Two satellites of masses m and 1.5 m are revolving around the earth with different speeds in two circular orbits of heights R _E and 2 R _E respectively, where R _E is the radius of the earth. The ratio of the minimum and maximum gravitational forces on the earth due to the two satellites is

Step-by-step solution

Maximum force, F _ = F ₁+ F ₂= CM _ m (2 R _ E )^2 + 1.5 GM _ m (3 R _ E )^2 = 5 12 GM _ m R _ E ^2 aligned & Minimum force, F _ = F ₁- F ₂ & = GM _ m (2 R _ E )^2 - 1.5 CM _ m (3 R _ E )^2 = 1 12 GM _ m R _ E ^2 aligned F _ F _ = GM _ m 12 R _ E ^2 12 R _ E ^2 5 GM _ m = 1 5 =1: 5