If a satellite is revolving around the earth in a circular orbit in a plane containing earth’s axis of rotation. If the angular speed of satellite is equal to that of earth, find the time in hours that  it takes to move from a point above north pole to a point above the equator.

A satellite which rotates with angular speed equal to earth’s rotation has an orbit radius $7R_e$
and the angular speed of revolution is

$\omega =\frac{2\pi }{T}=\frac{2\pi }{86400}=7.27\times \frac{{10}^{-5}\mathrm{rad}}{\mathrm{s}}$

When satellite moves from a point above north pole to a point above equator, it traces an

angle $\frac{\pi }{2}$, this time taken is

$\mathrm{t}=\frac{\pi /2}{\omega }=21600\mathrm{s}=6\mathrm{h}$