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Newton's Law of Universal Gravitation

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Imagine a line drawn from the center of the earth to the center of the moon. At some point on this line the magnitude of the gravitational attraction of the moon on a space vehicle would be equal to the magnitude of the earth's gravitational attraction on the vehicle. If the distance from the earth to the moon is about 4.0 x 10^5 km and the mass of the moon is about 1/80 that of the earth, at what distance from the earth's center will the resultant force acting on the space vehicle be zero?

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Newton's law of gravitation..

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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