In the figure,two satellites, A and B,both of mass m = 125kg, move in the same c

Question

In the figure,two satellites, A and B,both of mass m = 125kg, move in the same circular orbit of radius r = 7.87 x10^6 m around Earth but in opposite senses of rotation and therefore on a collision course.

(a) Find the total mechanical energy EA + EB of the two satellites + Earth system before the collision.
(b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision.
(c) Just after the collision,is the wreckage falling directly toward Earth’s center or orbiting around Earth?

Explanation / Answer

U = -GMm/r K = -GMm/2r

Total E = U + K U is the Earth system's energy, K is the satellites' energy

There are 2 satellites for (a), so I figure m = 2m r is radius of earth + radius of orbit

E = -GMm/2r

E = -GM(2)m

E = -6.67e-11 * 5.98e24 * 2(125) / (6.38e6 + 7.87e6)

E = -6344939986 J

For part (b), since m also equals 2m, I also get -6344939986 J

C. YES IT IS

Reference https://www.physicsforums.com/threads/satellites-orbits-and-gravitational-energy.306301/

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