**Problem : **
What is the gravitational potential energy of the moon with respect to the
earth? The mass of the moon is
7.35×10^{22}
kilograms and the mass of
the earth is
5.98×10^{24}
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
1.99×10^{30}
kilograms and the
mass of the earth is
5.98×10^{24}
kilograms. The mean earth-sun
distance is
150×10^{6}
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
5.98×10^{24}
kilograms and its radius is
6.38×10^{6}
m.

**Problem : **
Calculate the orbital energy and orbital speed of a rocket of mass
4.0×10^{3}
kilograms and radius
7.6×10^{3}
kilometers above the center of the
earth. Assume the orbit is circular. (
*M*
_{e} = 5.98×10^{24}
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
8.68×10^{3}
km above the center
of the earth. What is its speed in this orbit? (
*M*
_{e} = 5.98×10^{24}
and
*r*
_{e} = 6.38×10^{6}
m).

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