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Surface acceleration due to gravity

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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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