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A satellite is revolving in a circular o...

A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R, h ltltR). The minimum increase in its orbital velocity required, So that the satellite could escape from the erth's gravitational field, is close to :(Neglect the effect of atomsphere.)

A

`sqrt(2gR)`

B

`sqrt(g R`

C

`sqrt(g R//2)`

D

`sqrt(gR) (sqrt(2) -1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Orbital velocity, `upsilon_(0) = sqrt((GM)/(R + h)) = sqrt((GM)/(R )) ("as" h lt lt R)`
Velocity required to escape,
`upsilon_(e) = sqrt((2GM)/(R + h)) = sqrt((2GM)/(R ))`
Increase in velocity `= upsilon_(e) - upsilon_(p) = sqrt((2GM)/(R )) - sqrt((GM)/(R ))`
`= sqrt(2g R) - sqrt(g R) = (sqrt(2) -1) sqrt(g R)`
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