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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 close to: (Neglect the effect of atmosphere.)

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

Correct answer: √gR (√2 − 1)

Solution

The correct option, √gR (√2 − 1), represents the additional velocity needed for the satellite to reach escape velocity from its current orbital velocity. This is derived from the relationship between gravitational potential energy and kinetic energy, where the satellite must overcome the gravitational pull of the Earth to escape.

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