What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

Explanation

Energy of satellite on the surface of Earth,
`E_(1) = - (GM m)/(R )`. Energy of satellite at a distance
`(2R + R) = 3R`, from the centre of Earth is
`E_(2) = - (GM m)/(3R) + (1)/(2) m upsilon_(0)^(2)`
`= - (GM m)/(3R) + (1)/(2) m (GM)/((3R)) = - (GM m)/(6R)`
`:.` Energy required to launch the satellite
`= E_(2) - E_(1) = - (GM m)/(6R) - ((-GM m)/(R )) = (5GM m)/(6R)`