Two satellites, A and B, both of mass m = 138 kg, move in the same circular orbi
ID: 2252175 • Letter: T
Question
Two satellites, A and B, both of mass m = 138 kg, move in the same circular orbit of radius r = 8.20 106 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? Just after the collision, is the wreckage falling directly toward Earth's center or orbiting around Earth?Explanation / Answer
a)
total mechanical enrgy = potential enrgy/2
= -(G*Me*m/r)/2 + -(G*Me*m/r)/2
= -G*Me*m/r
= -6.67*10^-11*5.972*10^24*138/(8.2*10^6)
= -6.7*10^9 J
b)
kinetic energy becomes zero.
they will have only potential energy.
U = -G*Me*2*m/r
= -6.67*10^-11*5.972*10^24*2*138/(8.2*10^6)
= -13.4*10^9 J
c) their velocity becomes zero. so they fall towards the earth's center
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