Two satellites P and Q move in circular orbits around Earth of radius R. Satellite P is at height R/3 above the surface. If the ratio of gravitational acceleration at P to that at Q is 36/25, find the height of satellite Q.
Options

Question

Two satellites P and Q move in circular orbits around Earth of radius R. Satellite P is at height R/3 above the surface. If the ratio of gravitational acceleration at P to that at Q is 36/25, find the height of satellite Q.

Options

G1 Physics · Accepted Answer

For a circular orbit at height h, gravitational acceleration is g = GM/(R+h)². For P, R+h = 4R/3. Let the orbital radius of Q be r. Given g at P divided by g at Q = 36/25, we have r²/(4R/3)² = 36/25, so r = 8R/5. Therefore height of Q = 8R/5 - R = 3R/5. Correct answer: A.