Using iteration I've got a satellite flying around two gravity sources. (See picture) When using the iteration over a 100 times I see that TE, total energy slowly sinks so I need to make a correction after each iteration to insure that TE is constant. Trouble is I have several possibilities : Example : at the start I have : PE = -100 KE = 125 => TE = 25 after one iteration I have TE = 20 (a quite exaggerated difference in this example) I have lost 5 Joules. to compensate : A should I increase the KE by 5, increasing the magnitude of the velocity by sqrt(5)? B should I increase the PE by moving the satellite a bit farther away from the GS bodies? C should I split the difference evenly? Each should compensate 2.5 Joules. D should I split the different 4:5 or 5:4 due to the different sizes of PE and KE? Maybe I need a Math professor for this one.