Movimento orbital de satélites artificiais: efeitos ressonantes
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Data
2013-03-08
Autores
Sampaio, Jarbas Cordeiro [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
O crescente número de objetos orbitando a Terra justifica a grande atenção e interesse no espaço entre o Planeta e a Lua nos últimos anos. Estes estudos envolvem diferentes perturbações e ressonâncias nos movimentos orbitais destes objetos distribuídos por diferentes altitudes. Neste trabalho, o problema da ressonância no movimento de satélites artificiais é estudado. O desenvolvimento do geopotencial inclui os harmônicos zonais J20 e J40 e os harmônicos tesserais J22 e J42. Através de um procedimento de média e sucessivas transformações de Mathieu, a ordem do sistema dinâmico é reduzida e o sistema final é resolvido por integração numérica. No modelo dinâmico simplificado, três ângulos críticos são estudados. A semi-largura da separatriz é calculada através de um modelo linearizado, o qual descreve o comportamento do sistema dinâmico na vizinhança de cada ângulo crítico. Através do critério de sobreposição das ressonâncias, os possíveis movimentos regulares e irregulares são investigados pelo comportamento no tempo do semi-eixo maior, argumento do pericentro e excentricidade. O maior expoente de Lyapunov é usado como ferramenta para verificar o movimento caótico. Nos estudos sobre os objetos ressonantes, os TLE (Two-Line Elements) do NORAD (North American Defense) são estudados observando o período ressonante dos objetos orbitando a Terra e a ressonância principal na região LEO (Low Earth Orbits). O comportamento no tempo do semi-eixo maior, excentricidade e inclinação de alguns satélites artificiais e detritos espaciais são estudados. Possíveis movimentos irregulares são observados pela presença de diferentes ângulos ressonantes descrevendo a dinâmica orbital destes objetos
The increasing number of objects orbiting the Earth justifies the great attention and interest in the space between the Planet and the Moon in the last years. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J20 and J40 and the tesseral harmonics J22 and J42. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semimajor axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion. In the studies about the resonant objects the TLE (Two-Line Elements) of the NORAD are studied observing the resonant period of the objects orbiting the Earth and the main resonance in the LEO region. The time behavior of the semi-major axis, eccentricity and inclination of some artificial satellites and space debris are studied. Possible irregular motions are observed by the presence of different resonant angles describing the orbital dynamics of these objects
The increasing number of objects orbiting the Earth justifies the great attention and interest in the space between the Planet and the Moon in the last years. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J20 and J40 and the tesseral harmonics J22 and J42. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semimajor axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion. In the studies about the resonant objects the TLE (Two-Line Elements) of the NORAD are studied observing the resonant period of the objects orbiting the Earth and the main resonance in the LEO region. The time behavior of the semi-major axis, eccentricity and inclination of some artificial satellites and space debris are studied. Possible irregular motions are observed by the presence of different resonant angles describing the orbital dynamics of these objects
Descrição
Palavras-chave
Satelites artificiais, Ressonancia, Resonance
Como citar
SAMPAIO, Jarbas Cordeiro. Movimento orbital de satélites artificiais: efeitos ressonantes. 2013. 151 p. Tese (doutorado) - Universidade Estadual Paulista, Faculdade de Engenharia de Guaratinguetá, 2013.