Problem 11.5

11.5.

We are looking for the point where the gravitational accelerations are the same.
$\frac{G M_{e}}{d_{e}^{2}} ~=~ \frac{G M_{m}}{d_{m}^{2}}$
Solving we find that
$d_{m} = d_{e} \sqrt{\frac{M_{m}}{M_{e}}}$
or $d_{m} = \frac{d_{e}}{9.01}$
and since we know that
$d_{e}+d_{m}=3.84 \times 10^{8} m$
we can see that the point where the accelerations are equal is when the capsule is a distance of
$d_{e} = 3.46 \times 10^{8} m$ away from the center of the earth.