Answer: sqrt(GM/(R+h)).
- A sqrt(GM/R)
- B sqrt(GM/(R+h))
- C sqrt(2GM/(R+h))
- D sqrt(gR<sup>2</sup>/(R+h))
Correct answer: B. sqrt(GM/(R+h))
Explanation: Orbital velocity: v<sub>o</sub> = sqrt(GM/(R+h)) for a satellite at height h.
g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.
Concept context
Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.