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The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite?

1. (R²g/ω²)¹/³
2. (Rg/ω²)¹/³
3. (R²ω²/g)¹/³
4. (R²g/ω)¹/³

Correct answer: (R²g/ω²)¹/³

Solution

A geostationary satellite must have the same angular speed as Earth's rotation. Equating the centripetal force to gravitational force, we get the radius of the orbit as (R²g/ω²)^(1/3).

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