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Evasion Maneuvers with Double Lunar Flyby for Interplanetary Missions

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Evasion Maneuvers with Double Lunar Flyby for Interplanetary Missions POLITECNICO DI TORINO Department of Mechanical and Aerospace Engineering Master degree course in Aerospace Engineering Master Degree Thesis Evasion maneuvers with double lunar flyby for interplanetary missions Supervisor Candidate Lorenzo Casalino Sebastiano Bugno Matricola: 239257 Academic Year 2017-2018 Acknowledgements I would first like to thank my thesis advisor Professor Lorenzo Casalino of the Mechanics and Aerospace department (DIMEAS) at Politecnico of Turin. I owe him a special thanks, because he was always available for every problem or doubt about this thesis and his help it was essential for the success of the work. In addition, I must express my very profound gratitude to my family for providing me with unfailing support and continuous encouragement throughout my years of study and for the moving to Turin. This accomplishment would not have been possible without them. Thank you so much. Contents List of Figures iii List of Tables v 1 Introduction 1 2 Evasion maneuvers 3 2.1 Short background on interplanetary missions................3 2.2 Escape......................................5 2.3 Flyby......................................8 3 Approximate analytical approach 11 3.1 Introduction................................... 11 3.2 Trajectory analysis............................... 12 3.2.1 Moon to Escape............................ 13 3.2.2 Moon to Moon............................. 13 3.2.3 Perigee to Moon............................ 15 3.3 Calculations................................... 16 4 Exact numerical solution 19 4.1 Solution description.............................. 19 4.2 Equations.................................... 22 4.3 Perturbations.................................. 23 4.3.1 Earth asphericity............................ 24 4.3.2 LuniSolar perturbation......................... 24 4.3.3 Solar radiation pressure........................ 26 5 Approximate analytical approach results 27 5.1 Features..................................... 27 5.2 Case 0 (comparison between exact and approximated solution)...... 29 5.3 Comparison between solutions with the same escape date......... 34 5.4 Comparison between solutions with the same V∞ .............. 38 i 6 Exact numerical solution results 43 6.1 Comparison between solutions with the same escape date......... 43 6.2 Comparison between solutions with the same V∞ .............. 49 6.3 Comparison between exact and approximated solutions........... 54 6.3.1 Case 2.................................. 54 6.3.2 Case 4.................................. 57 6.3.3 Case 5.................................. 60 6.3.4 Case 6.................................. 63 7 Conclusions 67 Glossary 70 Bibliography 71 ii List of Figures 2.1 Hohmann transfer from inner planet 1 to outer planet 2 [4]........5 2.2 Departure of a spacecraft on a mission from an inner planet to an outer planet [4]....................................6 2.3 Trailing-side planetary flyby [4]........................9 2.4 Changes in the inclination angle of the spacecraft orbit as result of gravity assist maneuver [8]............................... 10 3.1 Lunar escape trajectory with backflip..................... 11 3.2 Approximate analytical solution, 3D view.................. 12 3.3 Approximate analytical solution, XY plane................. 14 3.4 Position at the flyby, with respect to the Moon............... 17 4.1 Software solution output............................ 21 4.2 Schematic geometry of gravitational perturbations [5]............ 25 5.1 Asteroid 2008 EV5’s orbit (white) compared with the nearest planets, in the heliocentric reference system [14]..................... 28 5.2 3D visual of the asteroid and Earth orbit in the heliocentric reference system [14].................................... 29 5.3 Zoom on FB1, comparison between exact and approximate solution.... 31 5.4 Zoom on FB2, comparison between exact and approximate solution.... 32 5.5 Comparison between exact and approximate solution, Case 0....... 34 5.6 Comparison between solutions with the same escape date......... 38 5.7 Comparison between solutions with the same V∞ .............. 42 6.1 Comparison between solutions as the V∞ varies, 3D view......... 47 6.2 Comparison between solutions as the V∞ varies, XY view......... 48 6.3 Comparison between solutions as the V∞ varies, YZ view......... 48 6.4 Comparison between solutions as the escape date varies, 3D view..... 52 6.5 Comparison between solutions as the escape date varies, XY view..... 53 6.6 Comparison between solutions as the escape date varies, YZ view..... 53 6.7 Comparison between exact and approximate solution, Case 2....... 57 6.8 Comparison between exact and approximate solution, Case 4....... 60 6.9 Comparison between exact and approximate solution, Case 5....... 63 6.10 Comparison between exact and approximate solution, Case 6....... 66 iii List of Tables 5.1 Escape conditions................................ 28 5.2 Comparison of S/C-Moon positions at the two flybys between exact and approximate solution.............................. 30 5.3 Comparison of relative positions at the two flybys between exact and ap- proximate solution............................... 30 5.4 Comparison of S/C positions between exact and approximate solution.. 31 5.5 Time comparison between exact and approximate solution......... 32 5.6 Comparison of orbital parameters between exact and approximate solution, part 1...................................... 32 5.7 Comparison of orbital parameters between exact and approximate solution, part 2...................................... 33 5.8 Energy comparison between exact and approximate solution........ 33 5.9 Comparison of S/C-Moon positions at the two flybys between solutions with the same escape date........................... 34 5.10 Comparison of relative positions at the two flybys between solutions with the same escape date.............................. 35 5.11 Comparison of S/C positions between solutions with the same escape date 36 5.12 Time comparison between solutions with the same escape date...... 36 5.13 Comparison of orbital parameters between solutions with the same escape date, part 1................................... 37 5.14 Comparison of orbital parameters between solutions with the same escape date, part 2................................... 37 5.15 Energy comparison between solutions with the same escape date..... 38 5.16 Comparison of S/C-Moon positions at the two flybys between solutions with the same V∞ ............................... 39 5.17 Comparison of relative positions at the two flybys between solutions with the same V∞ .................................. 39 5.18 Comparison of S/C positions between solutions with the same V∞ .... 40 5.19 Time comparison between solutions with the same V∞ ........... 40 5.20 Comparison of orbital parameters between solutions with the same V∞, part 1...................................... 40 5.21 Comparison of orbital parameters between solutions with the same V∞, part 2...................................... 41 5.22 Energy comparison between solutions with the same V∞ .......... 41 v 6.1 Mass and times as the V∞ varies....................... 43 6.2 Comparison of the periselenium radius at the 2 flybys........... 44 6.3 Comparison of S/C-Moon positions at the two flybys............ 44 6.4 Adimensional spherical coordinates of the S/C in points of particular in- terest as the V∞ varies............................. 45 6.5 Adimensional velocities of the S/C in points of particular interest as the V∞ varies.................................... 46 6.6 Initial and final semi-axis and energy..................... 46 6.7 Mass and times as the date of escape varies................. 49 6.8 Comparison of the periselenium radius at the 2 flybys........... 49 6.9 Comparison of S/C-Moon positions at the two flybys............ 50 6.10 Adimensional spherical coordinates of the S/C in points of particular in- terest as the date of escape varies....................... 51 6.11 Adimensional velocities of the S/C in points of particular interest as the date of escape varies.............................. 51 6.12 Initial and final semi-axis and energy..................... 52 6.13 Comparison of S/C-Moon positions at the two flybys between exact and approximate solution.............................. 54 6.14 Comparison of relative positions at the two flybys between exact and ap- proximate solution............................... 54 6.15 Comparison of S/C positions between exact and approximate solution.. 55 6.16 Time comparison between exact and approximate solution......... 55 6.17 Comparison of orbital parameters between exact and approximate solution, part 1...................................... 55 6.18 Comparison of orbital parameters between exact and approximate solution, part 2...................................... 56 6.19 Energy comparison between exact and approximate solution........ 56 6.20 Comparison of S/C-Moon positions at the two flybys between exact and approximate solution.............................. 57 6.21 Comparison of relative positions at the two flybys between exact and ap- proximate solution............................... 58 6.22 Comparison of S/C positions between exact and approximate solution.. 58 6.23 Time comparison between exact and approximate solution......... 58 6.24 Comparison of orbital parameters between exact and approximate solution, part 1...................................... 59 6.25 Comparison of orbital parameters between exact and approximate solution, part 2.....................................
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