Answer: 2*pi*sqrt(d 3 /(2GM)).
- A 2*pi*sqrt(d<sup>3</sup>/(2GM))
- B 2*pi*sqrt(d<sup>3</sup>/(GM))
- C pi*sqrt(d<sup>3</sup>/(2GM))
- D 2*pi*sqrt(d<sup>3</sup>/(4GM))
Correct answer: A. 2*pi*sqrt(d<sup>3</sup>/(2GM))
Explanation: Each star orbits at distance d/2 from center. Centripetal force = GM<sup>2</sup>/d<sup>2.</sup> (d/2)x omega<sup>2</sup> x M = GM<sup>2</sup>/d<sup>2.</sup> omega<sup>2</sup> = 2GM/d<sup>3.</sup> T = 2*pi/omega = 2*pi*sqrt(d<sup>3</sup>/(2GM)).
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.