Answer
The variation is $U = -5.372\times 10^{33}~J$ at the closest distance and $U = -5.196\times 10^{33}~J$ at the farthest distance for a difference of $1.8\times 10^{32}~J$
Work Step by Step
We can find the gravitational potential energy at the closest distance:
$U = -\frac{GMm}{r}$
$U = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(1.98\times 10^{30}~kg)(5.98\times 10^{24}~kg)}{1.47\times 10^{11}~m}$
$U = -5.372\times 10^{33}~J$
We can find the gravitational potential energy at the farthest distance:
$U = -\frac{GMm}{r}$
$U = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(1.98\times 10^{30}~kg)(5.98\times 10^{24}~kg)}{1.52\times 10^{11}~m}$
$U = -5.196\times 10^{33}~J$
The variation is $U = -5.372\times 10^{33}~J$ at the closest distance and $U = -5.196\times 10^{33}~J$ at the farthest distance for a difference of $1.8\times 10^{32}~J$.
