Hi PhysicsForums! I'm a game developer planning a project involving simplified, idealized orbital mechanics. I made this reddit post which did not generate the sort of response I was hoping for, but it summarizes my issue in greater detail for anyone curious: https://www.reddit.com/r/AskPhysics...d_simple_path_planning_for_orbital_maneuvers/ I'd like to offer players the ability to choose a vehicle and a desired situation, and what I need is a "nice looking" approximation of the "best path" to transition from one situation to another. I was seeking a way to "fake" predictions and maneuver planning with some light math, as distinct from actually creating a full-fledged simulation in which to compute accurate solutions. Thanks to knowing the start and end situations in advance, I imagined a simple way to compute a convincing curve from one to the other without - well - rocket science. The only response I received suggested that I create a full simulation regardless, which may be my best option after all. In which case I'm still in need of an efficient path-solving algorithm, and I have no clever ideas about improving its structure. The only approach which comes to mind involves expensive heuristics, testing hundreds if not thousands of prograde thrust vectors applied at hypothetical times and magnitudes, until one such combination brings the predicted path close to the desired situation (then another round of retro tests at the periapsis of the destination to enter and circularize the orbit). Surely there are some principles I can apply which might reduce the number of samples required (put me in the ballpark), which is what brings me here. Or better still, an approach which might avoid this simulated model altogether while still producing convincing results. It only needs to look nice, after all. Any commentary will be most welcome, Thanks for your time!