Answer
$E = -1.27\times 10^{10}~J$
Work Step by Step
Let $v$ be the linear velocity of satellite A just before the collision.
Then $-v$ is the linear velocity of satellite B just before the collision.
We can use conservation of linear momentum to find the velocity after the collision:
$p_f = p_i$
$(2m)~v_f = mv+m(-v)$
$(2m)~v_f = 0$
$v_f = 0$
Therefore, the kinetic energy in the system is zero.
We can find the total mechanical energy after the collision:
$E = U+K$
$E = U+0$
$E = -\frac{GM(2m)}{r}$
$E = -\frac{2GMm}{r}$
$E = -\frac{(2)(6.67\times 10^{-11}~N~m^2/kg^2)(5.98\times 10^{24}~kg)(125~kg)}{7.87\times 10^6~m}$
$E = -1.27\times 10^{10}~J$
