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:

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

where

$\mathrm{d}\overrightarrow{\mathrm{s}}=\mathrm{dr}\hat{\mathrm{r}};\mathrm{G},{\mathrm{m}}_{1},\mathrm{and}{\mathrm{m}}_{2}\mathrm{are}\mathrm{constants};\mathrm{and}\mathrm{r}0.$

Find

$\mathrm{U}\left({\mathrm{r}}_{\mathrm{f}}\right)-\mathrm{U}\left({\mathrm{r}}_{0}\right)={\int}_{{\mathrm{r}}_{0}}^{{\mathrm{r}}_{\mathrm{f}}}\overrightarrow{{\mathrm{F}}_{\mathrm{G}}}\xb7d\overrightarrow{\mathrm{s}}$,

Express your answer in terms of G, m_{1}, m_{2}, r_{0}, and r_{f}.

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