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A satellite or moon orbits a planet with a period Ps. At the same time, the...

A satellite or moon orbits a planet with a period Ps. At the same time, the satelliteplanet system orbits a star with a period Pp. Assume that the satellite–planet distance is smaller than the Hill instability limit, so that this system is stable. Show that this implies that P?s < P?p. Assume coplanar circular orbits for simplicity, and assume that ms < m?p < m?t, where m?s, m?p, and m?t are the masses of the satellite, planet, and star, respectively.

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