Question

A planet of mass 'm' revolves around the sun (of mass M) in an elliptical orbit. The semi major axis of the orbit is 'a'. Find out the total mechanical energy of the planet.

Answer 1

$K.E=\frac{1}{2}{mv}^{2}P.E=\frac{-GMm}{r}$

By conservation of mechanical energy

Total mechanical energy,

$E=\frac{1}{2}{mv}^2-\frac{GMm}{r}=\frac{-GMm}{2a}$

where, $v=\sqrt{GM(\frac{2}{r}-\frac{1}{a})}$