# Problem: Consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and of such a force are given by Newton's law of gravity:F→G=-Gm1m2r2r→,whereds→=drr^; G, m1, and m2 are constants; and r&gt;0.FindU(rf)-U(r0)=∫r0rfFG→·ds→,Express your answer in terms of G, m1, m2, r0, and rf.

###### Problem Details

Consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and of such a force are given by Newton's law of gravity:

${\stackrel{\to }{\mathrm{F}}}_{\mathrm{G}}=-\frac{{\mathrm{Gm}}_{1}{\mathrm{m}}_{2}}{{\mathrm{r}}^{2}}\stackrel{\to }{\mathrm{r}}$,

where

Find

$\mathrm{U}\left({\mathrm{r}}_{\mathrm{f}}\right)-\mathrm{U}\left({\mathrm{r}}_{0}\right)={\int }_{{\mathrm{r}}_{0}}^{{\mathrm{r}}_{\mathrm{f}}}\stackrel{\to }{{\mathrm{F}}_{\mathrm{G}}}·d\stackrel{\to }{\mathrm{s}}$,

Express your answer in terms of G, m1, m2, r0, and rf.

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