Use the result of Exercise 35 to calculate the work required to place a 2000-kg satellite in an orbit 1200 km above the surface of the earth. Assume that the earth is a sphere of radius R_e = 6.37 × 10⁶ m and mass M_e = 5.98 × 1024 kg. Treat the satellite as a point mass.

Data From Exercise 35

The gravitational force between two objects of mass m and M, separated by a distance r, has magnitude GMm/r², where G = 6.67 × 10⁻¹¹ m³kg−1s⁻¹.

Show that if two objects of mass M and m are separated by a distance r₁, then the work required to increase the aseparation to a distance r₂ is equal to W = GMm(r₁⁻¹ − r₂⁻¹).