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A planet of mass m revolves in elliptica...

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.

A

`L=msqrt((GMr_(p)r_(a))/((r_(p)+r_(a))))`

B

`L=msqrt((2GM_(p)r_(a))/((r_(p)+r_(a))))`

C

`L=Msqrt((Gm_(p)r_(a))/((r_(p)+r_(a))))`

D

`L=Msqrt(((r_(p)+r_(a)))/(Gmr_(p)r_(a))))`

Text Solution

Verified by Experts

The correct Answer is:
B
From conservation of energy
`-(GMm)/(r+1/2mv_(p)^(1))=(-GMm)/(r+1/2mv_(a)^(2)`
`L=mv_(p)r_(p)=mv_(a)r_(a)`
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