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Let the Earth have mean radius R, angular velocity ω about its own axis, and surface gravitational acceleration g. The orbital radius of a geostationary satellite is:

1. (R² g / ω²)^(1/3)
2. (Rg / ω²)^(1/3)
3. (R² ω² / g)^(1/3)
4. (R² g / ω)^(1/3)

Correct answer: (R² g / ω²)^(1/3)

Solution

The correct option is derived from balancing the gravitational force acting on the satellite with the centripetal force required for circular motion, leading to the relationship that defines the orbital radius of a geostationary satellite in terms of Earth's radius, gravitational acceleration, and angular velocity.

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