the ratio of kinetic energy required to be given to the satellite to escape from earth surface to the kinetic energy required to be given to the same satellite to revolve around the earth in an orbit just above earth surface is??

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Solution

$t h a t d e p e n d o n t h e h e i g h t w h i c h y o u w a n t t o p l a c e t h e s a t e l l i t e . l e t t h e h e i g h t b e h t h e n t h e r a d i u s o f t h e o r b i t i s R + h . s p e e d o f t h e s a t e l l i t e v = \sqrt{\frac{G M}{R + h}} . K E a t e a r t h = \frac{G M m}{R} - \frac{G M m}{R + h} + \frac{m v^{2}}{2} = \frac{G M m}{R} - \frac{G M m}{R + h} + \frac{G M m}{2 (R + h)} = \frac{G M m}{R} - \frac{G M m}{2 (R + h)} = G M m (\frac{R + 2 h}{2 R (R + h)}) o f t h e s a t e l l i t e . K E f o r t h e e s c a p e v e l o c i t y = \frac{m (\frac{2 G M}{R})}{2} = \frac{G M m}{R} r a t i o = \frac{\frac{G M m}{R}}{G M m (\frac{R + 2 h}{2 R (R + h)})} = \frac{2 R^{2} (R + h)}{R + 2 h} R E g a r d s$

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