Question
A planet rotates about the sun in an elliptical orbit whose eccentricity is e. What is the ratio of maximum to a minimum velocity of the planet?
Solution
Let a planet rotate about the sun in an elliptical orbit whose semi-major axis is a and eccentricity is e as shown.
Since, angular momentum of planet is constant
i.e., mvr = constant,
therefore v is maximum when planet is at the nearest point.
i.e., at P1 and minimum when it is at the farthest point i.e. at P2.
Distance of P1 from the sun =a - ae
=a( 1- e)
Distance of P2 from the sun =a + ae
=a( 1 + e)
According to the law of conservation of angular momentum, 
