question_answer

A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the time spent by the planed between the ends of the minor axis and major axis close to the sun is

A) \[\frac{T\pi }{2e}\]

B) \[T\left( \frac{2e}{\pi }-1 \right)\]

C) \[\frac{Te}{2\pi }\]        

D) \[T\left( \frac{1}{4}-\frac{e}{2\pi } \right)\]

Correct Answer: D

Solution :

  As areal velocity of a planet around the sun is constant. Therefore, the desired time is If a = semi-major axis and b = semi-minor axis of ellipse, then,