KVPY SX SB Exam 2012 Question Paper

Question : 25 of 120

Marks: +1, -0

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

$v_P/v_A={1+e}/{1-e}$
$v_P/v_A={1+e^2}/{1-e}$
$v_P/v_A=1$
$v_P/v_A={1+e^2}/{1-e^2}$

Validate

Solution:

Using conservation of angular momentum

v_p.r_p=v_A.r_A

v_p/v_a=r_A/r_p={a+ae}/{a-ae}

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