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A satellite orbits in a circle at height h above the Earth's surface, with h much smaller than the Earth's radius R. What is the minimum extra orbital speed it must gain to escape Earth's gravity? (Neglect atmospheric effects.)

1. sqrt(gR) * (sqrt(2) - 1)
2. sqrt(2gR)
3. sqrt(gR)
4. sqrt(gR)/2

Correct answer: sqrt(gR) * (sqrt(2) - 1)

Solution

For a low orbit, the orbital speed is sqrt(gR) and escape speed is sqrt(2)*sqrt(gR). The minimum boost is their difference.

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