Question

A planet of mass M is in an elliptical orbit around the sun with time period T. The semi major axis and semi minor axis are equal to a and b respectively. Find the angular momentum of the planet.

Answer 1

$$\begin{gathered} Weknowthat\frac{M{v}^2}{a}=\frac{G{M}_{s}M}{a^2} \\ or\frac{M{\omega }^2{a}^2}{a}=\frac{G{M}_{s}M}{a^2} \\ or{\omega }^2=\frac{G{M}_s}{a^3} \\ or\omega =\sqrt{\frac{G{M}_s}{a^3}} \\ Nowangularmomentum=I\omega =M{a}^2\times \sqrt{\frac{G{M}_s}{a^3}}=M\sqrt{G{M}_{s}a} \end{gathered}$$