Irodov Problem 1.224

Let w be the satellites angular velocity w.r.t the axis of rotation of Earth and let wE be the Earth's angular velocity.
Earth rotates from West to East (since sun rises in the East and sets in the West). The satellite is also moving from West to East i.e. in the same direction as that of Earth's rotation about its axis. The angular velocity seen by an observer wo on the Earth will thus be w-wE. Thus, we have,

The force of gravity at the satellite is acting radially inwards, its centripetal acceleration is . The mass of the satellite being m and M is the mass of the Earth. So we have,