A satellite is revolving round the earth in a circular orbit of radius a with velocity v 0 . A particle is projected from the satellite in forward direction with relative velocity v= 
v 0 . Calculate, during subsequent motion of the particle its minimum and maximum distance from earth’s centre.
Text Solution
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Sol. 
orbital speed of satellite…..(i)
mass of earth
Absolute velocity of particle would be:
Since, 
lies between orbital velocity and escape velocity, path of the particle would be an ellipse with r being the minimum distance.
Let 
be the maximum distance and 
its velocity at that moment.
Then from conservation of angular momentum and conservation of mechanical energy, we get
Solving the above
Eqs. (i), (ii), (iii) and (iv), we get
Hence, the maximum and minimum distance are 
and 
respectively.
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