A planet of mass m moves along an ellipse around the sum of mass M so that its maximum and minimum distances from sum are a and b respectively. Prove that the angular momentum L of this planet relative to the centre of the sun is `L=msqrt((2GGMab)/((a+b)))`

Explanation

To prove that the angular momentum \( L \) of a planet of mass \( m \) moving in an elliptical orbit around the sun of mass \( M \) is given by

\[ L = m \sqrt{\frac{2G M a b}{a + b}}, \]

where \( a \) is the maximum distance (aphelion) and \( b \) is the minimum distance (perihelion), we can follow these steps:

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