A satellite is orbiting Earth in a circular orbit of radius R. At some point the satellite has to be returned to Earth and so it is given a sudden negative velocity boost in the direction opposite the satellite's forward velocity). The radius of the Earth is r, and the gravitational acceleration at the surface of the Earth is g. Find the minimal boost required to bring the satellite down. (neglect air resistance). Ok, this seems pretty straight forward and not too difficult, however it's proving to be quite difficult. I know that initially the satellite is moving in a circular orbit so the eccentricity is zero. But when it slows down the orbit becomes elliptical with the perigee on the surface of the earth. Any help whatsoever will be greatly appreciated! Thanks!