Development and Optimization of Low Energy Orbits for Advancing Exploration of the Solar System Item Type text; Electronic Thesis Authors Kidd, John Nocon Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 24/09/2021 01:16:00 Link to Item http://hdl.handle.net/10150/560837 DEVELOPMENT AND OPTIMIZATION OF LOW ENERGY ORBITS FOR ADVANCING EXPLORATION OF THE SOLAR SYSTEM by John N. Kidd Jr. ____________________________ A Thesis Submitted to the Faculty of the SYSTEMS AND INDUSTRIAL ENGINEERING DEPARTMENT In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE In the Graduate College THE UNIVERSITY OF ARIZONA 2015 1 STATEMENT BY AUTHOR This thesis has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: John N. Kidd Jr. APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: 04/28/2015 Roberto Furfaro Date Assistant Professor of Systems and Industrial Engineering 2 Table of Contents Table of Contents .......................................................................................................................................... 3 List of Figures ............................................................................................................................................... 6 List of Tables .............................................................................................................................................. 12 Abstract ....................................................................................................................................................... 13 1. Introduction ........................................................................................................................................ 14 1.1. Circular Restricted Three Body Problem .................................................................................... 16 1.1.1. Introduction ......................................................................................................................... 16 1.1.2. Transformation between inertial and rotating systems ....................................................... 18 1.1.3. Gravitational Potential ........................................................................................................ 20 1.1.4. Equations of Motion............................................................................................................ 21 1.1.5. Energy Integral and Jacobi Constant................................................................................... 25 1.1.6. Energy Surface, Equilibrium Points, and the Realms of Possible Motion .......................... 25 1.1.7. Existence of Periodic Orbits near Libration Points ............................................................. 29 1.2. A Brief History of Missions Utilizing the Three Body Problem ................................................ 39 1.2.1. The ISEE-3 Mission ............................................................................................................ 39 1.2.2. SOHO Mission .................................................................................................................... 50 1.2.3. ACE and WIND Missions ................................................................................................... 53 2. System Architecture ........................................................................................................................... 59 2.1. System Elements ......................................................................................................................... 60 2.2. System Architecture Development ............................................................................................. 62 3 3. Methodology ...................................................................................................................................... 65 3.1. Introduction ................................................................................................................................. 65 3.2. Tools ........................................................................................................................................... 66 3.2.1. MAnE .................................................................................................................................. 66 3.2.2. MDTOP ............................................................................................................................... 67 3.2.3. MATLAB ............................................................................................................................ 67 3.2.4. GMAT ................................................................................................................................. 67 3.3. Interplanetary Transfers .............................................................................................................. 68 3.4. Implementing High Energy Orbits .............................................................................................. 69 3.5. Nonlinear Optimization............................................................................................................... 70 3.6. Multiple Shooting Method .......................................................................................................... 71 3.7. Designing the Staging Orbit ........................................................................................................ 74 3.7.1. Single Lunar Swingby ......................................................................................................... 74 3.8. End – to – End Optimization....................................................................................................... 82 4. Results ................................................................................................................................................ 83 4.1. Baseline Parking Orbit Design .................................................................................................... 83 4.2. Cis-Lunar Exploration and Initial Architecture .......................................................................... 86 4.2.1. Characterization of the BPO ............................................................................................... 86 4.2.2. Lunar Surface Exploration .................................................................................................. 93 4.3. Mars Exploration ........................................................................................................................ 98 4.3.1. Earth-Mars Transfer Orbit ................................................................................................ 100 4 4.4. Methods to Depart Earth-Moon System ................................................................................... 106 4.5. Possible Mars Proximity Operations ......................................................................................... 110 5. Discussion and Conclusion .............................................................................................................. 116 5.1. Future Work .............................................................................................................................. 119 References ................................................................................................................................................. 121 5 List of Figures Figure 1: CRTBP Rotating Reference Frame with the orbital plane contained within the page while the Z axis is oriented out of the page.................................................................................................................... 17 Figure 2: CRTBP system normalized. ........................................................................................................ 18 Figure 3: CRTBP Rotational coordinate system with respect to the inertial coordinate system of the Barycenter of the m1-m2 system. ................................................................................................................. 19 Figure 4: The location of the five equilibrium points, L1, L2, L3, L4, and L5, of the CRTBP for a system of M1 and M2, with example Lagrangian orbits illustrated [5]. ....................................................................... 28 Figure 5: The 5 unique cases for the Hill sphere of the CRTBP [5]. .......................................................... 29 Figure 6: Projection onto the η-ξ plane [5]. ...............................................................................................