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Newton's law of gravitation

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The planet Uranus has a radius of 25,560 km and a surface acceleration due to gravity of 11.1 m/s^2 at its poles. Its moon Miranda (discovered by Kuiper 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 10^19 kg and a radius of 235 km.

1) Calculate the mass of Uranus from the above data.
2) Calculate the magnitude of Miranda's acceleration due to its orbital motion about Uranus.
3) Calculate the acceleration due to Miranda's gravity at the surface of Miranda.

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The problem has been solved using Newton's law of gravitation.

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SOLUTION

As per Newton's law of gravitation force experienced by an object of mass m on the surface of a planet of mass M and radius R is given by : F = G mM/R2 where G = Universal gravitational constant = 6.67 x 10-11 Nm2kg-2. ...........(1)

As per Newton's second law : Force F = Mass x Acceleration ...

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