Answer
$5.144 \times 10^{10}$ joules
Work Step by Step
Here, we have $W=\int_a^b\dfrac{mMG}{r^2}dr$
or, $W=\dfrac{mMG}{\dfrac{1}{a}}-\dfrac{mMG}{\dfrac{1}{b}}$
This implies that
$W=mMG(\dfrac{1}{a}-\dfrac{1}{b})$
Plug in the values.
$W=(1000)(5.975 \times 10^{24}) (6.6720 \times 10^{-11})(\dfrac{1}{6370000}-\dfrac{1}{35780000})$
Thus, $W=5.144 \times 10^{10}$ joules
