What is the relationship between Eq (15.21), which is the gravitational potential energy n...

What is the relationship between Eq (15.21), which is the gravitational potential energy neglecting the variation of the gravitational force with height, and Eq. (15.23), which accounts for the variation? Express the distance from the center of the earth as r = RE + y, where RE is the earth’s radius and y is the height above the surface, so that Eq. (15.23) can be written as

By expanding this equation as a Taylor series in terms of y/REand assuming that y/RE ≪ 1. show that you obtain a potential energy equivalent lo Eq. (15.21).