Geostationary orbits: For communications satellites to work properly, they should appear from the surface of the Earth to remain stationary. That is, they should orbit the Earth exactly once each day....

Geostationary orbits: For communications satellites to work properly, they should appear from the surface of the Earth to remain stationary. That is, they should orbit the Earth exactly once each day. For any satellite, the period P (the length of time required to complete an orbit) is determined by its mean distance A from the center of the Earth. For a satellite of negligible mass, P and A are related by a power function A = cP2/3 .

a. The moon is 239,000 miles from the center of the Earth and has a period of about 28 days. How high above the center of the Earth should a geostationary satellite be? (Hint: You want the distance A for a satellite with period 1 28 that of the moon. The homogeneity property of power functions is applicable.)

b. The radius of the Earth is about 3963 miles. How high above the surface of the Earth should a geostationary satellite be?