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Orbital Dynamics of Space Nuclear Propulsion

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Orbital Dynamics of Space Nuclear Propulsion ORBITAL DYNAMICS OF SPACE NUCLEAR PROPULSION SYSTEMS by LARA SCHOEFFLER Submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical and Aerospace Engineering CASE WESTERN RESERVE UNIVERSITY May 2021 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Lara Schoeffler candidate for the degree of Master of Science* Committee Chair Dr. Paul J. Barnhart Committee Member Dr. Yasuhiro Kamotani Committee Member Dr. Sunniva Collins Committee Member Dr. James Gilland Date of Defense 3/19/2021 *We also certify that written approval has been obtained for any proprietary material contained therein. 2 TABLE OF CONTENTS TABLES ................................................................................................................................ 5 FIGURES ............................................................................................................................... 7 NOMENCLATURE .................................................................................................................. 9 ABSTRACT ......................................................................................................................... 10 I. INTRODUCTION ............................................................................................................... 11 II. METHOD OF ANALYSIS .................................................................................................. 15 A. Derivation of Equations ............................................................................................ 15 B. Numerical Methodology Capabilities ....................................................................... 28 1) Orbits with No Applied Thrust ............................................................................. 29 2) Comparisons of Numerical and Exact Results...................................................... 40 3) Outbound Circular Spiral Orbit with Applied Thrust ........................................... 44 4) Inbound Circular Spiral Orbit with Applied Thrust .............................................. 46 5) Radial Thrust Orbit ............................................................................................... 48 C. Test Cases ................................................................................................................. 51 1) Test Case One: Circumferential Earth Escape ...................................................... 51 2) Test Case Two: Tangential Earth Escape ............................................................. 55 3) Test Case Three: NASA Dawn Mission ............................................................... 59 4) Test Case Four: Jupiter Transit ............................................................................. 64 III. MISSION ANALYSIS ...................................................................................................... 71 A. Electric Propulsion .................................................................................................... 71 B. Nuclear Thermal Propulsion ..................................................................................... 86 C. Nuclear Fusion Propulsion ...................................................................................... 102 IV. RESULTS AND DISCUSSION ........................................................................................ 133 V. CONCLUSION ............................................................................................................... 139 VI. FUTURE WORK .......................................................................................................... 143 APPENDIX A: DERIVATION OF THE TWO-BODY PROBLEM ............................................... 145 3 APPENDIX B: INITIAL CONDITIONS FOR MISSION ANALYSIS CALCULATIONS .................. 156 APPENDIX C: MATLAB CODE FOR ORBITAL DYNAMICS CALCULATIONS ...................... 164 BIBLIOGRAPHY ................................................................................................................ 169 4 TABLES Table 1: Initial conditions for a circular orbit with no thrust ............................................ 31 Table 2: Initial conditions for an elliptical orbit with low eccentricity and no thrust....... 33 Table 3: Initial conditions for an elliptical orbit with high eccentricity and no thrust ..... 34 Table 4: Initial conditions for a parabolic orbit with no thrust ......................................... 37 Table 5: Initial conditions for a hyperbolic orbit with no thrust ....................................... 38 Table 6: Initial conditions for an elliptic orbit with no thrust ........................................... 41 Table 7: Orbit characteristics for exact radius calculations .............................................. 42 Table 8: Initial conditions for an outbound spiral orbit with applied thrust ..................... 44 Table 9: Initial conditions for an inbound spiral orbit with applied thrust ....................... 47 Table 10: Initial conditions for a radial thrust orbit .......................................................... 49 Table 11: Initial conditions for circumferential, circular Earth escape orbit .................... 52 Table 12: Comparison of circumferential escape trajectories ........................................... 52 Table 13: Comparison of dimensional and non-dimensional orbit characteristics ........... 54 Table 14: Initial conditions for tangential, circular Earth escape orbit ............................. 55 Table 15: Comparison of tangential escape trajectories ................................................... 56 Table 16: Comparison of dimensional and non-dimensional orbit characteristics ........... 58 Table 17: Dawn mission spacecraft characteristics [4]..................................................... 61 Table 18: Initial conditions for Mars trajectory ................................................................ 62 Table 19: Comparison of Mars trajectories ...................................................................... 63 Table 20: Known Jupiter mission characteristics [5] ........................................................ 67 Table 21: Assumed Jupiter mission characteristics .......................................................... 68 Table 22: Initial conditions for Jupiter trajectory ............................................................. 68 Table 23: Comparison of Jupiter trajectories .................................................................... 69 Table 24: Performance characteristics of conceptual nuclear electric propulsion system 75 Table 25: NEP flight characteristics after interplanetary flight and arrival at Mars ......... 76 Table 26: NEP flight characteristics for Mars arrival flight ............................................. 78 Table 27: NEP Mars escape flight leg of mission............................................................. 79 Table 28: NEP flight characteristics after interplanetary flight and arrival at Earth ........ 81 Table 29: NEP flight characteristics for Earth arrival flight ............................................. 83 Table 30: Final mission characteristics for NEP mission to Mars .................................... 85 Table 31: Performance characteristics of conceptual nuclear thermal propulsion system 88 Table 32: NTP Earth escape flight leg of Mars mission ................................................... 89 Table 33: NTP spacecraft flight characteristics upon reaching the edge of Earth's sphere of influence ....................................................................................................................... 91 Table 34: NTP flight characteristics after interplanetary flight and arrival at Mars ......... 92 Table 35: NTP flight characteristics for Mars arrival flight ............................................. 94 Table 36: NTP Mars escape flight leg of mission............................................................. 95 Table 37: NTP spacecraft flight characteristics upon reaching the edge of Mars’ sphere of influence ............................................................................................................................ 97 Table 38: NTP flight characteristics after interplanetary flight and arrival at Earth ........ 98 Table 39: NTP flight characteristics for Earth arrival flight ........................................... 100 Table 40: Mission characteristics for NTP mission to Mars........................................... 101 Table 41: Performance characteristics of conceptual fusion propulsion system [14] .... 103 Table 42: Nuclear fusion Earth escape flight leg of Mars mission ................................. 105 5 Table 43: Nuclear fusion spacecraft flight characteristics upon reaching the edge of Earth's sphere of influence .............................................................................................. 107 Table 44: Nuclear fusion flight characteristics after interplanetary flight and arrival at Mars ................................................................................................................................ 108 Table 45: Nuclear fusion flight characteristics for Mars arrival flight ........................... 110 Table 46: Nuclear fusion Mars escape flight leg of mission .......................................... 111 Table 47: Nuclear fusion spacecraft flight characteristics upon reaching the edge of Mars’ sphere of influence .........................................................................................................
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