Answer
The variation is $E = -2.69\times 10^{33}~J$ at the closest distance and $E = -2.60\times 10^{33}~J$ at the farthest distance for a difference of $9.0\times 10^{31}~J$
Work Step by Step
We can find the total energy at the closest distance:
$E = -\frac{GMm}{2r}$
$E = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(1.98\times 10^{30}~kg)(5.98\times 10^{24}~kg)}{(2)(1.47\times 10^{11}~m)}$
$E = -2.69\times 10^{33}~J$
We can find the total energy at the farthest distance:
$E = -\frac{GMm}{2r}$
$E = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(1.98\times 10^{30}~kg)(5.98\times 10^{24}~kg)}{(2)(1.52\times 10^{11}~m)}$
$E = -2.60\times 10^{33}~J$
The variation is $E = -2.69\times 10^{33}~J$ at the closest distance and $E = -2.60\times 10^{33}~J$ at the farthest distance for a difference of $9.0\times 10^{31}~J$
