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The planet Uranus has a radius of 25,560 km and a surface acceleration due to gravity of11.1 rn/s2 at its poles. Its moon Miranda (discovered by Kniper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km above the planet s surface. Miranda has a mass of 6.6 X 10 9 kg and a radius of 235 km.
(a) Calculate the mass of Uranus from the given data.
(b) Calculate the magnitude of Miranda s acceleration due to its orbital monon about Uranus.
(c) Calculate the acceleration due to Miranda s gravity at the surface of Miranda.
(d) Do the answers to parts (b) and (c) mean that an object released 1 m above Miranda s surface on the side toward Uranus will fall up relative to Miranda? Explain. |
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