Question

A satellite of mass m is in elliptical orbit around the Earth. The speed of the satellite is at its nearest position is =√6GM/5r

where r is the perigee (nearest point) distance from the center of the Earth. It is desired to transfer the satellite to the circular orbit of radius equal to its apogee (farthest point) distance from the center of the Earth. The change in orbital speed required for this purpose is
A. 0.35√Gme/r
B. 0.075√Gme/r
C. √2Gme/r
D. Zero

Answer 1

The change in orbital speed required to transfer the satellite from an elliptical orbit to a circular orbit with a radius equal to its apogee distance is √2Gme/r. Hence the correct option is c.

To transfer the satellite from its elliptical orbit to a circular orbit with a radius equal to its apogee distance, we can apply the principle of conservation of energy. The speed of the satellite at its nearest position is given as
`√(6Gm/5r)`. In a circular orbit, the speed is
`√(GM/r)`. The change in kinetic energy during this transfer is equal to the change in potential energy.

By equating the initial kinetic and potential energies to the final kinetic and potential energies, and solving for the change in speed, we find that the required change in orbital speed is
`√(2) √(GM/r)`. Hence the correct option is c.