An improved algorithm for satellite orbit decay and re-entry prediction

A study to improve the accuracy and capabilities of an existing algorithm for satellite orbit decay and debris impact prediction has been completed. The existing algorithm, program LIFETIME 3.0, was developed by The Aerospace Corporation to predict satellite orbital lifetimes. Although its accuracy is quite good (10% error), the algorithm's semi-analytic method does not account for the intrack motion of the satellite. Additionally, the program's propagation routine limits the minimum step size and causes some uncertainty in impact time prediction. Furthermore, no geographical impact location is computed. This study sought to correct these deficiencies and to perform a sensitivity study on factors affecting impact prediction accuracy. Using NORAD data of actual decayed objects, inaccuracies in satellite period calculation by the existing algorithm as well as inconsistancies in the data conversion method were discovered. These were corrected using a new method of period calculation and an improved data conversion routine. A numerical integration scheme was developed to calculate the final portion of the satellite's decay. Improved output capabilities included groundtrack and debris impact area plots on a world map and an altitude decay history. These major changes and upgrades formed a new program version, LIFETIME 4.0. Comparisons between version 3.0 and 4.0 were made using four actual decayed objects. Results show that version 4.0 is significantly more accurate than version 3.0 during decay curve fitting. Comparison of impact prediction shows some increase in accuracy with version 4.0 for some cases. Generally, LIFETIME 4.0 is an improved algorithm with less uncertainty in impact prediction than LIFETIME 3.0, and it has enhanced output capabilities. The impact error sensitivity results indicate some improved accuracy by using long data spans, short prediction spans, and estimated solar flux values equal to the value on the last day of data. These results are not definitive and further research is recommended. Thesis Supervisor: Company Supervisor: Dr. Walter Hollister Dr. C.C. (George) Chao Professor of Aeronautics & Astronautics Manager, Orbit Dynamics The Aerospace Corporation Acknowledgments I would first like to express my deep appreciation for the advice and technical assistance I received from many members of The Aerospace Corporation during my two summer work sessions and long thesis research session at the company. Most notable is my thanks to Dr. C.C. (George) Chao, manager of the Orbit Dynamics Section of the Astrodynamics Department, without whom this research would never have even gotten off the ground. George, whose constant desire for improving computational methods and models through intense investigation motivated me through this project, was a never-ending source of knowledge, ideas, support, and guidance. My sincere thanks, George. Three other Astrodynamics members deserve special thanks and recognition for their unique and important roles in the completion of this research. First, I thank Daniel Oltrogge for his expertise with numerical integration routines, knowledge of Macintosh computers, dedication to improving the accuracy and efficiency of any computer code, extensive library, stash of snacks, never-ending support, and lively sense of humor. Dan put in a lot of effort with the integration routine additions, algorithm testing, and Macintosh software packaging. Second, I thank Cassandra Johnson, without whose help the enhanced output plots of LIFETIME 4.0 would not have been possible. Cassandra is also the caretaker of the menudriven version of LIFETIME, and she put in much effort in working with me to adapt LIFETIME 4.0 to the menu shell program. Last to thank is my office-mate for seven months, Matthew Hart. Matt's hard work ethic was an inspiration and his diverse interests helped make months of intense research almost enjoyable. Some other members of the Astrodynamics Department also deserve mention here. Thanks go to: Hans Karrenberg, the reason I came to The Aerospace Corp.; Jimmy Miyamoto, patient teacher; Jim Gidney, mentor and friend; Karolyn Young, for support, comic relief, and reality check; and Brian von Kleek, for coffee. I also want to extend my appreciation to the rest of the members of the Astrodynamics Department and The Aerospace Corporation as a whole for all help, guidance, and support over the past three years. A special note of thanks goes to Debbie Nerio of the Space Test Range, Sunnyvale, CA. Her interest and funding efforts both initiated this research and supported it to its conclusion. Her office is entirely responsible for the financial support that made this thesis possible, and I offer my sincere appreciation. Back at MIT, Professor Walter Hollister was a major inspiration on my approach to my graduate studies. Additionally, his support and critiques in the final phases of research and writing were helpful and insightful. Thank you so much, Professor. Of final mention are those family and friends who have been of personal support and inspiration over my college career, especially through the trying times of this research. First and foremost I want to thank the brothers of the Alpha Tau Omega Fraternity for valuable lessons and experiences in friendship, love, and respect. These virtues leave an impression that is everlasting. In particular, thanks goes to Tyler Worden, fellow thesis workaholic, for his companionship and steadfast friendship. Thanks are also in order for Celia Liu, fellow internist at The Aerospace Corporation, confidant, matchmaker, and friend. I thank Melonie, who lent caring support and managed to make daily life as unpredictable as possible. My most sincere appreciation goes to Rende, whose beauty, intelligence, and outlook on life have been a source of happiness and firm support over this last year at MIT. Final thanks, above all others, goes to my parents. Their love and guidance over the years have been a true inspiration. I can only hope that someday I can return to them a fraction of the love, support, and strength they have given to me. This research and writing was conducted at The Aerospace Corporation, El Segundo, California, from June 1992 to January 1993, and at MIT from January to May 1993. It was financially supported by the Space Test Range through The Aerospace Corporation, along with an Aerospace Graduate Fellowship and cooperation with the MIT Engineering Internship Program. This report was prepared on a Macintosh LC III computer using Microsoft Word 5.1a® as the text editor. Additional plots and figures were created using LIFETIME 4.0@, Cricket Graph®, and MacDraw II®. Table of