Questions on astronomical objects orbiting a star massive enough to be rounded, not massive enough to cause fusion, and which have cleared its orbit of planetesimals.

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Does earth have retrograde motion?

I am a beginner. Please let me know whether earth has retrograde motion If it does not, let me know the reason
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Formulas for gravitatitional equilibrium

I am trying to calculate at which point gravitational equilibrium sets in for various bodys (planets stars neutron stars etc.) assuming they are perfect spheres. However the radius i get is not equal ...
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material exchange between a planet and its host

Of the exo-planets found so far, there is one that can exchange material much with its host? How to prove that? Io may be a good example, but it is not a planet.
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Determining planetary positions on the celestial sphere by Right Ascension and Declination

How would one go about determining the position of the different planets in our solar system with respect to the celestial sphere based on the following data set? Is there a practical way to calculate ...