Chapter 9, Problem 25P

The variation of gravitational acceleration g with altitude y is given by:

$g=\frac{R_2}{{(R+y)}^2}{g}_0$

where R = 6371 km is the radius of the Earth, and g₀ = 9.81 m/s² is the gravitational acceleration at sea level. The change in the gravitational potential energy, ?U, of an object that is raised from the Earth is given by:

$\Delta U={\displaystyle {\int }_0^{h}mhdy}$

Determine the change in the potential energy of a satellite with a mass of 500 kg that is raised from the surface of the Earth to a height of 800 km.