Let's say we have a mass M at the ground of the earth with speed U going upwards so its energy is E= kinetic. The speed is enough to surpass earth's gravitational field so now it has a speed U2<U and its energy now is E= kinetic+potential. So my question now is: Is this potential energy lost? I mean when it's in the gravitational field its kinetic energy converts to potential and potential to kinetic when back down... So when it exits the field potential can no longer convert to kinetic? If this is the case where does potential energy goes ?