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Study of Lunar Constellations for Situational STUDY OF LUNAR CONSTELLATIONS FOR SITUATIONAL AWARENESS AND SURVEILLANCE By Devon Sanders A Thesis Submitted to the Faculty of Mississippi State University in Partial Fullfillment of the Requirements for the Degree of Master of Science in Aersospace Engineering in the Department of Aerospace Engineering Mississippi State, Mississippi Novemeber 2006 STUDY OF LUNAR CONSTELLATIONS FOR SITUATIONAL AWARENESS AND SURVEILLANCE By Devon Sanders Approved: __________________________________ __________________________________ Carrie D. Olsen Pasquale Cinnella Assistant Professor of Aerospace Professor of Aerospace Engineering Engineering Graduate Coordinator of the Department (Director of Thesis) of Aerospace Engineering __________________________________ __________________________________ Keith Koenig Roger King Professor of Aerospace Engineering Associate Dean of the Bagley College of (Committee Member) Engineering __________________________________ Gregory D. Olsen Assistant Professor of Aerospace Engineering (Committee Member) Name: Devon Stetson Sanders Date of Degree: December 8, 2006 Institution: Mississippi State University Major Field: Aerospace Engineering Major Professor: Dr. Carrie D. Olsen Title of Study: STUDY OF LUNAR CONSTELLATIONS FOR SITUATIONAL AWARENESS AND SURVEILLANCE Pages in Study: 101 Candidate for Degree of Master of Science Lunar constellations providing the capabilities of situational awareness and surveillance for future mission operators are analyzed in this study. The use of specialty orbits, such as sun-synchronous and frozen orbits, are analyzed to determine the applicability of these unique orbits. Additionally, altitude and inclination trades are performed to determine the degree to which mission objectives are achieved through ranges of these orbital parameters. Using the analyzed orbits, constellations of varying patterns are developed and surface coverage figures of merit are used to evaluate them. The research concludes with calculation of the yearly cross-track and in-track stationkeeping costs of a representative constellation. This stationkeeping is necessary for preservation of the designed coverage statistics. DEDICATION I would like to dedicate this to my parents, Don and Daphne Sanders, and my sister Dana. ii ACKNOWLEDGEMENTS The author expresses his sincere gratitude to those people who provided assistance in this thesis. First of all, thanks are due to Dr. Carrie D. Olsen, my major professor, for her seemingly unlimited guidance and support. Thanks are also due to the other two members of my committee, Dr. Greg Olsen and Dr. Keith Koenig, for the help that they provided in reviewing this thesis. The author also expresses gratitude towards the Mississippi State University Bagley College of Engineering for their support of his graduate studies. iii TABLE OF CONTENTS Page DEDICATION........................................................................................................... ii ACKNOWLEDGEMENTS....................................................................................... iii LIST OF TABLES..................................................................................................... v LIST OF FIGURES ................................................................................................... vi LIST OF SYMBOLS ................................................................................................. viii CHAPTER I. INTRODUCTION ......................................................................................... 1 II. BACKGROUND ........................................................................................... 4 Earth-Moon System Theory........................................................................... 6 Lunar Gravity Field Model ............................................................................ 10 Lunar Constellation Design ........................................................................... 11 III. DEFINITION OF REQUIREMENTS........................................................... 16 IV. SINGLE ORBIT TRADES............................................................................ 18 STK Propagator Selection.............................................................................. 18 Altitude Analysis........................................................................................... 32 Inclination Analysis....................................................................................... 36 RAAN Analysis............................................................................................. 41 V. SPECIALTY ORBIT TRADES .................................................................... 46 Sun-Synchronous Orbit.................................................................................. 47 Frozen Orbit – Park & Junkins, 101.5 degrees .............................................. 55 iv VI. CONSTELLATION TRADES ...................................................................... 62 Streets of Coverage Constellations ................................................................ 65 Walker Constellations.................................................................................... 67 Constellation Comparison.............................................................................. 68 Constellations with Equatorial Orbits............................................................ 73 VII. LONG TERM COVERAGE & STATIONKEEPING .................................. 80 Long Term Coverage..................................................................................... 81 Cross-Track Stationkeeping........................................................................... 86 In-Track Stationkeeping................................................................................. 90 VIII. SUMMARY AND CONCLUSIONS............................................................ 96 Future Work................................................................................................... 99 REFERENCES .......................................................................................................... 100 v LIST OF TABLES Table 1 - Earth & Moon Physical Constants ............................................................. 8 Table 2 - Earth & Moon (GLGM-1) Oblateness Parameters..................................... 9 Table 3 - Streets of Coverage Results........................................................................ 66 Table 4 - Walker Results (* = 180 degree planar spacing)........................................ 68 Table 5 - Streets of Coverage Constellations with Equatorial Orbits........................ 74 Table 6 - Streets of Coverage Constellation Best Results ......................................... 74 Table 7 - Walker Constellations with Equatorial Satellites....................................... 76 Table 8 - Walker Constellations Best Results............................................................ 76 Table 9 - Coverage After 3 years for Streets of Coverage Constellation .................. 82 Table 10 - 3 year Coverage for Modified Streets of Coverage Constellation ........... 88 Table 11 - 1 year Coverage of Modified Streets of Coverage Constellation............. 88 Table 12 - Change in RAAN After 1 Year ................................................................ 89 Table 13 - Initial and Final Argument of Latitude of 4 Satellites in 1 Plane............. 94 Table 14 - In-Track Stationkeeping Cost for 1 Plane with 4 Satellites ..................... 95 vi LIST OF FIGURES Figure 1 - Variation in RAAN for Polar Orbit........................................................... 20 Figure 2 - Variation in Eccentricity for Polar Orbit................................................... 21 Figure 3 - Variation in Inclination for Polar Orbit..................................................... 21 Figure 4 - Variation in Semi-Major Axis for Polar Orbit .......................................... 22 Figure 5 - Variation in RAAN for Inclined Orbit...................................................... 23 Figure 6 - Variation in Inclination for Inclined Orbit................................................ 24 Figure 7 - Variation in Eccentricity for Inclined Orbit.............................................. 24 Figure 8 - Variation in Semi-Major Axis for Inclined Orbit ..................................... 25 Figure 9 - Third Body Effects of RAAN for Polar Orbit........................................... 27 Figure 10 - Third Body Effects on Inclination for Polar Orbit.................................. 27 Figure 11 - Third Body Effects of Eccentricity for Polar Orbit................................. 28 Figure 12 - Third Body Effects of Semi-Major Axis for Polar Orbit ........................ 28 Figure 13 - Third Body Effects on RAAN for Inclined Orbit ................................... 30 Figure 14 - Third Body Effects on Eccentricity for Inclined Orbit ........................... 30 Figure 15 - Third Body Effects on Inclination for Inclined Orbit ............................. 31 Figure 16 - Third Body Effects on Semi-major Axis for Inclined Orbit ................... 31 Figure 17 - Inclination Variations at Various Orbital Altitudes ................................ 33 Figure 18 - Eccentricity Variations at Various Orbital Altitudes .............................. 34 Figure 19 - Instantaneous Access Area...................................................................... 35 Figure 20 - Percent Coverage by Latitude ................................................................
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