An earth satellite moves in a circular orbit with speed v at height h above the earth's surface. A thruster reduces its speed instantaneously to v, where 0 < v < v without changing its direction of motion. Neglecting air drag and any irregularities of the earth's mass density profile, show that the satellite collides with the earth if and only if v ≤ v √ 2re 2re h, where re is the radius of the earth.