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Consider two satellites A and B of equal...

Consider two satellites `A` and `B` of equal mass, moving in the same circular orbit of radius `r` around the earth but in the opposite sense and therefore a collision occurs.
(a) Find the total mechanical energy `E_(A) + E_(B)` of the two satellite-plus-earth system before collision.
(b) If the collision is completely inelastic, find the total mechanical energy immediately after collision. Describe the subsequent motion of the combined satellite.

Text Solution

Verified by Experts

Initial total energy of each satellite `=-(GMm)/(2r)`
Hence, total energy of both satellites
`2xx(-(GMm)/(2r))=(GMm)/r`
When satellite travelling in opposite directions collide, the final velocity `v` is given by
`(2mv)=mv-mv=0`
`impliesv=0`
Therfore the wreckage comes to rest and it will fall freely under gravity.
After collision, total energy of satellite is
`2(-(GMm)/r)=(-(2GMm)/r)`
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