A satellite revolves in a circular polar orbit with an angular speed equal to the angular speed of t

Question

A satellite revolves in a circular polar orbit with an angular speed equal to the angular speed of the earth's rotation. If the satellite is directly above the north pole at some instant, find the time it takes to come over the equatorial plane.

Professor PC Thomas Classes · Answer

Since the angular speed matches the earth's rotation, its time period is $T = 24~hours$. Moving from the north pole to the equator covers one-fourth of the orbit, so the time taken is $T/4 = 24/4 = 6~hours$.