# Satellites, Orbits and Gravitational Energy

Two satellites, A and B, both of mass m = 110 kg, move in the same circular orbit of radius r = 7.45 x 10^6 m around Earth but in opposite senses of rotation and therefore on a collision course.

(a) What is 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), what is the total mechanical energy immediately after the collision?

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

E = -GMm/2r
E = -GM(2)m
E = -6.67e-11 * 5.98e24 * 2(110) / (6.38e6 + 7.54e6)
E = -6344939986 J

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

Is there anything wrong? Because my online thing isn't accepting my answer...

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D H
Staff Emeritus
You have several things wrong here.
1. K = -GMm/2r
Kinetic energy, 1/2mv2, is always positive.

2. 6.38e6 + 7.54e6
Your problem statement indicates r=7.54e6 meters is the orbital radius, not the orbital altitude. Which is correct?

3. For part (b), since m also equals 2m, I also get -6344939986 J
What is the kinetic energy after the collision?