Obtain an expression for the minimum speed required by the body to become a satellite of earth, in terms of mass of the earth and its distance from the centre of earth.

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Solution

Dear Student,

$A b o d y r e v o l v i n g a r o u n d E a r t h a t a c e r t a i n s p e e d, e x p e r i e n c e s t w o f o r c e s C e n t r i f u g a l f o r c e a c t i n g o u t w a r d F_{C} = \frac{m_{s} {v_{s}}^{2}}{R_{o r b i t}} G r a v i t a t i o n a l f o r c e o f a t t r a c t i o n, i n w a r d t o w a r d s e a r t h : F_{G} = G \frac{M_{E a r t h} m_{s}}{{R_{o r b i t}}^{2}} F o r a f i x e d o r b i t a l d i s \tan c e, C e n t r i f u g a l f o r c e = G r a v i t a t i o n a l f o r c e o f a t t r a c t i o n F_{C} = F_{G} o r, \frac{m_{s} {v_{s}}^{2}}{R_{o r b i t}} = G \frac{M_{E a r t h} m_{s}}{{R_{o r b i t}}^{2}} o r, v_{s} = \sqrt{\frac{G M_{E a r t h}}{R_{o r b i t}}} {T h i s i s t h e o r b i t a l s p e e d o f a s a t e l l i t e f o r a s p e c i f i c o r b i t} W h e r e : G = g r a v i t a t i o n a l c o n s t a n t M_{Earth} = mass of earth R_{orbit} = Radius of the orbit from the centre of earth v_{s} = speed of the body / satellite$

Regards.

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