Two satellites, A and B, both of mass m 120 kg, move in the same circular orbit

Question

Two satellites, A and B, both of mass m 120 kg, move in the same circular orbit of radius r 8.20 x 106 m around Earth but in opposite senses of rotation and therefore on a collision course. Earth Earth system before the collision? (a) What is the total mechanical energy EAEB of the two satellites -6565695473XJ (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass 2m), what is the total mchaical energy immediately after the collision? 6565695473 x (c) Just after the collision, is the wreckage falling directly toward Earth's center or orbiting around Earth? wreckage falling directly toward Earth's center O wreckage orbiting around Earth

Explanation / Answer

(A) for circular motion,
  
G M m / r^2 = m v^2 / r

m v^2 = G M m / r

KE = m v^2 / 2 = G M m / 2 r

PE =- G M m / r

ME = KE + PE = - G M m / 2 r

ME = - (6.67 x 10^-11 x 5.972 x 10^24 x 120) / (8.20 x 10^6)

ME = - 5.83 x 10^9 J ....Ans

(b) after collision they will stop,

so ME = 2 (- G M m / r)

= - 1.166 x 10^10 J ....Ans

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