A satellite with kinetic energy `E_(k)` is revolving round the earth in a circular orbit. How much more kinetic energy should be given to it so that it may just escape into outer space

Explanation

Let `upsilon_(0), upsilon_(e)` be the orbital and escape speeds of
the satellite, then `upsilon_(e) = sqrt(2) upsilon_(0)`
Energy in the given orbit,
`E_(1) = (1)/(2) m upsilon_(0)^(2) = E` ..(i)
Energy for the escape speed,
`E_(2) = (1)/(2) m upsilon_(e)^(2) = (1)/(2) m (sqrt(2) upsilon_(0))^(2) = 2E`
`:.` Energy required to be supplied
`= E_(2) - E_(1) = E`