Question

If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a, show that the orbital speed of the satellite when it is at a distance r from the focus will be given by :

Answer 1

A sin case of elliptical orbit of a satellite mechanical energy  remains constant, at any position of satellite in the orbit,

Now, if at position r, v is the orbital speed of satellite,

So from Eqs. (i) and (ii), we have