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A planet orbits in an elliptical path of...

A planet orbits in an elliptical path of eccentricity e around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by P and the point where it is farthest is denoted by A. Let `v_(p)` and `v_(a)` be the respective speeds at P and A. Then–

A

`(V_p)/(V_A)=(1+e)/(1-e)`

B

`(V_p)/(V_A)=1`

C

`(V_p)/(V_A)=(1+e^2)/(1-e)`

D

`(V_p)/(V_A)=(1+e^2)/(1-e^2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Angular momentum conservation about S
`V_p(a-ae)=V_a(a+ae)`
`(V_p)/(V_A)=(a+ae)/(a-ae)`
`(V_P)/(V_A)=(1+e)/(1-e)`
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