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Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Gravitation
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Speed of a planet in an elliptical orbit with semi major axis 'a' about sum of mass M at a distance r from the sun is

\[(a)\;\sqrt {GM \bigg(\frac{2}{r}-\frac{1}{a}\bigg)} \quad (b)\;\sqrt {GM \bigg(\frac{1}{r}-\frac{1}{a}\bigg)} \quad (c)\;\sqrt {GM \bigg(\frac{1}{r}-\frac{2}{a}\bigg)} \quad (d)\;\sqrt {\frac{GMr}{2a^2}} \]

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Total energy of a planet in an elliptical orbit is
$E= \large\frac{-GMm}{2a}$ (m= mass of planet )
By conservation of mechanical energy
$ KE+P.E= E$
$\large\frac{1}{2} $$mv^2 -\large\frac{GMm}{r}=\frac{-GMm}{2a}$
$v=\sqrt {GM \bigg(\large\frac{2}{r}-\frac{1}{a}\bigg)}$
Hence a is the correct answer
answered Aug 29, 2013 by meena.p
edited Jul 3, 2014 by lmohan717

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