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# If a planet orbiting around sun,then what is the Velocity of a Planet at Apogee and Perigee ???

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For the below figure

$r_1=r_{p}=a-c$

$r_2=r_{a}=a+c$

If Eccentricity is given by

(e) = $\frac{c}{a}$

Then the velocity of the planet at Apogee and Perigee in terms of Eccentricity is given by

$V_{a}=\sqrt{\frac{GM}{a}\left ( \frac{1-e}{1+e} \right )}$

$V_{p}=\sqrt{\frac{GM}{a}\left ( \frac{1+e}{1-e} \right )}$

$V_{A}=$ The velocity of the planet at apogee

$V_{p}$=The velocity of the planet at apogee

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