Question

A satellite of mass m is in an elliptical orbit around the Earth, which has mass M_e and radius R_e. The orbit varies from closest approach of distance a at point A to maximum distance of b from the center of the Earth at point B. At point A, the speed of the satellite is v₀. Assume that the gravitational potential energy U_g = 0 when masses are an infinite distance apart. Express your answers in terms of some or all the variables a, b, m, M_e, R_e, v₀, and G.

Write the expression for the total mechanical energy of the satellite when it is at point A.

Write the expression for the speed of the satellite as it passes point B in its orbit.

As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth. Write the expression for the speed of the satellite for this circular orbit.

Write the expression for the work done by the rocket engine to effect this change.

Answer 1