Question

Two satellites of same mass are launched in the same orbit round the earth so as to
rotate opposite to each other. They soon collide inelastically and stick together as
wreckage. Obtain the total energy of the system before and just after the collision. Describe the subsequent motion of the wreckage.​

Answer 1

AnSwer :-

In case of satellite motion, energy of a satillite in an orbit is given by

$\sf E = - \dfrac{GMm}{2r}$

So the total energy of the system before collision

$\sf E_i = E_1 + E_2 = 2E = - \dfrac{GMm}{r}$

As the satellites of equal mass are moving in opposite direction and collide inelastically, the velocity of wreckage just after collision, by conservation of linear Momentum will be

mv - mg = 2mv, .i.e., v = 0

.i.e., just after collision wreckage comes to rest in the orbit. So energy of the wreckage just after collision will be totally potential and will be

$\sf E_p = -\dfrac{GM(2m)}{r} = -\dfrac{2GMm}{r}$

And as after collision the wreckage comes to rest in the orbit, it will move along the radius towards the earth under its gravity.

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