Hi! I hope I'm posting in the correct section. I found this very similar topic in this forum: https://www.physicsforums.com/threads/orbital-ellipse.482713/ Aside from very helpful formula for calculating semi-major axis, the question was left unanswered. I have a working simulation of orbital motion of satellites and spaceships, but I'd like to visually represent this flight path based on distance from planet's center of mass and satellite's velocity. I assume the best way to do this is by drawing an ellipse, for which I need to know semi-major axis, semi-minor axis and eccentricity or focus. What would be the best process to do this? I don't mind doing some research and reading myself, but I'd like to understand at least the sequence of calculations I need to do. Thanks for help in advance. Edit: I forgot to mention that I'm simulating everything in two dimensional plane.