A satellite travels around the Earth in a circular orbit of radius R. The angular speed of...

A satellite travels around the Earth in a circular orbit of radius R. The angular speed of a satellite varies inversely with its distance from Earth according to ω2 = k/R3, where k is a constant. Observers hi die satellite see an object moving nearby, also presumably in orbit about Earth. To describe its motion, they use a coordinate system fixed to the satellite with x-axis pointing away from Earth and y-axis pointing in the direction in which the satellite is moving. Show that die equations of motion for die nearby object with respect to die observers’ frame of reference are given approximately by

(see Example 2.3.2 for the force of gravity that Earth exerts on an object at a distance r from it and ignore the gravitational effect of the satellite on the object).