**Quote:**With the 65536 sec. time step, I have noticed that Mercury's orbit starts looking a little funny after about a half a million years...

At that timestep, Mercury's orbit will unnaturally precess due to math error. The best way to figure out how fast is too fast is to run a simulation at a given time step, then run it again at 1/2 that time step and compare your results. As you get slower and slower, your results will begin to converge upon a value, and slowing the time step further will just waste time.

Mercury's orbit precesses naturally too. The biggest factor is the pertabutions from the other planets, which Gravity Simulator accounts for. And a much smaller factor is General Relativity, which Gravity Simulator does not take into account.

**Quote:**At what time step is the inner solar system reasonably stable over, say, 10 million years?

65536 should keep the inner solar system stable (16384 if you include Earth's Moon), but the objects will not be in their correct positions after 10 million years. There isn't a timestep slow enough to keep the planets in their correct positions for that long of a period of time. This is because Gravity Simulator only models point mass gravity. Since that is by far the most dominant force shaping the solar system, the results are very good. However, lots of other forces that are insignificant in the short term add up to something significant in the long term. Chaos had a lot to do with this. There are no simulators or mathamatical models that can accurately predict where the planets will be in 10 million years. But that's not to say that the system isn't stable. In 10 million years, the planets will still have orbits with basically the same orbital elements, both in real life and in Gravity Simulator. It's just where in those orbits the planets will be that causes the most uncertainty.

To give you an example of the accuracy, I started with the simulation Fullsystem, propogated it about 40 years into the future, then compared the position of Earth and the Moon to their positions as predicted by JPL Horizons. The Earth was within 1 Earth diameter of its JPL-predicted position, and the Moon was within 1 Moon diameter of the JPL-predicted position. So in the short term Gravity Simulator is almost accurate enough to predict eclipses. The same type of experiment didn't fare quite as well for the moons of Saturn. The closer ones were off by a few tens of thousands of km after only 2 years, while the further ones remained truer to their JPL-predicted positions. Not horrible considering that some of these moons travelled a half a billion kilometers relative to Saturn during this time. But in real life, Saturn bulges at the equator by a noticable amount and this will cause an error.

**Quote:**Since extremely close flybys introduce mathematical errors, I was thinking of making my Lagrange population's diameters artificially large...

That's a good idea. Sometimes you have to play tricks like this to make up for the fact that a simulator is not real life. You could start with a given exxagerated size, count your collisions, do it again with an exaggerated size half the original, count your collisions, do it again half size... etc., then see if you can recognize a trend line. Where would the trend line be when the objects approached heir real sizes? Is it linear or polynomial or something else?

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Another thing to consider when choosing a time step for simulations involving collisions is that if your time step is too large, objects destined to collide with each other can simply pass through each other unaffected. If your moons are 100 km wide, but are advancing 1000 km / time step, they're not likely to occupy the same space at the same time.

The Lagrange points 4 and 5 are simply stable points with a 1:1 resonance. The Lagrange points are not the only stable areas where objects can congregate and coalesce. Consider Neptune's 3:2 resonant points. Pluto is trapped in one of them, as well as other objects now refered to as "Plutinos". Here's an animated GIF I made with Gravity Simulator of Pluto's orbit in a rotating frame. The blue dot is Neptune, the purple path is Pluto's orbit. Notice what happens to Pluto's orbit when its perihelion gets too close to Neptune. Neptune seemingly repels it, preventing it from ever coming too close.

If you get a chance, post some of your simulations, or e-mail them to me and I'll post them for you.