# Gravitation: Potential

### Problems on Potential Energy

Problem : What is the gravitational potential energy of the moon with respect to the earth? The mass of the moon is 7.35×1022 kilograms and the mass of the earth is 5.98×1024 kilograms. The earth moon distance is 384 400 kilometers.

Problem : What is the gravitational potential with respect to the sun at the position of the earth? The mass of the sun is 1.99×1030 kilograms and the mass of the earth is 5.98×1024 kilograms. The mean earth-sun distance is 150×106 kilometers.

Problem : What is the total energy of a 90 kilogram satellite with a perigee distance 595 kilometers and apogee distance 752 kilometers, above the surface of the earth? The mass of the earth is 5.98×1024 kilograms and its radius is 6.38×106 m.

Problem : Calculate the orbital energy and orbital speed of a rocket of mass 4.0×103 kilograms and radius 7.6×103 kilometers above the center of the earth. Assume the orbit is circular. ( M e = 5.98×1024 kilograms).

Problem : A satellite of mass 1000 kilograms is launched with a speed of 10 km/sec. It settles into a circular orbit of radius 8.68×103 km above the center of the earth. What is its speed in this orbit? ( M e = 5.98×1024 and r e = 6.38×106 m).

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