The distance between Earth's surface and an object of mass \(m\) is changed by an amount \(\Delta x\). Show that when \(x \approx R_{\mathrm{E}}\) and \(\Delta x \ll R_{\mathrm{E}}\), where \(R_{\mathrm{E}}\) is the radius of Earth, the general expression for gravitational potential energy, Eq. 13.9, reduces to the expression \(\Delta U^{G}=m g \Delta x\) (Eq. 7.19).

Data from Eq. 13.9

Data from Eq. 7.19

Transcribed Image Text:

AUG = Gmm x; xf,