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A satellite is describing a circular orbit around a massive planet of radius 'R' The altitude of the orbit above the surface of planet is 3R. To place the satellite in elliptical orbit which will bring it closer to the planet its velocity reduced from $v_{0}$ to $β v_{0} (β < 1) .$ The smallest permissible value of $β$ if satellite is not to crash on the surface of planet is $\sqrt{\frac{2}{K}}$ the value of K is

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answer is 5.

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Detailed Solution

Path of satellite after reducing velocity is as shown.

$\Rightarrow E = \frac{- G M m}{5 R} = \frac{- G M m}{4 R} + \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{\frac{G M m}{10 R}} \Rightarrow β = \sqrt{\frac{2}{5} .}$

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