I’m going back to including a short summary and linking to the page with the demo. Unfortunately, there are just fewer issues that way. So I’ve got another view of the inverse square potential, this time, many test bodies starting at the same point with multiple velocities. Some of the interesting features of this setup are that it covers elliptic to hyperbolic orbits. Those that are bound to the main body and trajectories that escape it.
Unlike the things we deal with on a day to day basis, there is no friction in these equations. That makes things very simple. Either a test mass is bound to the body or not. There aren’t any complex orbits that lead to the body being captured, or slowly spiraling into a collision. Either it is in an elliptic orbit and bound to orbit forever, or it will travel out to infinity in a hyperbolic or parabolic orbit and never return again.
So please click through and check it out. More gravity.