Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-23-2017 Investigating Analytical and Numerical Methods to Predict Satellite Orbits Using Two-Line Element Sets Adam T. Rich Follow this and additional works at: https://scholar.afit.edu/etd Part of the Astrodynamics Commons, and the Space Vehicles Commons Recommended Citation Rich, Adam T., "Investigating Analytical and Numerical Methods to Predict Satellite Orbits Using Two-Line Element Sets" (2017). Theses and Dissertations. 1722. https://scholar.afit.edu/etd/1722 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. INVESTIGATING ANALYTICAL AND NUMERICAL METHODS TO PREDICT SATELLITE ORBITS USING TWO-LINE ELEMENT SETS THESIS Adam T. Rich, Captain, USAF AFIT-ENY-MS-17-M-286 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A. APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENY-MS-17-M-286 INVESTIGATING ANALYTICAL AND NUMERICAL METHODS TO PREDICT SATELLITE ORBITS USING TWO-LINE ELEMENT SETS THESIS Presented to the Faculty Department of Aeronautics and Astronautics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Master of Science in Astronautical Engineering Adam T. Rich, B.S. Captain, USAF March 2017 DISTRIBUTION STATEMENT A. APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED AFIT-ENY-MS-17-M-286 INVESTIGATING ANALYTICAL AND NUMERICAL METHODS TO PREDICT SATELLITE ORBITS USING TWO-LINE ELEMENT SETS Adam T. Rich, B.S. Captain, USAF Committee Membership: William E. Wiesel, Ph.D. Chair Lt Col Christopher D. Geisel, Ph.D. Member Lt Col Kirk W. Johnson, Ph.D. Member AFIT-ENY-MS-17-M-286 Abstract As Low Earth Orbit (LEO) contains an ever-increasing number of objects, the prediction of future object positions must be precise in order to avoid collisions. Object positions are distributed in two-line element (TLE) sets and are generated using the analytical propagator known as Simplified General Perturbations 4 (SGP4). However, a numerical integrator called Special Perturbations (SP) provides an alternative approach to TLE generation and propagation. In this thesis, TLE accuracy was determined with both models, and the length of time that a single element set can provide valid information was also established. With two-line element sets as data, comparisons were made between the numerical integrator and the analytical model for objects in LEO, particularly the Hubble Space Telescope (HST). The results obtained indicated that the propagated position error using SGP4 remained within 1 km of the expected position during a 7 day period from the epoch of the initial element set. Additionally, the majority of comparisons between SGP4 and SP resulted in a higher error while using the numerical integrator, although some comparisons showed a lower propagated position error with SP. This final result shows a potential for SP to provide more accurate position information than SGP4 in future research. iv Acknowledgments I would like to thank my loving wife for her continued support throughout this long process. Thank you for your encouragement, as it has provided me with a source of inspiration. I would also like to thank my research advisor, Dr. Wiesel. Thank you for your guidance and your dedication to assisting me with this project. Adam T. Rich v Table of Contents Page Abstract .............................................................................................................................. iv Table of Contents ............................................................................................................... vi List of Figures .................................................................................................................... ix List of Tables ..................................................................................................................... xi I. Introduction .....................................................................................................................1 1.1 Motivation ..............................................................................................................2 1.2 Problem Statement..................................................................................................3 1.3 Research Questions ................................................................................................4 1.4 Scope ......................................................................................................................4 II. Literature Review ............................................................................................................6 2.1 A Brief History of Orbit Propagation .....................................................................6 2.2 Classical Orbital Elements .....................................................................................7 2.3 Two-Line Element Sets ..........................................................................................9 2.4 Orbit Accuracy .....................................................................................................10 2.5 Lyapunov Exponents ............................................................................................14 2.6 Simplified General Perturbations vs. Special Perturbations.................................15 2.6.1 Atmosphere Models...........................................................................................16 2.6.2 Nongravitational Force Models .........................................................................17 2.6.3 Gravitational Force Models ...............................................................................18 III. Methodology ................................................................................................................19 3.1 Introduction ..........................................................................................................19 3.2 SGP4 Modeling ....................................................................................................21 3.3 Special Perturbations ............................................................................................26 vi 3.4 Additional LEO Objects .......................................................................................29 3.5 Alternative Model .................................................................................................31 IV. Results..........................................................................................................................32 4.1 Test Case 1 ...........................................................................................................32 4.2 Test Case 2 ...........................................................................................................34 4.3 Test Case 3 ...........................................................................................................35 4.4 Test Case 4 ...........................................................................................................36 4.5 Test Case 5 ...........................................................................................................38 4.6 Test Case 6 ...........................................................................................................39 4.7 Test Case 7 ...........................................................................................................41 4.8 Test Case 8 ...........................................................................................................43 4.9 Test Case 9 ...........................................................................................................44 4.10 Test Case 10 .......................................................................................................45 4.11 Test Case 11 .......................................................................................................48 4.12 Test Case 12 .......................................................................................................49 4.13 Test Case 13 .......................................................................................................50 4.14 Test Case 14 .......................................................................................................51 4.15 Test Case 15 .......................................................................................................52 4.16 Test Case 16 .......................................................................................................53 4.17 Test Case 17 .......................................................................................................53 4.18 Test Case 18 .......................................................................................................54 4.19 Test Case 19 .......................................................................................................55