Asatellite moves in a circular orbit around the earth at a speed of 5 km/s. determine the satellite’s altitude above the surface of the earth. assume the earth is a homogeneous sphere of radius 6370 km and mass 5.98 x 10^24 kg. the value of the universal gravitational constant is 6.67259 x 10^−11 n* m^2 /kg^2 . answer in units of km.

Explanation:

Writing Newton's 2nd Law and Newton's Gravitational Law on the satellite (of mass m, experimenting an acceleration a) orbiting Earth (of mass M) with r as the distance between their centers we have:

Since this acceleration is centripetal, we can write:

So we have:

Or:

This distance r is the sum of Earth's radius R and the satellite's altitude h (r=R+h), so for our values we have (in S.I.):