While trying to get my head around Gravitational Potential Energy I devised the following simple system: Point Mass A of 1kg is 1000m away from Point Mass B of 100kg within an empty universe. The gravitational force exerted by A on B is G*10^-16; by B on A is G*10^-4. At time=0 these two unmoving bodies possess no kinetic energy. Both posses the same amount of gravitational potential energy (mgh) with respect to each other of G*10^-1. At t=1 second they've attracted each other and moved closer. Body A at a speed of G*10^-4 and B at a speed of G*10^-8. They therefore posses kinetic energy equal to .5mv^2. Their potential energy has also changed due to both the reduced distance and the increase in relative gravities. However when I run the figures I end up with ~2.2*10^-29 Joules over. Given the tiny value it may be rounding errors in my calculation programme or a flaw in my basic assumptions, but if not where has this energy come from?