Question

Gravitational potential energy of interaction of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $r$
$U=-\frac{G{m}_1{m}_2}{r}$.

Answer 1

$F=\frac{G{m}_1{m}_2}{r^2}$

Potential energy $=+{\int }_0^{r}Fdr$

$\Rightarrow PE=+{\int }_0^r\frac{G{m}_1{m}_2}{r^2}dr$

$\Rightarrow PE=\frac{-G{m}_1{m}_2}{r}$