A planet of mass `m` revolves in elliptical orbit around the sun of mass `M` so that its maximum and minimum distance from the sun equal to `r_(a)` and `r_(p)` respectively. Find the angular momentum of this planet relative to the sun.

Options

A. `L=msqrt((GMr_(p)r_(a))/((r_(p)+r_(a))))`
B. `L=msqrt((2GMr_(p)r_(a))/((r_(p)+r_(a))))`
C. `L=Msqrt((GMr_(p)r_(a))/((r_(p)+r_(a))))`
D. `L=Msqrt(((r_(p)+r_(a)))/(GMr_(p)r_(a)))`

Answer

B

Explanation

From conservation of energy
`-(GMm)/(r_(p))+1/2mv_(p)^(2)=(-GMm)/(r_(a))+1/2mv_(a)^(2)`
`L=mv_(p)r_(p)=mv_(a)r_(a)`