Lobstrosity

Quite right, Rhaedas. The main problem is that this program is attempting to numerically solve a differential equation:

d²r/dt² = ∑ G Mi (r - ri(t)) / |r - ri(t)|³

where the summation is on all i point-particles (or perfect spheres) present, Mi is the mass of the ith particle, and ri is the time-dependent vector from the origin to the ith particle (or center of the ith sphere). Since there is no closed-form solution for r as a function of t, errors will be introduced as the program attempts to numerically solve for the path as a series of discrete steps forward in time. The magnitude of these errors depends on the size of these steps coupled with the method by which the solution to the above differential equation is approximated (e.g. first-order, second-order, ...).

In other news, I currently have thirteen satellites in stable orbits Earth, where they have been following their happy little elliptical paths for over an hour now. Beat that, suckers! [insert deranged maniacal laughter here]

Jayjay

I can easily get around 20-30 revolutions around the moon... but everytime, the orbit becomes longer and longer and finally "snaps".

Jeremy Pallant

Well, I hate JayJay for introducing me to this site, but as of right now, I have eight satellites in, apparently, stable orbits. I did have one in orbit around the moon and the earth both, but it didn't last.