Modelo do pêndulo para ressonância em mecânica celeste
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Data
2022-02-02
Autores
Signor, Alan Cefali
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Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho, realizamos o estudo a respeito dos tópicos necessários para o desenvolvimento do modelo analítico para ressonâncias de movimento médio, conhecido como Modelo do Pêndulo. Inicialmente, estudamos sobre a geometria da ressonância de movimento médio, de modo que por meio do tempo de conjunção e da órbita no referencial sinódico para certas ressonâncias foi possível compreender sobre alguns aspectos deste mecanismo. A partir do processo de expansão da função perturbadora usual, realizamos uma mudança de variáveis para desenvolver o Modelo do Pêndulo para a ressonância retrógrada no problema circular restrito de três corpos. Com a aplicação do modelo as ressonâncias retrógradas 2/1 e 3/1 comparamos as curvas teóricas de amplitude de libração com mapas de estabilidade obtidos através de integrações numéricas. O processo foi analogamente realizado para as ressonâncias prógradas 2/1 e 3/1; desta forma, pudemos também comparar os resultados de nosso problema para os dois tipos de ressonância de movimento médio existentes na natureza.
In this work, we carry out the study of the necessary topics for the development of the analytical model for mean motion resonances, known as the Pendulum Model. Initially, in order to understand how resonant relationships behave to repeated encounters, we focused on the geometry of the mean motion resonance, thus by conjunction time and rotation frame orbits it was possible to understand some aspects of this mechanism. Through the process of the expansion of the usual disturbing function, we perform a change of variables to develop the Pendulum Model for the retrograde resonance in the circular restricted three-body problem. Through the application of the model for the retrograde resonances 2/1 and 3/1 we compare the theoretical curves of the amplitude libration with the stability maps obtained by numerical integrations. The same process was realized for the prograde resonances 2/1 and 3/1; in this way, we were able to compare the results of our problem for the two type of mean motion resonances present in nature.
In this work, we carry out the study of the necessary topics for the development of the analytical model for mean motion resonances, known as the Pendulum Model. Initially, in order to understand how resonant relationships behave to repeated encounters, we focused on the geometry of the mean motion resonance, thus by conjunction time and rotation frame orbits it was possible to understand some aspects of this mechanism. Through the process of the expansion of the usual disturbing function, we perform a change of variables to develop the Pendulum Model for the retrograde resonance in the circular restricted three-body problem. Through the application of the model for the retrograde resonances 2/1 and 3/1 we compare the theoretical curves of the amplitude libration with the stability maps obtained by numerical integrations. The same process was realized for the prograde resonances 2/1 and 3/1; in this way, we were able to compare the results of our problem for the two type of mean motion resonances present in nature.
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Palavras-chave
Asteroides, Mecânica celeste, Ressonâncias de movimento médio, Celestial mechanics, Mean-motion resonances, Asteroids