Question

a planet of mass M revolves around the sun in an elliptical Orbit who's semi major axis is a and eccentricity is e
then find the minimum and maximum speed of planet if the mass of sun is equal to M ​

Answer 1

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Answer 2

The orbits are ellipses, with focal points F1 and F2 for the first planet and F1 and F3 for the second planet. The Sun is placed in focal point F1.

The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2.

The total orbit times for planet 1 and planet 2 have a ratio {\textstyle \left({\frac {a_{1}}{a_{2}}}\right)^{\frac {3}{2}}} {\textstyle \left({\frac {a_{1}}{a_{2}}}\right)^{\frac {3}{2}}}.