Possíveis variações da obliquidade de planetas
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Data
2018-06-06
Autores
Oliveira, Marina Gonzaga de [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
É quase um consenso que os planetas ao serem formados, nasceram com obliquidades quase nulas. No entanto, para os planetas gigantes, exceto Júpiter, as atuais obliquidades estão longe de zero. Para Saturno, Urano e Netuno elas são, respectivamente, 25,61°, 97,86°, 28,31°. Em geral, as razões que alteraram as obliquidades estão associadas a efeitos gravitacionais como colisões ou capturas em ressonâncias. Neste trabalho pretendemos montar o sistema médio que governa a dinâmica de longo período da variação da obliquidade de um planeta considerando o Sol e um satélite com massas e distâncias diversas. Usaremos variáveis de Andoyer pois, por serem canônicas, as médias podem ser realizadas de forma rigorosa sempre que feitas em variáveis ação - ângulo. A questão do “wooble” pode ser facilmente incorporada se necessário. Pretendemos com este modelo estudar a variação da obliquidade de Netuno, mas em princípio pode ser usado também nos casos de exoplanetas (ARMSTRONG et al., 2014). O planeta Netuno, aparentemente é o único que não tem nenhum satélite regular primordial, ao contrário dos demais. Boué e Laskar (2010) fizeram uso de um satélite adicional para explicar a obliquidade de Urano. Porém, a presença de um satélite adicional de massa muito elevada, poderia desestabilizar os primordiais já existentes. No caso de Netuno, as massas dos satélites adicionais que pretendemos usar podem ser muito menores do que aquelas usadas por Boué e Laskar, o que elimina de vez, possível desestabilização de eventuais satélites primordiais regulares, caso eles tenham existido.
It is almost a consensus that the planets, when formed, were born with almost zero obliquities. However, for giant planets except Jupiter, the current obliquities ( ) are far from zero. For Saturn, Uranus, and Neptune they are, respectively, 25 . 6 ◦ , 97 . 8 ◦ , 28 . 3 ◦ . In general, the reasons that changed the obliquities are associated to gravitational effects such as collisions or captures in resonances. In this work we intend to build the average system that governs the long period dynamics of the variation of the obliquity of a planet considering the Sun and a satellite with different masses and distances. We will use Andoyer variables, because they are canonical, so averages can be performed rigorously whenever they are made in angle-action variables. The “wooble” issue can be easily incorporated if necessary. We intend with this model to study the variation of the Neptune’s obliquity, but in principle it can also be used in the case of exoplanets (ARMSTRONG et al., 2014). The planet Neptune, apparently is the only one that has no regular primordial satellite, unlike the others. Boué e Laskar (2010), used an additional satellite to explain the Uranus’ obliquity. However, the presence of an additional satellite with very high mass could destabilize the existing primordial ones. In the case of Neptune, the masses of the additional satellites that we intend to use may be much smaller than those used by Boué and Laskar, which eliminates possible destabilization of eventual regular primordial satellites, if they existed.
It is almost a consensus that the planets, when formed, were born with almost zero obliquities. However, for giant planets except Jupiter, the current obliquities ( ) are far from zero. For Saturn, Uranus, and Neptune they are, respectively, 25 . 6 ◦ , 97 . 8 ◦ , 28 . 3 ◦ . In general, the reasons that changed the obliquities are associated to gravitational effects such as collisions or captures in resonances. In this work we intend to build the average system that governs the long period dynamics of the variation of the obliquity of a planet considering the Sun and a satellite with different masses and distances. We will use Andoyer variables, because they are canonical, so averages can be performed rigorously whenever they are made in angle-action variables. The “wooble” issue can be easily incorporated if necessary. We intend with this model to study the variation of the Neptune’s obliquity, but in principle it can also be used in the case of exoplanets (ARMSTRONG et al., 2014). The planet Neptune, apparently is the only one that has no regular primordial satellite, unlike the others. Boué e Laskar (2010), used an additional satellite to explain the Uranus’ obliquity. However, the presence of an additional satellite with very high mass could destabilize the existing primordial ones. In the case of Neptune, the masses of the additional satellites that we intend to use may be much smaller than those used by Boué and Laskar, which eliminates possible destabilization of eventual regular primordial satellites, if they existed.
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Palavras-chave
Obliquidade, Variáveis de Andoyer, Netuno, Obliquity, Andoyer’s variable, Neptune