PROBLEM $11\mathrm{.}158$

A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to $g(\frac{R}{r}{)}^2,$ where $g=9\mathrm{.}81\frac{m}{s^2},R=$ radius of the earth $=6370km,$ and $r=$ distance from the center of the earth to the satellite. Assuming that the orbit of the moon is a circle of radius $384{10}^{3}km,$ determine the speed of the moon relative to the earth.