A satellite is revolving in a circular orbit at a height 'h' from the earth's surface(radius of earth R; h<<R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is closed to(Neglect the effect of atmosphere.)
A
2gR
B
gR
C
gR/2
D
gR(2−1)
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Solution
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Correct option is D)
For a satellite in orbit, the velocity can be evaluated from the following equation,
r2GMm=rmvo2
vo=rGM
Here, r=R+h
For satellite to escape, total energy of satellite must be zero. Let escape velocity of satellite at height h be ve.