Two satellites, A and B, both of mass m = 130 kg, move in the same circular orbi

Question

Two satellites, A and B, both of mass m = 130 kg, move in the same circular orbit of radius r = 8.62 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? (c) Just after the collision, is the wreckage falling directly toward Earths center or orbiting around Earth? wreckage falling directly toward Earths center wreckage orbiting around Earth

Explanation / Answer

a)

EA = -G*Me*m/(2*Re)

EB = -G*Me*m/(2*Re)

EA + EB = -G*Me*m/(2*Re) - G*Me*m/(2*Re)

= -G*Me*m/Re

= -6.67*10^-11*5.98*10^24*130/(8.62*10^6)

= -6.015*10^9 J

b) When completely inelastic collsion, takes place, final kinetic energy will be zero.

so, EA + EB = 2*(-6.015*10^9)

= -1.203*10^10 J

c) wreckage falling towards earth center

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