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A satellite of mass m moves in a circular orbit around the Earth. If the Earth has radius R and the satellite is at a height x above the Earth's surface, and g denotes the acceleration due to gravity at the Earth's surface, then the satellite's orbital speed is

1. gR²/(R+x)
2. gR/(R−x)
3. gx
4. (gR²/(R+x))^(1/2)

Correct answer: (gR²/(R+x))^(1/2)

Solution

The correct option derives from the balance of gravitational force and centripetal force acting on the satellite. The gravitational force decreases with distance from the Earth's center, and the orbital speed can be calculated using the formula for circular motion, leading to the expression for speed as the square root of the gravitational force per unit mass at that height.

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