KSP Keostationary Orbits broken

There's something beautiful about the Keplerian 2-body approximation when you ignore collisions and SOI transitions:

You don't need to calculate forces, velocities, positions, or anything like that timestep after timestep. You don't need to integrate any laws of motion, because there's a closed-form solution to position given time.

You just take your 6 stored orbital elements, the current clock, plug it into an equation, and get out your new position.

That's largely what KSP does: it checks each vessel to see if there's an impact or SOI transition it has to handle, else it simply just updates the clock, and moves the vessel to the new position blissfully ignorant of where it was before.

Again, I tested this. I set up a constellation of satellites using Hyperedit, warped time forwards a few years at max timewarp, and they were still perfectly aligned.

If using some sort of iterative physics solver, solar systems will tear themselves apart given time. Even under Keplerian 2-body physics, unless you have an integration scheme that conserves all the relevant quantities, it'll tear itself apart due to these floating-point issues. Under N-body physics, not only is an iterative physics solver necessary*, it's a chaotic system; the solar system will fall apart, with some bodies colliding with the central body, and other bodies ejected off to infinity.

*Technically there's a non-iterative way to do it, but it's an infinite sequence of terms that, even when truncated, is very impractical as more than a demonstration.

While setting a large timestep makes inaccuracies manifest themselves sooner, an N-body system such as the real-world solar system is literally fated to fall apart. Major changes have already happened; it's thought that Uranus and Neptune switched places long ago in the early Solar System, and we quite possibly had another body ejected from the system entirely. Even if you had infinite precision and an infinitely short timestep (no numerical issues at all), N-body physics is inherently chaotic.KSP Keostationary Orbits broken

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