7. Mission profile utilizing a free-return trajectory. . . . . . . . . . . . . 4.8. Comparison of the mission profile for redundant PM and free-return options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Number of available targets below a given absolute Magnitude H. . . 5.2. Visualization of the count-value for all targets within the 2015 – 2035 time-frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Plot of the count-value restricted to targets below 21.5 magnitudes. . 5.4. Contour plot showing the ∆v requirements depending om mission duration and the departure date for all available asteroids. . . . . . . 5.5. Minimum ∆v requirements for individual departure dates and mission durations for asteroids with magnitudes below 21.5. . . . . . . . . . 5.6. Minimum ∆v plotted over dtmission for individual targets (H ≤ 21.5). The red line indicates the ∆v to achieve Earth escape from the given parking orbit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7. Minimum ∆v requirements for the NEO 2000 SG344 . . . . . . . . . . 5.8. Minimum ∆v for Apophis(99942). The launch window in 2028 overlaps with that of 2000 SG344 (Figure 5.7). . . . . . . . . . . . . . . 5.9. Contour plot of minimum in-LEO masses for all available targets. . . 5.10. Contour plot of in-LEO masses for available targets with magnitudes below 21.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11. Minimum mass requirements for individual targets with magnitudes below 21.5. The red line indicates the Payload Mass of a Saturn V. . 5.12. Minimum in-LEO mass requirements for Apophis(99942) for the entire launch window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13. Minimum in-LEO mass requirements for 2000 SG344 . . . . . . . . . . 5.14. View of the Apophis example mission in the sun-centered inertial frame. 5.15. Sun-Earth rotating frame view of the Apophis mission with Earth as the coordinate system’s origin. . . . . . . . . . . . . . . . . . . . . . 6.1. Contour plot of minimum in-LEO masses for all available targets. . . 6.2. Selection of promising targets based on size and low ∆v requirements. 6.3. Overview of minimum in-LEO mass requirements over mission duration for a selection of promising NEOs. . . . . . . . . . . . . . . . . 6.4. Trajectory for the minimum mass mission to 2000 SG344 in the suncentered inertial frame. . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures 6.5. The 2000 SG344 minimum mass mission shown in the Sun-Earth rotating frame. Coordinate origin in located at Earth. . . . . . . . . . 6.6. Contour plot of the flyby mission’s minimum in-LEO masses for all available targets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Mission Profile for the lowest mass mission to 2000 SG344 in the Sun centered frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. Mission Profile for the lowest mass mission to 2000 SG344 in the Earthcentered rotating frame . . . . . . . . . . . . . . . . . . . . . . . . 6.9. Flyby Mission Profile to 99942(Apophis) in the Sun-centered inertial frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10. Flyby Mission Profile to 99942(Apophis) in the Earth-centered rotating frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11. Contour of available launch windows with a maximum ∆v of 7.5 km/s. Marked targets show strong similarities to results in [ZM10]. . . . . . 6.12. Comparison of the baseline mass estimation model with Equation (6.1) (blue line). EM and heat-shield mass is not considered as part of the spacecraft in this comparison. . . . . . . . . . . . . . . . . . . . . . 7.1. Difference in number of total NEOs and those for which the rotation rate is known. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Yearly discovery rate of NEOs with magnitudes below 21.5. . . . . . A.1. Schematic showing the concept of the ED-VEGA maneuver. The four stages are Earth SOI departure (1), the over one year trajectory (2) and the resulting Earth flyby maneuver using SEP (3) which places the spacecraft onto its final trajectory (4). . . . . . . . . . . . . . . A.2. ∆v requirements for a departure from a 400 km parking orbit around Earth and the resulting v∞ . . . . . . . . . . . . . . . . . . . . . . . A.3. Plot of values of the Jacobi Constant CJ for the Sun-Earth System. . A.4. Plot of values of the Jacobi Constant CJ for the Earth-Moon System. A.5. Sketch showing the alignment of the 5 Libration Points within the SunEarth System in the rotating frame. This configuration also applies to the Earth-Moon and any other three body system. . . . . . . . . . A.6. Position of the masses for the three body problem for the Euler Configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7. Graphical representation of the angles α and β, used to describe the spatial orientation of a vector in the Sun-Earth rotating frame in plane (a) and out of plane (b). . . . . . . . . . . . . . . . . . . . . . . . . A.8. Outline of NEO mission possibilities within the multi-mission design. . A.9. Accessible and Inaccessible regions for departure from SEL. Angles are according to Figure A.7 in Section A.1.3. . . . . . . . . . . . . . . .

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List of Figures A.10.Departure directions of the NEO population accessible within 8.00 km/s with inaccessible regions marked red. . . . . . . . . . . . . . . . . . B.1. Detailed flowchart showing the entire trajectory profile calculation process for a given list of NEOs. . . . . . . . . . . . . . . . . . . . . . B.2. Comparison of position and velocity data of the NEO calculation program with other available sources [JPL11b]. . . . . . . . . . . . . . B.3. ∆v requirements for an Earth-Mars transfer plotted over transfer-time dt. The ∆v spike for the dt around the ideal Hohmann transfer is clearly visible. It is caused by the strong influence of the inclination between the transfer trajectory and target orbit. . . . . . . . . . . . B.4. Contingency Scenario that requires immediate return of the spacecraft to Earth (anytime-return option). . . . . . . . . . . . . . . . . . . . B.5. ∆v for the anytime-return option during the outbound transfer trajectory for the minimum mass example missions to both Apophis and 2000 SG344 in Chapters 5.4 and 6.1.2. . . . . . . . . . . . . . . . . . B.6. ∆v for the anytime-return option during the stay at the target asteroid for the example missions. . . . . . . . . . . . . . . . . . . . . . . . B.7. ∆v for the anytime-return option during the inbound transfer trajectory for the example missions. . . . . . . . . . . . . . . . . . . . . . B.8. Spacecraft mass of baseline setup (open-loop; no laundry). . . . . . . B.9. Spacecraft mass for an open-loop system with on-board laundry. . . . B.10.Spacecraft mass for a regenerative system without on-board laundry. B.11.Spacecraft mass for a regenerative system with on-board laundry. . . B.12.Direct comparison of all four setups. Pressurized volume defines where water supplies completely cover rad. shielding requirements. . . . . . B.13.Alternative Earth Reentry Option, using a dedicated module (RM) for reentry instead of the CM option in Figure B.8. . . . . . . . . . . . . B.14.Spacecraft mass without dedicated radiation shielding compared to the shielding provided in the baseline in Figure B.8. . . . . . . . . . . B.15.Per person volume identical to submarine. . . . . . . . . . . . . . . B.16.Habitable volume at the performance limit. . . . . . . . . . . . . . . B.17.Lowest volume possible (tolerable limit at a constant 5 m3 /person). . B.18.Crewsize reduced to 2 for comparison with 3 person baseline (Figure B.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.19.Crewsize increased to 4 for comparison with 3 person baseline (Figure B.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.20.Iterative calculation of the EDS masses, identical to standard calculation for a single maneuver propulsion stage. . . . . . . . . . . . . . B.21.Calculation of the PM considering the mass reduction between the ∆v2 and ∆v3 maneuvers. . . . . . . . . . . . . . . . . . . . . . . .

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102 103

104 104 105 106 107 107 108 108 109 110 111 111 112 113 113 115 116

List of Figures B.22.Bipropellant engine mass based on its thrust-to-weight ratio. . . . . . 116 B.23.Payload-ratio of EDS over a range of ∆v using the exact iterative approach and an analytical estimation. For the iterative approach a number of payload masses is used to account for the payload range between 10 and 100 metric tons. The lower graph shows the error between the iterative value (mean) and the analytical approach. . . . 117 B.24.Payload ratio of the PM, identical to Figure B.23. . . . . . . . . . . 117 B.25.Number of available targets compared to the free-return option and the entire NEO population. . . . . . . . . . . . . . . . . . . . . . . 118 B.26.Comparison between all available mission profiles and those restricted to free-return trajectories. . . . . . . . . . . . . . . . . . . . . . . . 118 B.27.Increase in minimum ∆v requirements between all available and freereturn only mission profiles for targets sorted by size (magnitude). . . 119 B.28.Count value of each individual NEO without restriction to free-return trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 B.29.Contour plot of the minimum ∆v requirements without the free-return restriction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 B.30.Plot of minimum in-LEO masses for missions with PM redundancy instead of free-return trajectories as safety feature. Results are limited to values up to 500 metric tons. . . . . . . . . . . . . . . . . . . . . 121 B.31.Contour plot for minimum in-LEO masses without safety requirements. 122 C.1. Minimum ∆v requirements for NEOs grouped by absolute magnitude; for all available mission profiles. . . . . . . . . . . . . . . . . . . . . C.2. Minimum ∆v requirements for NEOs grouped by absolute magnitude; only free-return options are considered. . . . . . . . . . . . . . . . . C.3. Minimum Mass requirements for NEO missions without additional safety requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . C.4. Minimum Mass requirements for NEO missions utilizing free-return trajectories only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.5. Minimum Mass requirements for NEO missions equipped with a redundant PM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

135 137 139 141 143

Page XV

List of Tables 2.1. Explanation of groups within the NEO population based on orbital parameters [JPL11d]. Parameters used to define these groups are: aphelion Q and perihelion q distance, the semi-major axis a and the orbital period P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Overview of past and present robotic NEO/Asteroid missions . . . .

7 14

3.1. Trajectory shapes from slices of conic sections, defined by combinations of a and e. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

4.1. 4.2. 4.3. 4.4.

Time parameters of a trajectory profile. . . . . . . . . . . . . . . . . ∆v parameters resulting from the trajectory calculations. . . . . . . . Overview of the NEO spacecraft subsystems for the baseline design. . Supply and accommodation mass requirements. All supplies include a 25% packing ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Breakdown of the EM mass. . . . . . . . . . . . . . . . . . . . . . .

33 35 36

5.1. List of Launch windows with the ten lowest ∆v requirements. . . . . 5.2. Launch windows for all targets below 21.5 magnitudes. . . . . . . . . 5.3. Breakdown of the main NEO spacecraft mass for the free-return setup (dtmission = 366 days). . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Parameters of the minimum mass mission profile to 99942(Apophis). 5.5. Overview of the spacecraft masses for the mission profile shown in Table 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48 50

6.1. List of the best launch windows for a selection of targets with in-LEO mass requirements of less than 500000 mT. . . . . . . . . . . . . . . 6.2. Parameters of the minimum mass mission profile to 2000 SG344 . . . . 6.3. Breakdown of the in-LEO spacecraft mass for the mission profile shown in Table 6.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Breakdown of the main NEO spacecraft mass for the alternative flyby mission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Parameters of the minimum mass flyby mission to 2000 SG344 . . . . . 6.6. Overview of the spacecraft masses for the mission profile shown in Table 6.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37 42

54 58 58 63 64 64 66 69 69

Page XVII

List of Tables 6.7. Parameters of the minimum mass flyby mission to 99942(Apophis). . 6.8. Overview of the spacecraft masses for the mission profile shown in Table 6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9. Comparison of available trajectory data with [LKA+ 07] in regards to departure dates and ∆v (in km/s) requirements, given for specific targets and mission durations (in days). . . . . . . . . . . . . . . . . 6.10. Comparison of minimum ∆v (in km/s) and mission duration (in days) with data from [ZM10]. Variations are caused by use of discrete departure dates and mission durations. . . . . . . . . . . . . . . . . A.1. Location of the two main co-linear Euler Libration Points in the SunEarth (SEL) and Earth-Moon (ELL) System. . . . . . . . . . . . . . A.2. Velocities resulting from departure of a DSP during an Earth flyby (h = 1000 km). The Available ∆v is the amount compared to a direct departure from a parking orbit with the same height. . . . . .

69 71

72

73 87

97

B.1. List of chemical bipropellant fuels applicable for use in the EDS and PM including the estimates for both modules, used in the calculation [WL99]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 B.2. Minimum mass requirements for both free-return redundant PM options for a selection of promising targets. . . . . . . . . . . . . . . . 121 C.1. Fact sheet describing the bulk parameters of the Sun, Earth and Moon.123 C.2. Fact Sheet describing the orbital parameters of both Earth and the Moon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 C.3. Overview of NEO search programs an their equipment, based on data from [SEL02]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 C.4. Orbital data for all 118 NEOs that have been identified as target candidates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 C.5. List of the best launch windows for a selection of targets with in-LEO mass requirements of less than 500000 mT. . . . . . . . . . . . . . . 128

Page XVIII

Symbols and Variables AU

1.496 × 108 km

Astronomical Unit – one Earth radius

G

6.67259 × 10−20 km3 /kgs2

Gravitational Constant

g

9.80665 m/s2

Earth’s gravitational constant

µ

m3 /s2

standard gravitational parameter

µ

1.327 × 1011 km3 /s2

standard gravitational parameter of the Sun

µ⊕

3.986 × 105 km3 /s2

standard gravitational parameter of Earth

q

AU or km

perihelion distance

Q

AU or km

aphelion distance

a

km or AU

semi-major axis

b

km or AU

semi-minor axis

e

–

eccentricity

i/inc

deg or rad

inclination

Ω

deg or rad

right ascension of ascending node

ω

deg or rad

argument of periapsis

θ

deg or rad

true anomaly

T /P

sec or years

orbital period

Tdeparture

–

departure date

ε

m2 /s2

specific orbital energy

H

–

absolute magnitude

JD

days

Julian Day number

v

km/s or m/s

velocity

Page XIX

Symbols and Variables v∞ / vinf

km/s or m/s

velocity outside of Sphere of Influence

ve

km/s or m/s

exhaust velocity

∆v / dv

km/s or m/s

velocity change

Isp

sec

Specific Impulse ve /g

dt

days

duration

dtmission

days

mission duration

dt1

days

outbound trajectory transfer time

dttarget

days

time spent at target NEO

dt2

days

inbound trajectory transfer time

V

m3

volume

Page XX

Acronyms and Abbreviations AU

Astronomical Unit

LEO

Low Earth Obrbit

NEO

Near-Earth Object

NEA

Near-Earth Asteroid

NEC

Near-Earth Comet

TNO

Trans-Neptunian Object

PHA

Potentially Hazardous Asteroid

MOID

Minimum Orbit Intersection Distance

NASA

North American Space Administration

JPL

Jet-Propulsion Laboratory

JAXA

Japan Space Exploration Agency

ESA

European Space Agency

CEV

Crew Exploration Vehicle

HLV

Heavy Lift Vehicle

ISRU

In-Situ Resource Utilization

ISS

International Space Station

COM

Center of Mass

RAAN

Right Ascension of Ascending Node

SOI

Sphere of Influence

EI

Entry Interface

EVA

Extravehicular Activity

SC

Spacecraft

DHCS

Data-Handling and Command System

ADCS

Attitude Determination and Control System

TCS

Thermal Control System

EPS

Electric Power System

LSS

Life-Support System

ECLSS

Environmental Control and Life-Support System

CM

Command Module

HM

Habitation Module

RM

Reentry Module

HS

Heat-Shield

PM

Propulsion Module

EDS

Earth Departure Stage

LM

Logistics Module

EM

Equipment Module

Page XXI

Acronyms and Abbreviations EMU

Extravehicular Mobility Unit

MMU

Manned Maneuvering Unit

LH

Liquid Hydrogen

LOX

Liquid Oxidizer

MMH

Monomethylhydrazine

NTO

Nitrogen Tetroxide

VEGA

Venus Earth Gravity Assist

EDVEGA

Electric Delta-VEGA

SEL

Sun-Earth Libration Point

EML

Earth-Moon Linbration Point

LOC

Loss of Crew

DSP

Deep-Space Port

SEP

Solar-Electric Propulsion

NEP

Nuclear-Electric Propulsion

mT

metric Tons

Page XXII

1. Introduction 1.1. Increase of Interest in NEOs as Targets for Manned Missions For a long time the main targets for human exploration within the solar system have been the Moon and Mars. The Moon with its close proximity to Earth offers easy access, with transfer times of only a few days between LEO and the Moon surface. This is also the reason why it is the only celestial body next to Earth that humans have set foot on. Mars, on the other hand, is considered the main goal of today’s human space exploration efforts. This is based on it’s location as Earth’s neighboring planet, and its likeliness to Earth. Next to these two established targets, another group of objects within the solar system is gaining increased interest as potential target for robotic and human space exploration missions: Near-Earth Objects (NEOs). NEOs are more easily accessible than the Moon in terms of ∆v requirements while at the same time they provide an intermediate target for an exploration road-map aimed at reaching Mars. This has caused them to be declared as a first target for human space exploration missions by US president Barack Obama. After the cancellation of the Constellation Program, he plans to send astronauts to a Near-Earth Asteroid (NEA) by the year 2025 as a precursor for manned Mars missions in the mid 2030s [Oba11].

1.2. Research Goals The aim of this study is to provide a selection of NEOs that provide promising targets for human exploration missions within the near future; in the time-frame between 2015 and 2035. For these missions a set of initial requirements and restrictions exist. Available targets are selected based on easy access and the scientific value that they provide. The on-orbit mass requirements are also taken into account and provide an additional method for selecting promising target candidates. They also allow estimating the costs associated with such missions.

Page 1

Requirements and Constraints The main goal of providing a list of likely candidate NEOs is achieved by evaluating the objects in the NEO population according to: • suitability of the NEO for human exploration • availability of mission opportunities • transfer times between Earth and the NEO • ∆v requirements of the transfer trajectories • initial in-LEO mass of the required spacecraft For a NEO to be considered as a suitable target, it must provide sufficient scientific interest and be accessible within the initially set constraints to mission duration and ∆v. The most promising targets can then be chosen based on low delta-v and in-LEO mass requirements. The accessibility of a target, based on the number of available mission opportunities also needs to be taken into account. The same applies to the exact amount of interest in the scientific exploration of a specific NEO based on its properties. NEOs that are both easily accessible and of great interest are considered ideal target candidates; while a trade-off is necessary for less favorable NEOs.

1.3. Requirements and Constraints For the type of NEO mission discussed in this research, a number of initial requirements and constraints apply. While a first human NEO mission is likely to focus on a footprint mission, this alone would not justify the associated efforts. The targeted asteroids should therefore provide sufficient interest for performing scientific research; preferably in the form of sample-return operations. This leads to additional requirements, besides sending a manned spacecraft on a round-trip mission to an arbitrary NEO. The spacecraft must be sufficiently equipped to perform scientific proximity and surface operations and to allow EVA activities. For this purpose the targeted asteroid must be chosen accordingly, as must the mission profile. This results in the following initial requirements for a human NEO mission: • time spent at the target for proximity/surface operations of ≥ 5 days • 3 person crew to allow EVA activities at the NEO • scientifically interesting target with the possibility of sample-return operations

Page 2

Introduction The constraints under which such a mission is carried out provide a basic outline for the maximum duration and ∆v requirements under which a NEO mission is to be conducted. The purpose hereby, is to eliminate unreasonably high requirements from the list of possible mission opportunities early on and to keep the mission technically feasible. The main constraints are: • total mission duration limited to one year • ∆v requirements ≤ 8.00 km/s (7.00 km/s + 1 km/s margin) • use of chemical propulsion systems for short transfer times • ballistic Earth-reentry speed not exceeding 12.00 km/s • NEOs must be accessible within the time-frame between 2015 and 2035 These requirements and constraints provide the outline for the search and evaluation of NEO target candidates in this study.

1.4. Research Outline In order to provide the data necessary for evaluating each asteroid from the NEO population, a number of steps are necessary. These steps are described in Chapters 2 to 4: Chapter 2 Provides an overview of the NEO population, including an analysis of the interest in NEO exploration in order to determine: • the number and location of known objects in the NEO population • the orbital and physical properties of NEOs (size, rotation) • reasons for (human) NEO exploration and the associated requirements Chapter 3 provides an overview of the orbital mechanics needed to compute the transfer trajectories of NEO missions. This provides the means to generate all required data for the mission profiles. This data includes departure dates, transfer times and ∆v requirements among others. Chapter 4 defines a baseline mission design that gives an overview of the mission architecture and spacecraft setup. The architecture allows determining the exact ∆v requirements based on the calculation methods in Chapter 3. The spacecraft setup provides a model for estimating the on-orbit masses needed to conduct such a mission.

Page 3

Research Outline With the target properties and mission outline defined, the data necessary to evaluate promising mission opportunities can be acquired. NEOs that do not fulfill the initial requirements are eliminated during this process. As a result, a list of possible targets for the time-frame between 2015 and 2035 can be generated. The targets can be accessed by individual mission profiles; defined by the target NEO, departure date and transfer times. Chapter 5 provides an overview of these targets and mission profiles, including the associated ∆v and in-LEO masses. Promising target candidates are then evaluated based on: • the number of launch windows and mission opportunities (accessibility) • minimal ∆v requirements • a short mission duration • low in-LEO mass requirements • the physical properties of the targeted NEO (scientific value) It is hereby discovered that the need for large target asteroids is the main influence on the number of available NEOs and mission opportunities. Chapter 6 addresses the issue of limited target availability in the 2015–2035 timeframe. By suggesting a trade-off between the initial NEO size requirement and accessibility, the number of available mission opportunities is increased at the cost of reducing scientific value. A final selection of targets based on this trade-off is then presented. In the context of some of these NEOs having reduced incentive for human exploration, an alternative flyby mission is also described; it requires less in-LEO mass making missions where the NEO surface cannot be accessed more attractive by reducing their cost. As result of the obtained data, Chapter 7 suggests methods to improve the number of available mission opportunities. This can be achieved by increasing the efforts directed toward the discovery of unknown NEOs and by preforming more detailed surveys of the currently known NEO population. As a possible option for future studies on human NEO mission, Chapter 8 mentions the design of more advanced mission concepts to further reduce in-LEO mass and therefore provide better access to a larger number of NEOs. The implementation of future technologies to the baseline mission design is also suggested as another option that can reduce spacecraft mass.

Page 4

2. NEOs as Targets for Manned Missions An object is defined as a NEO if its orbit comes within a distance of 0.3 AU to that of Earth. NEOs therefore have a perihelion distance q of less than 1.3 AU, while there is no limitation to the aphelion distance Q. [BLD+ 02]. This Chapter provides an overview of the origins and properties of NEOs. A summary of ongoing NEO research activities is also provided, and the reasons behind the interest in (human) exploration of NEOs are discussed.

2.1. Origin of NEOs The NEO population consists of a number of different objects. The two largest groups are asteroids and comets. Their origin is linked to regions in the Solar System where these types of objects have accumulated. The Main Asteroid Belt, centered around 2.7 AU, is considered the origin of most Near-Earth Asteroids (NEAs). Asteroids from this region are transferred into NEO orbits through resonance effects with the larger planets such as Jupiter and Saturn [Mor99]. The Yarkowsky effect hereby provides a continuous supply of new asteroids by slowly moving objects into the regions of these resonance effects [VF98]. The origin of Near-Earth Comets (NECs) lies beyond Neptune, in the area of the Kuiper Belt and the Scattered Disc. The objects in this region are referred to as Trans-Neptunian Objects (TNO) and are the main source of comets within the Solar System [TJL00].

2.2. The NEO Population As of May 2011 a total of 8049 NEOs have been discovered (Figure 2.2). The size of the NEO population offers a large number of potential targets for human exploration. It also indicates an increased chance of finding ideal targets within this large number of available NEOs.

Page 5

The NEO Population

(a) inner SOL System

(b) outer SOL System

Figure 2.1.: View of all known objects in the Solar System. Visible accumulations of objects are the Main Belt (a), the Jupiter Trojans (a) and the Trans-Neptunian Objects (TNO) (b).

4

4

sun

3

3

Earth Orbit

2

2

1

1

Z Axis [AU]

Y Axis [AU]

NEO pop.

0 −1

0 −1

−2

−2

−3

−3

−4 −4

−2

0 X Axis [AU]

2

4

−4 −4

−2

0 X Axis [AU]

2

Figure 2.2.: NEO population within Earth proximity as of May 2011.

Page 6

4

NEOs as Targets for Manned Missions

2.2.1. Types and Classes Asteroids, which make up the majority of the NEO population are divided into a number of groups, according to their orbital parameters [SWHW79] (Table 2.1). Table 2.1.: Explanation of groups within the NEO population based on orbital parameters [JPL11d]. Parameters used to define these groups are: aphelion Q and perihelion q distance, the semi-major axis a and the orbital period P . Group

Description

Parameters

NEC

Near-Earth Comet

NEA

Near-Earth Asteroid

q < 1.3 AU, P < 200 a q < 1.3 AU

Atira

Orbit contained completely within Earth’s orbit

Aten

Earth-crossing with a smaller than 1 AU

Apollo

Earth-crossing with a larger than 1 AU

Amor

Earth-approaching with orbits between Earth and Mars

PHA

Orbits have a Minimum Orbit Intersection Distance (MOID) with Earth

a < 1.0 AU, Q < 0.983 AU a < 1.0 AU, Q > 0.983 AU a > 1.0 AU, q < 1.017 AU a > 1.0 AU, 1.017 < q < 1.3 AU MOID ≤ 0.05 AU, H ≤ 22

Asteroids can also be divided into classes based on their spectral properties as a result of differences in their composition [CCM+ 02].

2.2.2. Absolute Magnitude H of NEOs One physical property that has a significant effect on the interest in exploration of a NEO is its size. A common method of describing the size of an object in astronomy is the absolute magnitude H. It is defined as: "[...] the visual magnitude an observer would record if the asteroid were placed 1 Astronomical Unit (AU) away, and 1 AU from the Sun at a zero degree phase angle." [JPL11a] The absolute magnitude can be converted to a diameter, assuming a spherical shape and based on how well the object’s surface reflects light (Equation 2.1) [CCM+ 02]. D = 1329 km · 10−

H/5

α−0.5

(2.1)

α hereby describes the percentage of light reflected by the surface, referred to as albedo. As it is dependent on surface properties such as structure and material

Page 7

The NEO Population composition it is not exactly known. For NEOs the albedo can range from 0.04 to 0.40 while a range of 0.05 to 0.25 can usually be assumed for most objects [JPL11a]. Figure 2.3 shows the inverse relationship between an object’s size (diameter) and the absolute magnitude, provided by Equation 2.1. 10,000 1000

Diameter [km]

100 10 1 0.1 0.01 0.001 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 absolute Magnitude [H]

Figure 2.3.: Magnitude – Diameter relation for the albedo range from 0.05 to 0.25.

Because the absolute magnitude of an object can be determined fairly easy from the apparent magnitude (known from visual observations), a look at the overall size distribution for the entire NEO population is possible (Figure 2.4).

2.2.3. NEO Rotation Rates Another property that is important in determining the suitability of a NEO for human exploration is its rotation rate. Fast-rotating objects make it difficult or impossible to perform any type of surface operations. Proximity operations around a fast-rotating asteroid also increase risks for the crew and spacecraft. Missions that require proximity and surface operations can therefore only be performed on targets that have suitable rotation rates. The problem hereby is that the rotation rates of most NEOs are unknown. It is however possible to determine a maximum rotation rate for asteroids that consist of a rubble pile structure; which can be assumed for most reasonably sized asteroids. For these objects a threshold exists above which the rotational acceleration on the asteroid’s surface is higher than the gravitational force. If the rotation rate exceeds

Page 8


number of available objects ≤ H

10,000

1,000

100

10

1 8

10

12

14

16 18 20 22 absolute Magnitude [H]

24

26

28

30

Figure 2.4.: Size distribution of known NEOs. It shows that the majority of NEOs have diameters below 1 km (H ≤ 19).

this threshold, material from the surface is accelerated away from the asteroid and it would not be able to exist as a rubble pile structure. This maximum rotation rate can be determined through a simplified model in which only the gravitational and rotational forces are taken into account (Figure 2.5):

Rotational Force

Particle on Surface

NEO Surface Gravitational Force Figure 2.5.: Simple model of forces acting on a particle on the NEO surface.

In this model a spherical asteroid with a mass M and a diameter 2R is rotating with an angular velocity ω. Its rotational period T corresponds to 2πω. M can be calculated as

Page 9

The NEO Population

4 M = ρV = ρ πr3 , 3

(2.2)

using a mean density ρ of 2.6 g/cm3 [CCM+ 02]. A particle on the asteroid’s surface has the mass m, with only gravitational (2.3) and rotational (2.4) forces acting on it.

Fgrav = −G Frot =

M ·m r2

(2.3)

4π 2 r mv 2 = mrω 2 = m 2 r T

(2.4)

The accelerations that the particle experiences are: ggrav =

GM , R2

arot = Rω 2 =

4π 2 R . T2

(2.5)

(2.6)

The gravitational acceleration ggrav is hereby directed towards the asteroid, while the rotational acceleration arot is acting in opposite direction. Their sum ∆a = ggrav − arot ,

(2.7)

is shown in Figure 2.6 for a number of different rotational periods T . Positive values for ∆a indicate rotation rates where the gravitational force is sufficient to keep the particle attached to the surface. For cases where the rotational acceleration is strong enough to launch the particle away from the object’s surface ∆a becomes negative. Figure 2.6 suggest that rubble-pile asteroids can only exist if their rotation period is longer than 2 h. Higher rates would cause such an object to be torn apart by its own rotational speed. This leads to the conclusion that in reverse, an existing rubble-pile asteroid must have a rotational period slower than 2 h. The results of this simple model correspond well with known rotation rates of asteroids (Figures 2.7a and 2.7b). Both figures show that larger objects (H ≤ 21.5) only exist when they have a rotation period above 2 hours. Since this cutoff for the asteroid size occurs at 21.5 absolute magnitudes, it indicates that asteroids above this size are almost exclusively comprised of a rubble pile structure.

Page 10

NEOs as Targets for Manned Missions 1

3h 2h

∆acceleration [mm/s 2]

0 1h 45min

1h 30min

−1 1h

−2

−3

−4

16

18

20 22 absolute magnitude − H

24

26

28

Figure 2.6.: Sum of grav. and rot. acceleration over H for different periods T .

With crew and equipment on the NEO surface experiencing the same accelerations as described by the model, matching speeds with the surface of a fast-rotating asteroid while keeping close to or on its surface is extremely difficult. Only NEOs below a magnitude of 21.5 can therefore provide some certainty that their rotating speed lies within a range that makes proximity and surface operations possible. While this does not automatically exclude all asteroids that have a larger absolute magnitude, in depth study of these objects is necessary to determine whether they allow surface access or not.

2.3. Past and Present NEO Research 2.3.1. Remote NEO Research Technological advances have made it possible to discover and study the large number of small asteroids that are orbiting the sun in close proximity to Earth. The increase in NEO search programs in recent years has led to a constant rise in the number of discovered objects. An overview of these programs and their equipment is shown in Table C.3 in Appendix C.2. A complete listing of NEO discoveries and yearly discovery rates is shown in Figure 2.8. This torrent of sightings has also increased awareness regarding possible collisions of Potentially Hazardous Asteroids (PHAs) with Earth and provides further incentive for investigating the NEO population.

Page 11

Past and Present NEO Research

Rotation Period T [h]

0.01

21.5

0.1

1

2h

10

100

1000

10,000 32

30

28

26

24

22 20 18 16 absolute Magnitude H

14

12

10

8

(a) NEO population

0.01

21.5

Rotation Period T [h]

0.1

1

2h

10

100

1000

10,000 35 33 31 29 27 25 23 21 19 17 15 13 11 9 absolute Magnitude H

7

5

3

1 −1 −3 −5

(b) All known Asteroids

Figure 2.7.: Distribution of magnitudes and available rotation rates for known NEOs (a) and the entire population of Solar System objects (b).

Page 12


(a) sum of NEO discoveries until present

(b) detailed breakdown of recent NEO discoveries

Figure 2.8.: Overview of NEO discoveries, as seen in [JPL11e]

Page 13

Reasons for Exploration of NEOs

2.3.2. Robotic Missions Next to studying NEOs via remote-sensing, research of selected asteroids and comets is conducted by robotic spacecraft. These missions allow more detailed exploration of a single object. The scope of these missions can range from flybys and impact behavior studies (Deep Impact) [Blu05],[RMAP05]; to complex proximity operations including mapping, landing and even sample-return [KFU08],[FKY+ 06]. Examples for past and present robotic missions are shown in Table 2.2. Table 2.2.: Overview of past and present robotic NEO/Asteroid missions S/C Name

Stardust

Deep Impact NEAR MUSES-C Hayabusa

Target

H

type

5535/Annefrank

14.2

flyby

81P/Wild 2

8.6

sample-return

9P/Tempel 1

13.1

flyby

9P/Tempel 1

13.1

impactor

103P/Hartley 2

14.6

flyby

433/Eros

11.16

flyby, landing

25143/Itokawa

19.2

flyby, landing, sample-return

Launch

End

1999-02-07

2011-03-25

2005-01-12

ongoing

1996-02-17

2001-02-12

2003-05-09

2010-06-13

2.3.3. Manned Mission Studies While manned missions to NEOs have not yet been performed, suggestions of using them as targets for this type of mission have been made as early as 1966. [Smi66] presented the possibility of using an upgraded Saturn V System and a modified version of the Apollo CM to perform a flyby mission of the asteroid Eros(433) during it’s close approach to Earth in 1975. A number of recent studies on manned NEOs missions are also being conducted due to the general increase of interest in NEO exploration. One example of such a study is [KLA08]; it discusses human NEO exploration possibilities using the Orion CEV and a future NASA HLV to perform such a mission.

2.4. Reasons for Exploration of NEOs Due to the immense cost associated with human spaceflight it is necessary for manned NEO exploration missions to provide sufficient incentive for conducting them. NEOs are able to fulfill this need by offering not just one, but a number of different reasons that encourage their exploration.

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2.4.1. Scientific Research The most important factor for space missions today is sufficient scientific interest in the target. This interest is provided by NEOs, as they are offer an insight into the creation and early stages of the solar system through sample-collection. Due to their relatively small size, asteroids have been preserved in a nearly unaltered form by the vacuum of space, since their creation. They provide pristine samples of material that can help to understand these early stages of the Solar System as well as its creation. Impacts of asteroids and comets on the young Earth have also been traced as an origin of carbonaceous matter and complex structures which formed the building blocks for life [CKB+ 01], [NZT+ 02], [Whi97].

2.4.2. PHA Mitigation Information about composition and properties of NEOs gathered during NEO exploration missions can also be used to develop methods for dealing with PHAs more effectively. Structure, shape, mass and composition of an asteroid are crucial when confronted with a potential impact threat and the more information is available on a PHA, the better a mitigation can be achieved. NEO missions can not only provide the means to gather the necessary data, but also provide a chance to test various mitigation strategies on a similar object first hand [SS04], [H+ 09], [Bel04].

2.4.3. In-Situ Resource Utilization Another possibility provided by NEO exploration is in-situ resource utilization (ISRU). ISRU is considered a key technology for establishing and sustaining human presence within the Solar System. Extensive research for applications on the Moon and Mars is already being conducted [TSCN05], [SFK00]. Application of ISRU at asteroids would further extend the use of of this technology to a group of targets that is widely available throughout the Solar System. Access to these objects is also provided more easily than to planetary bodies due to the lack of a strong gravitational field. This can be applied towards establishing a base of operations on Phobos and Deimos, in preparation of human exploration missions to the surface of Mars [Lee07].

2.5. Reasons for Manned Missions "Robotic missions are much cheaper and may provide more scientific information, but they don’t catch the public imagination in the same way

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Reasons for Manned Missions [as manned missions], and they don’t spread the human race into space, which I’m arguing should be our long-term strategy. [...] If the human race is to continue for another million years, we will have to boldly go where no one has gone before." [Haw08] This quote by Stephen Hawking mentions some of the main reasons that promote conducting manned missions. These reason are listed in the following:

2.5.1. Increased Public Interest High public interest makes it more likely for a specific mission to be considered as a promising endeavor by governments; providing increased funding to space agencies for realizing and sustaining space programs. Human exploration that reaches out beyond LEO hereby has the potential to provide public interest similar to the Apollo Moon Missions. They can also be realized earlier than Mars and would provide a continuous stream of new missions; sustaining public interest over a long period of time and climaxing in the first human mission to the surface of Mars.

2.5.2. NEOs as a Stepping Stone toward Mars With current human exploration efforts considering Mars as the final goal, NEOs provide an intermediate stepping stone for developing technologies needed for future missions that go beyond LEO. At the same time access to the NEO population is provided, as an additional group of targets for human exploration. While the Moon has always been considered a stepping stone towards Mars, its location within Earth’s gravitational influence results in completely different mission approaches. Unlike the transfer to Mars, which takes around 250 days [BB91], a Moon transfer can be performed in under five days [BMW71]. NEOs with their heliocentric orbits require transfer trajectories that are similar to those of a transit to Mars, both in duration and the traversed space environment. The need for payload and equipment is also reduced, because no surface habitats or ascend/descend vehicles are required for NEO missions; only the transfer spacecraft is needed. This reduces over-all system mass and shortens development time. At the same time the spacecraft systems that are developed for NEO missions can be used for the transfers between Mars and Earth with no or little alterations because of the similarity in space-environment.

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2.5.3. Development of Human Spaceflight Capabilities NEO missions do not just provide the option to develop human spaceflight technology; they also offer a chance to gradually increase experience with human deep space missions. Opportunities to accumulate data and experience with long-term missions under parameters similar to Mars transfers are also available. Advancing the experience with EVA and servicing under the conditions of long-duration missions is a step beyond the current operations at the ISS and essential for reaching out further into the Solar System, where these types of operations will be needed regularly.

2.5.4. Increase of Flexibility and Yield While the presented quote [Haw08] suggests that robotic missions usually provide more scientific data, the presence of a human crew has the potential to significantly increase the flexibility and yield of a scientific mission. Especially for sample-return missions the human ability to quickly adapt to new situations can be beneficial when maneuvering around or on the surface of an asteroid. The crew can decide on-site, which areas are of the most interest and at which locations samples should be taken. Performing real-time robotic operations at the target asteroid can also be improved, as time-lag is reduced to the point where real-time telecommanding becomes possible. This time-lag is the reason why robotic missions from Earth need to rely so heavily on autonomous spacecraft, limiting them in terms of flexibility. By increasing this flexibility due to the presence of a human crew, both the yield and quality of samples and science data can be significantly increased. [KLA08].

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3. Astrodynamics for NEO Trajectories This chapter discusses the basic orbital mechanics behind the calculation of orbits and transfer trajectories necessary for NEO missions. The large number of individual objects in the NEO population requires calculating each transfer trajectory individually. Detailed explanations of the computational methods used in this study can can be found in [BMW71], [Not98], [Cur05] and [Wal08]. They provide the basis of the calculations presented in this chapter.

3.1. The Two-Body-Problem The Two-Body Problem (2BP) describes the motion of two bodies under the influence of their gravitational forces acting on each other. It is used to describe the motion of objects on orbits around a large main body. Examples for this are the movement of planets, asteroids and spacecraft around the Sun or the movement of satellites around a planet.

M

F1 F2

r r1

m r2 X

Figure 3.1.: Model of the Two Body Problem.

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The Two-Body-Problem For a main body and a secondary body (Figure 3.1), with the respective masses M and m the vector r between them can be written as r = r2 − r1 .

(3.1)

The forces acting on each body as a result of the others gravitational influence F1 and F2 can be described as

GM m r, r3 GM m F 2 = m¨ r2 = − 3 r . r

F 1 = M r¨1 =

(3.2) (3.3)

This is based on Newton’s third law (3.4) and the universal law of gravitation (3.5):

m¨ r=

X

Fj ,

(3.4)

Mm . r2

(3.5)

j

F =G

Subtracting (3.3) and (3.2) from each other results in r¨ = −

µ G (M + m) r = − 3r . 3 r r

(3.6)

Written as r¨ +

µ r = 0, r3

(3.7)

it becomes the two-body equation of motion. The standard gravitational parameter µ is hereby substituted for G (m1 + m2 ) [BMW71]. In cases where M m , m can be omitted and µ becomes µ = G (M + m) ≈ GM .

(3.8)

This simplification is frequently used and provides accurate results for cases where the mass of the secondary body is negligible. It applies to the motion of planets around the Sun and to spacecraft orbiting planets. This special case of the 2BP is referred to as the Restricted 2BP (R2BP). Hereby, the center of mass (COM) of the two-body

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Astrodynamics for NEO Trajectories system lies in the COM of the main body. The position vector r between the primary and secondary body becomes equal to the distance of the secondary body from the system’s COM.

3.2. Specific Orbital Energy and the Vis-Viva Equation Based on the conservation of energy X

Eji = const ,

(3.9)

all energy forms j of all bodies i

the sum of kinetic and potential energy

1 Ekin = mv 2 , 2 µ Epot = U (r) = − m , r

(3.10) (3.11)

results in the specific orbital energy of an object within a spherical gravitational field:

ε=

v2 µ − . 2 r

(3.12)

This specific energy remains constant; unless additional energy is added or subtracted to the system. This is achieved through propulsive maneuvers which add a given amount of ∆v. Other influences are friction, caused by atmospheric drag and solar radiation pressure. These are not considered in the calculations performed in this study. Solving (3.12) for the velocity v and substituting ε with −µ/2a results in the vis-viva equation [Wal08]: s 2 1 v= µ − . r a

(3.13)

a refers to the semi-major axis of the secondary object’s orbit around the main body (see Section 3.3).

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Orbital Elements

3.3. Orbital Elements The three-dimensional state vectors of an object for position and velocity (r, v) can be used to define the exact position and orbit of an object moving around a central body. Another common set that also consists of six parameters are the Kepler Elements. They provide a better graphic representation of the orbit and object position and are therefore commonly used to describe the location of planets and spacecraft around a central body (Figure 3.2). k

Body Periapsis h a

r e

Orbital Plane

θ i ω Ω

Ecliptic Plane i Line of Nodes i

j

^

Figure 3.2.: Kepler Elements describing the position of an object in space around a central Body.

Three of these elements describe the orientation of the orbital plane. For heliocentric orbits this is done relative to the ecliptic, which is located in the x, y plane. The x-Axis hereby points towards the vernal equinox . For Earth orbiting objects the equatorial plane is used as the x, y plane. The three elements describing the orbit’s orientation are: right ascension of ascending node (RAAN) Ω : Angle between the origin of the coordinate system, pointing towards the vernal equinox and the upward moving node of the line of nodes.

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Astrodynamics for NEO Trajectories inclination i : Angle of the orbital plane, relative to the reference. Corresponds to the angle between z-Axis of the heliocentric/equatorial coordinate system and the orbit’s angular momentum vector h = r × v. argument of periapsis ω : Angle between the line of nodes facing the ascending node and the periapsis rp of the orbit. The orbit shape is described by two additional elements: semi-major axis a : The length measured from the center of an ellipse to its farthest edge (Figure 3.3). The shorter side is called the semi-minor axis b. eccentricity e : The eccentricity is defined as µ µe = v 2 − r − (r · v) v , (3.14) r Together with a, it describes the actual shape of the path in the orbital plane (Table 3.1).

b

r θ

a rapoapsis

rperiapsis

Figure 3.3.: View of the orbital plane showing the in-plane Kepler elements, as well as the apsis distances rapoapsis and rperiapsis .

Table 3.1.: Trajectory shapes from slices of conic sections, defined by combinations of a and e.

Shape

semi-major axis – a

eccentricity – e

Circle

= br

0

Ellipse

>0

0