Leis de Cassini

As Leis de Cassini fornecem uma descrição compacta do movimento da Lua. Foram estabelecidas em 1693 por Giovanni Domenico Cassini, um cientista proeminente do seu tempo.[1]

Estas leis foram refinadas para incluirem librações físicas,[1] e foram generalizadas para tratar outros satélites e planetas.[2][3]

Leis de Cassini

  1. a Lua tem ressonância orbital 1:1. Tal significa que o quociente rotação/órbita da Lua é tal que a face da Lua voltada para a Terra é sempre a mesma.
  2. o eixo de rotação da Lua mantém o ângulo de inclinação com o plano da eclíptica. O eixo de rotação da Lua forma um cone que intersecta o plano eclíptico como um círculo.
  3. o plano formado pela normal ao plano eclíptico e uma normal do plano orbital da Lua conterá o eixo de rotação da Lua.

No caso da Lua, o seu eixo de rotação aponta sempre cerca de 1,5 graus desviado do polo norte eclíptico. A normal ao plano orbital e o eixo rotacional encontram-se sempre em lados opostos da normal à eclíptica.

Portanto, tanto a normal ao plano orbital como o eixo rotacional da Lua giram em volta do polo eclíptico com o mesmo período. O período é de aproximadamente 18 anos e o movimento é retrógrado.

Estado de Cassini

Um sistema que obedeça a estas leis diz-se estar em estado Cassini, isto é: um estado rotacional evoluído onde o eixo de rotação, normal à órbita e a normal ao plano de Laplace são coplanares enquanto a obliquidade permanece constante.[2][4] O plano de Laplace é definido como sendo o plano à volta do qual a órbita de um planeta gira com inclinação constante relativamente aos planos equatorial e eclíptico.[4]

Referências e notas

  1. ↑ a b Para a redação original das leis ver V V Belet︠s︡kiĭ (2001). Essays on the Motion of Celestial Bodies. [S.l.]: Birkhäuser. p. 181. ISBN 3764358661 
  2. ↑ a b Marie Yseboodt & Jean-Luc Margot Evolution of Mercury’s obliquity
  3. ↑ V V Belet︠s︡kiĭ (2001). Essays on the Motion of Celestial Bodies. [S.l.]: Birkhäuser. p. 179. ISBN 3764358661 
  4. ↑ a b Y. Calisesi (2007). Solar Variability and Planetary Climates. [S.l.]: Springer. p. 34. ISBN 038748339X 

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