Hi!

When you're dealing with that much sparsely-populated space, and equations of that magnitude, its quite common to not deal with everything in a single space -- the numbers just start to break down unless you're willing to eat the cost of using math library with sufficiently-large precision, you won't get it out of floats or doubles. I'd probably have each planet be its own coordinate system, which itself orbits the sun's coordinate system. Likewise for moons as they relate to their planets. Then, based on the masses of the bodies involved, you'll be able to determine a radius within which that body is the one exerting the most force, and you can either switch over to just using that one, or you can also calculate for other bodies and interpolate the forces -- depends on how accurate you want to be.

If I'm going to play a space game it isn't going to be "Realistic Simulator of the Voyager Probe, Year 37", but something like EVE Online with active play and completely fake but very engaging physics rules.

OP never said it was a space game, maybe George does want to make an accurate solar system simulation (Orbiter-like, perhaps?) with possible time acceleration and faster than light camera movement (such as in Space Engine). In any case, fun game mechanics can also be designed around such simulations or at least a subset thereof, a space game doesn't *have* to have fake submarine physics and be action-based. But yes, modifying gameplay to have less need for such high accuracy is one available option.

Thanks for the help. I have solved it by using a coordinate system for each planet, and if the spacecraft is outside any of the planet's spheres of influence, I use the Sun. Just to clear it up, this isn't really for a game, it's for a project in which I need to simulate an interplanetary flight and then display the trajectory on screen. I figured that this is a common issue in space-related games though. Having the different coordinate systems makes it easier to display the results too.