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Estabilidade De Veículos Espaciais Em Ressonância sid.inpe.br/mtc-m21c/2018/03.12.13.05-TDI ESTABILIDADE DE VEÍCULOS ESPACIAIS EM RESSONÂNCIA Rubens Antonio Condeles Júnior Tese de Doutorado do Curso de Pós-Graduação em Engenharia e Tecnologia Espaciais/Mecânica Espacial e Controle, orientada pelos Drs. Antonio Fernando Bertachini de Almeida Prado, e Tadashi Yokoyama, aprovada em 06 de abril de 2018. URL do documento original: <http://urlib.net/8JMKD3MGP3W34R/3QMPS3E> INPE São José dos Campos 2018 PUBLICADO POR: Instituto Nacional de Pesquisas Espaciais - INPE Gabinete do Diretor (GBDIR) Serviço de Informação e Documentação (SESID) Caixa Postal 515 - CEP 12.245-970 São José dos Campos - SP - Brasil Tel.:(012) 3208-6923/6921 E-mail: [email protected] COMISSÃO DO CONSELHO DE EDITORAÇÃO E PRESERVAÇÃO DA PRODUÇÃO INTELECTUAL DO INPE (DE/DIR-544): Presidente: Maria do Carmo de Andrade Nono - Conselho de Pós-Graduação (CPG) Membros: Dr. Plínio Carlos Alvalá - Centro de Ciência do Sistema Terrestre (COCST) Dr. André de Castro Milone - Coordenação-Geral de Ciências Espaciais e Atmosféricas (CGCEA) Dra. Carina de Barros Melo - Coordenação de Laboratórios Associados (COCTE) Dr. Evandro Marconi Rocco - Coordenação-Geral de Engenharia e Tecnologia Espacial (CGETE) Dr. Hermann Johann Heinrich Kux - Coordenação-Geral de Observação da Terra (CGOBT) Dr. Marley Cavalcante de Lima Moscati - Centro de Previsão de Tempo e Estudos Climáticos (CGCPT) Silvia Castro Marcelino - Serviço de Informação e Documentação (SESID) BIBLIOTECA DIGITAL: Dr. Gerald Jean Francis Banon Clayton Martins Pereira - Serviço de Informação e Documentação (SESID) REVISÃO E NORMALIZAÇÃO DOCUMENTÁRIA: Simone Angélica Del Ducca Barbedo - Serviço de Informação e Documentação (SESID) Yolanda Ribeiro da Silva Souza - Serviço de Informação e Documentação (SESID) EDITORAÇÃO ELETRÔNICA: Marcelo de Castro Pazos - Serviço de Informação e Documentação (SESID) André Luis Dias Fernandes - Serviço de Informação e Documentação (SESID) sid.inpe.br/mtc-m21c/2018/03.12.13.05-TDI ESTABILIDADE DE VEÍCULOS ESPACIAIS EM RESSONÂNCIA Rubens Antonio Condeles Júnior Tese de Doutorado do Curso de Pós-Graduação em Engenharia e Tecnologia Espaciais/Mecânica Espacial e Controle, orientada pelos Drs. Antonio Fernando Bertachini de Almeida Prado, e Tadashi Yokoyama, aprovada em 06 de abril de 2018. URL do documento original: <http://urlib.net/8JMKD3MGP3W34R/3QMPS3E> INPE São José dos Campos 2018 Dados Internacionais de Catalogação na Publicação (CIP) Condeles Júnior, Rubens Antonio. C751e Estabilidade de veículos espaciais em ressonância / Rubens Antonio Condeles Júnior. – São José dos Campos : INPE, 2018. xxviii + 132 p. ; (sid.inpe.br/mtc-m21c/2018/03.12.13.05-TDI) Tese (Doutorado em Engenharia e Tecnologia Espaciais/Mecânica Espacial e Controle) – Instituto Nacional de Pesquisas Espaciais, São José dos Campos, 2018. Orientadores : Drs. Antonio Fernando Bertachini de Almeida Prado, e Tadashi Yokoyama. 1. Astrodinâmica. 2. Ressonância. 3. Perturbações orbitais. 4. Kozai-Lidov. 5. Estabilidade orbital. I.Título. CDU 629.7.017.2 Esta obra foi licenciada sob uma Licença Creative Commons Atribuição-NãoComercial 3.0 Não Adaptada. This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. ii Aluno (a): Rubens Antonio Condeles Júnior Titulo: "ESTABILIDADE DE VEÍCULOS ESPACIAIS EM RESSONÂNCIA" Aprovado (a) pela Banca Examinadora em cumprimento ao requisito exigido para obtenção do Titulo de Doutor(a) em Engenharia e Tecnologia Espaciais/Mecânica Espacial e Controle Dr. Rodolpho Vilhena de Moraes -"R---, 1( (, k! ( L I OtV2e , Presidente 11NPE / São José dos Campos - SP ( ) Partidpação por Video - Conferência Dr. Antonio Fernando Bertachini de Almeida Prado Orientador(a) / INPE / SJCampos - SP ( ) Participação por Viciei) - Conferência / Dr, Tadashi Yokoyama Orientador(a)/ UNESP / Rio Claro - SP ( ) Participação por Video - Conferência Dr. Diogo Merguizo Sanchez 04) • -: , dor(a) ;4 INPE / São José dos Campos - SP ( ) Participação por Vkieo - Conferência Dra. Rita de Cássia Domingos 2-"[C._ db._ c_..) Convidado(a)/ UNESP / São João da Boa Vista - SP ( ) Participação por Video - Conferência Dra. Vivian Martins Gomes Convidado(a) / UNESPIFEG 1 uaratinguetá - SP ( ) Participação por Video - Conferência Este trabalho foi aprovado por: ( ) maioria simples 1,1 unanimidade São José dos Campos, 06 de abril de 2018 A meus pais Rubens e Maria Cecília, a minha esposa Suzana, a minhas filhas Lauren e Rúbia, a meu filho Leonardo, a meus irmãos José Fernando, André, Pedro e Paulo e a minha irmã Elisabeth v AGRADECIMENTOS Agradeço a meus pais, Rubens e Maria Cecília que sempre me apoiaram. A minha esposa, Suzana, pelo apoio, carinho, compreensão e pela paciência. As minhas filhas, Lauren e Rúbia, pelo amor e carinho. Aos meus irmãos José Fernando, Elisabeth, André, Pedro e Paulo, pelo apoio e incentivo. Aos meus orientadores Bertachini, Tadashi e Diogo, pela amizade e orientação, pelo apoio no período que estive fora do INPE e principalmente pela compreensão no período em que estive mais afastado. Ao Geraldo pelo apoio e amizade. Aos Docentes do INPE. Aos funcionários do INPE. A todos os colegas de pós-gradução. À UFTM, por conceder meu afastamento remunerado para cursar o doutorado. vii RESUMO Neste trabalho é analisada a estabilidade de veículos espaciais em ressonância. Esco- lhemos o sistema de Haumea por ter propriedades únicas com relação aos sistemas já conhecidos, e é considerado um forte candidato para receber uma missão de explora- ção. O sistema foi modelado considerando o potencial gravitacional perturbador de Haumea até grau e ordem seis dos polinômios de Legendre e também adicionamos a perturbação de suas duas luas, Namaka e Hi’iaka. Analisamos o desempenho das forças perturbadoras do sistema sobre o veículo espacial através dos métodos da integral da perturbação. Por meio dos mapas da excentricidade máxima da órbita do veículo espacial, do tempo de vida do veículo espacial e da integral da perturba- ção, avaliamos a estabilidade das órbitas do veículo espacial no sistema de Haumea. Também avaliamos a estabilidade das órbitas nas ressonâncias de movimentos mé- dios, 1:1 veículo-Hi’iaka e 3:1 veículo-Namaka. Ao final do trabalho avaliamos o mecanismo Kozai-Lidov excêntrico em um sistema de pequenos corpos e aplicamos ao sistema de Haumea, também mostramos em quais cenários o mecanismo pode ocorrer no sistema de Haumea. Palavras-chave: Astrodinâmica. Ressonância. Perturbações orbitais. Kozai-Lidov. Estabilidade orbital. ix STABILITY SPACECRAFT IN RESONANCE ABSTRACT In this work the stability of spacecraft in resonance is analyzed. We chose the Haumea system because it has unique properties with respect to known systems, and is considered a strong candidate to receive an exploration mission. The system was modeled considering the disturbing gravitational potential of Haumea up to de- gree and order six of the Legendre polynomials and also added the perturbation of its two moons, Namaka and Hi’iaka. We analyze the performance of the disturbing forces of the system on the spacecraft through the perturbation integral methods. By means of the maps of the maximum eccentricity of the spacecraft orbit, of the life time of the spacecraft and of the perturbation integral, we evaluated the sta- bility of the orbits of the spacecraft in the Haumea system. We also evaluated the stability of the orbits in mean motion resonances, 1:1 spacecraft-Hi’iaka and 3:1 spacecraft-Namaka. At the end of the study, we evaluated the eccentric Kozai-Lidov mechanism in a of small bodies system and we apply to the Haumea system, we also show in which scenarios the mechanism can occur in the Haumea system Keywords: Astrodynamics. Kozai-Lidov. Orbital perturbation. Orbital stability. Res- onance. xi LISTA DE FIGURAS Pág. 3.1 Representação dos harmônicos esféricos. (a) Harmônicos zonais, (b) Harmônicos setoriais e (c) Harmônicos tesserais............... 12 3.2 Elipsoide triaxial com a > b > c........................ 14 4.1 Variação total da velocidade em função da inclinação inicial (I0) e do argumento do pericentro inicial (ω0), com e0 = 0 e a0 = 1920 km, em um período orbital, devida a contribuição dos termos C20 e C22, respectiva- mente, do potencial gravitacional de Haumea................ 22 4.2 Variação total da velocidade em função da inclinação inicial (I0) e do argumento do pericentro inicial (ω0) , sendo e0 = 0 e a0 = 1920 km, em um período orbital devida a contribuição dos termos C40, C42 e C44, respectivamente, do potencial gravitacional de Haumea........... 23 4.3 Variação total da velocidade em função da inclinação inicial (I0) e do argumento do pericentro inicial (ω0) , sendo e0 = 0 e a0 = 1920 km, em um período orbital devida a contribuição dos termos C60, C62, C64 e C66, respectivamente, do potencial gravitacional de Haumea........... 24 4.4 Variação total da velocidade em função da inclinação inicial (I0) e do argumento do pericentro inicial (ω0) , sendo e0 = 0 e a0 = 1920 km, em um período orbital devida a contribuição de todos os termos do potencial perturbador de Haumea............................ 25 4.5 Representação gráfica das órbitas....................... 25 4.6 Excentricidade máxima da órbita em função da inclinação inicial (I0) e do argumento do pericentro inicial (ω0) , sendo e0 = 0 e a0 = 1920 km, em um período orbital............................. 26 4.7 Integral da perturbação de Haumea em função do semi-eixo maior da órbita do veículo espacial. As órbitas são circulares e equatoriais. 27 4.8 Integral da perturbação de Haumea em função
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