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Copyright by Nadege Pie 2008 Copyright by Nadege Pie 2008 The Dissertation Committee for Nadege Pie certifies that this is the approved version of the following dissertation: Mission Design Concepts for Repeat Groundtrack Orbits and Application to the ICESat Mission Committee: _________________________________ Bob E. Schutz, Supervisor _________________________________ Srinivas V. Bettadpur _________________________________ George H. Born _________________________________ Wallace T. Fowler _________________________________ David G. Hull Mission Design Concepts for Repeat Groundtrack Orbits and Application to the ICESat Mission by Nadege Pie, Diplôme d’Ingénieur, M.S. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin December 2008 A ma Maman, pour ses sacrifices, sa patience, sa confiance et son amour … Acknowlegements I want to thank Dr. Bob E. Schutz for taking me under his wing exactly six years ago when I stepped into his office in search of an advisor. I have learned so much under his supervision, as a scientist but also as a person, that I know these six years will always stand out as a corner stone in my professional and personal life. I also want to express my deep gratitude to all my committee members for their support and encouragements. I knew I could always count on them when I needed their help, even when I lacked the discernment to ask for it. I also want to thank Charles Webb, Dr. Giacaglia, Dr. Lara and Dr. Klokočník for the invaluable discussions we had. And above all I want to thank my mother Monique, my family, my friends and all those who gave me love and the courage not to give up. v Mission Design Concepts for Repeat Groundtrack Orbits and Application to the ICESat Mission Nadège Pie, PhD. The University of Texas at Austin, 2008 Supervisor: Bob E. Schutz The primary objective of the NASA sponsored ICESat mission is to study the short and long term changes in the ice mass in the Greenland and Antarctica regions. The satellite was therefore placed into a frozen near-polar near-circular repeat groundtrack to ensure an adequate coverage of the polar regions while keeping the groundtrack periodic and reducing the variations in the orbital elements, and more specifically the semi-major axis of the ICESat orbit. After launch, a contingency plan had to be devised to compensate for a laser that dangerously compromised the lifetime of the ICESat mission. This new plan makes an intensive use of the ICESat subcycles, a characteristic of the repeat groundtrack orbits often over-looked. The subcycle of a repeat groundtrack orbit provide global coverage within a time shorter than the groundtrack repetition period. For a satellite with an off-nadir pointing capacity, the subcycles provide near-repeat tracks vi which represents added opportunity for altimetry measurement over a specific track. The ICESat subcycles were also used in a very innovative fashion to reposition the satellite within its repeat cycle via orbital maneuvers called phasing maneuver. The necessary theoretical framework is provided for the subcycle analysis and the implementation of phasing maneuvers for any future repeat orbit mission. In the perspective of performing cross-validation of missions like CryoSat using the ICESat off-nadir capacity, a study was conducted to determine the geolocations of crossovers between two different repeat groundtrack Keplerian orbits. The general analytical solution was applied to ICESat vs. several other repeat groundtrack orbit mission, including the future ICESat-II mission. ICESat’s repeat groundtrack orbit was designed using a disturbing force model that includes only the Earth geopotential. Though the third body effect from the Sun and the Moon was neglected in the orbit design, it does in fact disrupt the repeatability condition of the groundtrack and consequently implies orbit correction maneuvers. The perturbations on ICESat orbit due to the third body effect are studied as a preliminary work towards including these forces in the design of the future ICESat-II repeat groundtrack orbit. vii Table of Contents Acknowledgments v Abstract vi List of Figures xii List of Tables xvii CHAPTER 1: The ICESat Missions .................................................................... 1 1.1 The first ICESat Mission........................................................................ 1 1.1.1 Mission Description................................................................... 1 1.1.2 Orbit Requirements.................................................................... 3 1.2 Future ICESat Missions......................................................................... 4 1.2.1 Mission Objectives..................................................................... 4 1.2.2 Orbit Considerations.................................................................. 5 CHAPTER 2: Repeat groundtrack Orbits: Concept and Generation.............. 7 2.1 Background of Repeat Groundtrack Orbit Missions.............................. 7 2.2 General Characteristics of Repeat Groundtrack Orbits.......................... 10 2.3 Generation of Repeat Groundtrack Orbits in Full Geopotential............ 12 2.3.1 SADSaM.................................................................................... 13 2.3.2 Alternate Method....................................................................... 16 viii 2.4 ICESat Repeat Groundtrack Orbits........................................................ 21 2.5 Motivation and Outline of Work…........................................................ 23 CHAPTER 3: Subcycles........................................................................................ 26 3.1 Definitions............................................................................................... 27 3.1.1 Repeat Cycle............................................................................... 27 3.1.2 Near-Repeat Groundtracks.......................................................... 30 3.1.3 Subcycles.................................................................................... 34 3.2 Subcycles of the Three ICESat Repeat Orbits........................................ 38 3.3 Properties of the Chart of Subcycles....................................................... 42 3.3.1 Bounded Distribution.................................................................. 42 3.3.2 Symmetrical Distribution............................................................ 43 3.3.3 Linear Distribution...................................................................... 44 3.3.4 Subcycle Combination................................................................ 47 3.4 ICESat’s Sequence of Subcycles............................................................ 49 3.5 Influence of the Parameter N................................................................... 51 3.5.1 ICESat-II Repeat Orbit................................................................ 52 3.5.2 The Bezout Theorem................................................................... 55 CHAPTER 4: Phasing........................................................................................... 60 4.1 Definitions.............................................................................................. 61 4.1.1 Transition Orbit........................................................................... 62 4.1.2 Transition Opportunities............................................................. 66 ix 4.2 Number of Transition Opportunities...................................................... 71 4.3 Advantages............................................................................................. 74 CHAPTER 5: Crossovers...................................................................................... 80 5.1 Crossover Location Between Two Orbits.............................................. 83 5.1.1 Implicit Function......................................................................... 83 5.1.2 Explicit Function......................................................................... 87 5.2 Angle Between Tracks........................................................................... 92 5.3 Application to ICESat and CryoSat....................................................... 93 5.4 Application to ICESat and ENVISAT................................................... 101 5.5 Application to ICESat and ICESat-II..................................................... 109 CHAPTER 6: Third Body Perturbations............................................................ 112 6.1 Single-Average Disturbing Function...................................................... 113 6.2 Equations of Motion................................................................................ 122 6.3 Application to a Simplified Case............................................................ 127 6.4 Double-Average Disturbing Function..................................................... 138 6.5 Third Body in Inclined Orbital Plane 143 6.6 Application to Repeat Groundtrack Orbits 156 CHAPTER 7: Conclusions.................................................................................... 160 7.1 Subcycles................................................................................................ 161 7.2 Phasing.................................................................................................... 161 7.3 Crossovers..............................................................................................
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