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A satellite of mass m orbits the earth i...

A satellite of mass m orbits the earth in an elliptical orbit having aphelion distance `r_(a)` and perihelion distance `r_(p)`. The period of the orbit is T. The semi-major and semi-minor axes of the ellipse are `(r_(a) + r_(p))/(2)` and `sqrt(rho_(p)r_(a))` respectively. The angular momentum of the satellite is :

A

`(mpi(r_(a) + r_(p))sqrt(r_(a)r_(p)))/(T)`

B

`(2mpi(r_(a) + r_(p))sqrt(r_(a)r_(p)))/(T)`

C

`(mpi(r_(a) + r_(p))sqrt(r_(a)r_(p)))/(2T)`

D

`(mpi(r_(a) + r_(p))sqrt(r_(a)r_(p)))/(4T)`

Text Solution

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The correct Answer is:
A
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