Irodov Problem 1.225

Suppose that the angular velocity of the satellite w.r.t. to the axis of rotation of the Earth is w and that of Earth is wE.
The gravitational force experienced by the satellite is given by and its centripetal acceleration is given by . So we have,



Now the observer fixed to the rotating frame of the Earth is rotating along with the Earth West to East with angular velocity wE, while the satellite moves East to West with angular velocity w. The angular velocity of the satellite as seen by the observer fixed to the rotating axis of Earth wo will be w + wE. So we have,



The velocity of the satellite as seen by an observer who rotates with the Earth and is located at its center is given by,