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?

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Accepted Answer

(1) ((R²g)/(ω²))^1/3. A geostationary satellite turns with the earth, so its angular speed is ω. Gravity supplies the centripetal force: (GMm)/(r²)=mω²r. So r³=(GM)/(ω²). Writing GM=gR² puts this in terms of the quantities given: r³=(gR²)/(ω²). r=((R²g)/(ω²))^1/3.

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?

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