sid.inpe.br/mtc-m19/2012/11.22.12.22 -TDI DEPLOYMENT AND MAINTENANCE OF A SATELLITE FORMATION FLIGHT AROUND L4 AND L5 LAGRANGIAN POINTS IN THE EARTH-MOON SYSTEM BASED ON LOW COST STRATEGIES Francisco Javier Tipan Salazar Doctorate Thesis at Post Gradua- tion Couse in Applied Computing, advised by Drs. Elbert Einstein Macau, and Othon Cabo Winter, approved in December 04, 2012. URL of the original document: <http://urlib.net/8JMKD3MGP7W/3D43GKS> INPE S˜ao Jos´edos Campos 2012 PUBLISHED BY: Instituto Nacional de Pesquisas Espaciais - INPE Gabinete do Diretor (GB) Servi¸code Informa¸c˜ao e Documenta¸c˜ao (SID) Caixa Postal 515 - CEP 12.245-970 S˜ao Jos´edos Campos - SP - Brasil Tel.:(012) 3208-6923/6921 Fax: (012) 3208-6919 E-mail: [email protected] BOARD OF PUBLISHING AND PRESERVATION OF INPE INTEL- LECTUAL PRODUCTION (RE/DIR-204): Chairperson: Marciana Leite Ribeiro - Servi¸code Informa¸c˜ao e Documenta¸c˜ao (SID) Members: Dr. Antonio Fernando Bertachini de Almeida Prado - Coordena¸c˜ao Engenharia e Tecnologia Espacial (ETE) Dra Inez Staciarini Batista - Coordena¸c˜ao Ciˆencias Espaciais e Atmosf´ericas (CEA) Dr. Gerald Jean Francis Banon - Coordena¸c˜ao Observa¸c˜ao da Terra (OBT) Dr. Germano de Souza Kienbaum - Centro de Tecnologias Especiais (CTE) Dr. Manoel Alonso Gan - Centro de Previs˜ao de Tempo e Estudos Clim´aticos (CPT) Dra Maria do Carmo de Andrade Nono - Conselho de P´os-Gradua¸c˜ao Dr. Pl´ınio Carlos Alval´a- Centro de Ciˆencia do Sistema Terrestre (CST) DIGITAL LIBRARY: Dr. Gerald Jean Francis Banon - Coordena¸c˜ao de Observa¸c˜ao da Terra (OBT) DOCUMENT REVIEW: Marciana Leite Ribeiro - Servi¸code Informa¸c˜ao e Documenta¸c˜ao (SID) Yolanda Ribeiro da Silva Souza - Servi¸code Informa¸c˜ao e Documenta¸c˜ao (SID) ELECTRONIC EDITING: Maria Tereza Smith de Brito - Servi¸code Informa¸c˜ao e Documenta¸c˜ao (SID) sid.inpe.br/mtc-m19/2012/11.22.12.22 -TDI DEPLOYMENT AND MAINTENANCE OF A SATELLITE FORMATION FLIGHT AROUND L4 AND L5 LAGRANGIAN POINTS IN THE EARTH-MOON SYSTEM BASED ON LOW COST STRATEGIES Francisco Javier Tipan Salazar Doctorate Thesis at Post Gradua- tion Couse in Applied Computing, advised by Drs. Elbert Einstein Macau, and Othon Cabo Winter, approved in December 04, 2012. URL of the original document: <http://urlib.net/8JMKD3MGP7W/3D43GKS> INPE S˜ao Jos´edos Campos 2012 Cataloging in Publication Data Salazar, Francisco Javier Tipan. Deployment and maintenance of a satellite formation flight Sa31d around l4 and l5 Lagrangian points in the earth-moon system based on low cost strategies / Francisco Javier Tipan Salazar. – S˜aoJos´edos Campos : INPE, 2012. xxviii + 141 p. ; (sid.inpe.br/mtc-m19/2012/11.22.12.22 -TDI) Thesis (Doctorade in Applied Computing) – Instituto Nacional de Pesquisas Espaciais, S˜aoJos´edos Campos, 2012. Advisers : Drs. Elbert Einstein Macau, e Othon Cabo Winter. 1. three bodies. 2. lagrangian points. 3. low cost. 4. formation fligth. I.T´ıtulo. CDU 004:521.135 Copyright c 2012 do MCT/INPE. Nenhuma parte desta publica¸c˜aopode ser reproduzida, ar- mazenada em um sistema de recupera¸c˜ao,ou transmitida sob qualquer forma ou por qualquer meio, eletrˆonico, mecˆanico, fotogr´afico, reprogr´afico, de microfilmagem ou outros, sem a permiss˜ao escrita do INPE, com exce¸c˜aode qualquer material fornecido especificamente com o prop´osito de ser entrado e executado num sistema computacional, para o uso exclusivo do leitor da obra. Copyright c 2012 by MCT/INPE. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, microfilming, or otherwise, without written permission from INPE, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use of the reader of the work. ii \Thousands of years ago the first man discovered how to make fire. He was probably burned at the stake he had taught his brothers to light, but he left them a gift they had not conceived of, and he lifted darkness off the earth". Ayn Rand in \The Fountainhead", 1949 v In memory of my mother Rosa Mercedes Salazar vii ACKNOWLEDGEMENTS First of all, I'd like to thank to my advisors Dr. Elbert Einstein Nehrer Macau and Dr. Othon Cabo Winter, who gave me motivation, inspiration and encouragement during my graduate program. They also introduced me to many new topics and new ideas for research in Orbital Dynamics. They gave me a big share of their time at the National Institute for Space Research - INPE or at the S~aoPaulo State University - UNESP. Thanks also go to the other members of my graduate committee, Dr. Solon Ven^ancio de Carvalho, Dr. Joaquim Barroso de Castro, Dr. Rodolpho Vilhena de Moraes, Dr. Ernesto Vieira Neto and Dr. Pablo Miguel Cincotta for their corrections and comments to this thesis. Thanks also go to Prof. Josep Masdemont and Prof. Gerard G´omez of the Poly- technic University of Catalonia - Spain, who supervised my international research stage in Barcelona and contributed greatly in the success of this work. Their ideas, generosity and suggestions not only let me to write the last chapter of this thesis but they played a key role in the quality of this dissertation. I owe a great debt of gratitude to them. I'd also like to thank to the National Institute for Space Research - INPE and to the Funda¸c~aode Amparo `aPesquisa do Estado de S~aoPaulo - FAPESP, for the financial investment of sponsoring my four years of Ph.D. in S~ao Paulo and Barcelona. I also want to mention here friends at the National Institute for Space Research - INPE who had a positive influence on my project. In alphabetical order, I want to make a special thanks to Aline Soterroni, Caroline da Silva, Erica´ de Souza, Helaine Furtado, Laurita do Santos, Noemi Ara´ujo, Renata Rocha, Rita Ricarte, Rodolfo Almeida, Ros^angela Follman, Valentin Bageston and Wantuir de Freitas for their invaluable friendship and help during those four years. They have, in their own individual ways, left an indelible mark on my life. Thanks also go to my colleagues and former professors at the National Institute for Space Research - INPE for introducing me to the field of astrodynamics and giving me encouragement to finish my Ph.D. In particular, Dr. Antonio Bertachini de Almeida Prado and Dr. Marcelo Lopes Oliveira e Souza. Finally, I'd like to thank my parents Jos´eand Mercedes, my brother Jos´eand my sisters Mar´ıa and Gabriela for their love, support and unwavering belief in me, even when there have been many reasons not to believe. My ability to complete this work ix owes much to them. x IMPLEMENTA¸CAO~ E MANUTEN ¸CAO~ DE SATELITES´ EM VOO DE FORMA¸CAO~ AO REDOR DOS PONTOS LAGRANGIANOS L4 E L5 COM BASE EM ESTRATEGIAS´ DE BAIXO EMPUXO RESUMO Este trabalho est´afocado em m´etodos de transfer^encia a partir de uma ´orbita cir- cular ao redor da Terra at´e´orbitas peri´odicas ao redor dos pontos Lagrangianos L4 e L5 no sistema Terra - Lua, com aplica¸c~oes para colocar v´arios sat´elites em v^oo de forma¸c~ao. Os pontos Lagrangianos L4 e L5 est~aolocalizados a 60 graus acima e embaixo da linha que conecta a Terra com a Lua e formam com estes dois corpos um tri^angulo equil´atero. Estes pontos Lagrangianos s~ao est´aveis pela rela¸c~aode massa entre a Terra e a Lua. Devido `asua dist^ancia, radia¸c~oes eletromagn´eticas que pro- veem da Terra e chegam at´eeles s~ao substancialmente atenuadas. Dessa maneira, estes pontos Lagrangianos representam posi¸c~oes extraordin´arias para colocar obser- vat´orios astron^omicos. Inspirados nos recentes resultados em manobras assistidas por gravidade, os m´etodos de transfer^encia implementados neste trabalho usam o campo gravitacional da Lua para atingir os pontos Lagrangianos. N´os aplicamos tr^es diferentes t´ecnicas para intersectar a esfera de influ^encia da Lua: Transfer^encias de M´ınima Energia, Trajet´orias G e Orbitas´ Ca´oticas, e mostramos que existem novas trajet´orias alternativas para chegar at´enosso objetivo. N´osencontramos vantagens em rela¸c~ao `aTransfer^encia de Hohmann tais como gasto menor de combust´ıvel e a possibilidade de usar o mesmo lan¸cador para enviar os sat´elites at´eos pontos L4 e L5. O trabalho tamb´em apresenta um estudo das geometrias ao redor das ´orbi- tas peri´odicas centradas em L4 com boas propriedades para v^oos em forma¸c~ao. N´os consideramos a possibilidade da exist^encia de regi~oes com acelera¸c~ao radial relativa zero com respeito `atrajet´oria nominal. As simula¸c~oes num´ericas mostram que para evitar grandes varia¸c~oes das dist^ancias mutuas entre os sat´elites, a forma¸c~aotem que estar localizada n~ao ao longo da dire¸c~ao de acelera¸c~ao radial relativa nula sen~ao ao longo da dire¸c~ao de acelera¸c~aoradial relativa m´ınima. Este trabalho est´afeito utilizando o modelo Circular Restrito de Tr^es Corpos, considerando s´oo movimento no plano da ´orbita dos sistema Terra-Lua. xi ABSTRACT This thesis focuses on transfer methods from a circular parking orbit around the Earth to periodic orbits around the Lagrangian points L4 and L5 in the Earth-Moon system, with applications to place multiple satellites in formation flying. Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with re- spect to the Earth and form an equilateral triangle with the base of the line defined by those two bodies.