I am trying to write a program to show the flight of a satellite in the neighbourhood of two large planets. In all of this the mass of the satellite is negligible. I have the potential energy from planet1 = pe1 and the potential energy from planet2 = pe2 and the kinetic energy of the satellite = ke Using the sum of the two planets' acc vectors to create a !! single !! acc vector I can calculate the next position using the current position, the velocity vector and the movement caused by the !! single !! acc vector. This is good; (it works fine in a single planet and satellite model). The new velocity vector can also be similarly deduced adding the induced velocity from the acc vector to the original velocity vector. This is also good; (it also works fine in a single planet and satellite model). However Total Energy is just a bit off. Using my model with a short sliver of time I have a decrease of total energy by a factor 6.5 * 10**-4. Not a really big number but I want to find how I can reduce it to 0.0. I have three possibilities of tweaking the model to reach change in TE = 0.0 : 1. only increase the velocity and thereby the kinetic energy 2. only increase the distance from the two planets and thereby the potential energy 3. increase both vel and dist (in a certain proportion) to increase both KE and PE Does physics, nature, mathematics or logic define which of these three paths to explore?