Gravitational orbits — UPSC Physics Optional CSE 2016 Paper I

A body moving in an inverse square attractive field traverses on elliptical orbit with eccentricity e and period \gamma. Find the time taken by the body to traverse the half of the orbit that is nearer the centre of force. Explain briefly why a comet spends only 18\% of its time on the half of its orbit that is nearer the sun.