Planet Juggling

I don't think Antmaster conceives there being a difference between 'juggling' and two planets repeatedly stealing a moon from each other due to its highly eccentric orbit, given that he's described it the same way in every post, including the OP.

I, on the other hand, don't think you completely understand what the effect of squaring in the equasion does. The sun has a ridiculously large mass, and the distances are ridiculously long, not to mention multiplied by themselves, which is why other bodies will not, with the proper adjustments to the variables I pointed out, have more than marginal effect on orbits. As I realized that I might be wrong, I created and ran a simulation based on the logic I made. After a bit of variable tweaking, the simulation was so stable that, without any intervention, the planets would not leave their orbits. The only variations in orbit I saw turned out to be periodic changes caused and undone by the other planets.

Not to be confrontational here, but if you don't want to argue physics in a game forum, then why start a physics argument in a game forum? Also, on what basis were you saying that my code was subject to the issues the folks at Uber were having, if the mathematical formula is the one that applies in the real world?

I find it hard to believe that all of the changes in orbits were periodic and/or self-correcting. Perhaps I underestimated what your squared term would do in terms of orbit stability, but the point is not JUST keeping stable orbits; it is keeping stable orbits (planets) while promoting unstable ones (moons, but only sometimes).

Very fair question. If you look at my first post, I explained that the situation described in the OP is unrealistic because it is hard to simulate--which is still valid. You were the one that brought in the physics argument by taking my comment about how it would be next to impossible to do what the OP suggested and tried to prove me wrong. As for what basis I have on your code being subject to the same issues, squaring a positive number still gives a positive number, and any instabilities that exist in the first situation would exist in the second as well (just on smaller scales).

The periodic orbits, of course, over the course of thousands of cycles, turned out to be either closer or further from the "target" planet, suggesting an inevitable failure, but the amount of cycles would take an immensely long time to complete. The original suggestion of planet juggling is technically viable, but would require careful plotting.

I didn't even realize that it was, in fact, me who started the argument. The squaring does always return a positive number, but the unit direction will always be able to point to any direction. The undoing is caused by the fact that planets don't usually stay still in relation to each other and to the sun, meaning that they are going to be pulling each other in the opposite direction at some point. When the planets are pulling each other in the opposite direction, their distance, however, is not usually the same, which is what probably caused the small building up of error in the desired orbit.

You make a good point with your last statement. Perhaps I am wrong in assuming that any instability would be catastrophic on the scale of time when you compare maximum game length to orbit time scale (Don't you think that 1000 orbits is easily attainable in a medium game?), but from what I have observed, I would stand behind my assumptions. I think the point I was trying to make with the "squared positive numbers are still positive" argument was that a diverging system that is squared is still diverging (in this case, since the square affects the denominator more, it is less divergent), and that a better system would be one that somehow creates stable equilibrium points (Like local minimums in a potential energy vs radius curve, this way planets would be able to steal moons, and quite possibly even juggle them, all while keeping stable orbits.) Regardless, this is all moot because of the situation that KNight already described: Player altered orbits making a perfect compromise between awesome and realistic coding.