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Find total mechanical energy of an inelastic satellite collision; motion of wreckage

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Consider two satellites, A and B, both of mass m, moving in the same circular orbit of radius r around the Earth, of mass Me, but in opposite senses of rotation and therefore on a collision course.

a) In terms of G, Me, m, and r, find the total mechanical energy Ea and Eb of the two satellites plus Earth's system before 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 collision.

c) Describe the subsequent motion of the wreckage.

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The solution show the formulas and calculations to arrive at the answers.

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a.)Total mechanical energy:
Ea = (1/2) mv0^2 + (-GMem/r) + (-Gm^2/x)
where x is the distance between two masses at any given instant.
assuming m<< Me: ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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