Chapter 5 - Dynamics of Uniform Circular Motion - Problems - Page 139: 36

$T=1.44\times10^4s=4hr$

We have $M_E=5.98\times10^{24}kg$ and $G=6.67\times10^{-11}Nm^2/kg^2$ The radius of the orbit $r=2r_E=2\times6.38\times10^6=1.276\times10^7m$ The period of the satellite is $$T=\frac{2\pi r^{3/2}}{\sqrt{GM_E}}=1.44\times10^4s=4hr$$