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A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:

1. √gR(√2 - 1)
2. √2gR
3. √gR
4. √(gR)/2

Correct answer: √gR(√2 - 1)

Solution

For h << R, orbital speed = sqrt(gR) and escape speed = sqrt(2gR). Minimum extra speed = sqrt(2gR) - sqrt(gR) = sqrt(gR)(sqrt2 - 1).

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