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gaseous-giganticus
This program procedurally generates gas giant cubemap textures for the game Space Nerds In Space. https://www.patreon.com/smcameron
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> For a basic example-numbers implementation, replacing an n-body simulation that updates every 10 seconds, I was imagining that you might update the force vector 1/100th as often, every 1000 seconds. That's plenty fast to accurately handle a multi-day orbit around a lagrange point or a low energy transfer. The paths the craft take should look completely normal.
I'm honestly curious about what Principia's largest step size is when calculating predictions. Best I can tell, the step size starts large and shrinks until the tolerance-to-error ratio is small enough [0]. I can't seem to figure out how large the initial step is, though.
But in any case, I suppose it'd come down (again) to how important accuracy is.
I'm now extremely tempted to fire up KSP with Principia to see what happens if I were to mess with the timesteps. Don't think I'm familiar enough with the codebase to mess around with it properly, though.
> If you then combine a normal single-influence orbit with that force vector, you could summarize 1000 seconds of orbit into one moderately complex equation.
A lot hinges on the combination being as simple as the sentence makes it look. I'm not entirely convinced that the analysis is straightforwards (fewer forces, but you might lose some useful properties) but I'll be the first to admit that I'm not exactly an expert on this subject.
I really wish I had more time and knowledge; this sounds like a good candidate for some test code. I have absolutely no faith I'd be able to pull off something proper, though; good n-body integrators are well out of my skill range, and I don't know how I'd even begin approaching your proposed scheme outside naive integration (which wouldn't exactly be a fair comparison to high-quality n-body integrators).
Did you have a particular method of combination in mind?
> Treating the forces as constant over a stretch of time, when they actually are almost constant, shouldn't have all that much error, unless I'm missing something glaring.
Well, maybe; I'm honestly not confident enough in the possible models I had in mind to stand behind what I said (I was thinking in terms of the relative magnitude of the "correction" of the second force, but looking back I'm not entirely sure how relevant that is). I really shouldn't have been so confident in that particular line of questioning. Sorry about that.
[0]: https://github.com/mockingbirdnest/Principia/blob/f84c96953a...
> Simulating the bands of Jupiter is tricky but I've done some experiments with 2D fluids.
Nice! I've always wanted to do some fluid dynamics on the surface of a sphere, but the math is too hard for me. I found a video on youtube where someone has done some interesting things a few years ago: https://www.youtube.com/watch?v=Lzagndcx8go&t=1s but there's very little information about it. Then there was what was done for the film 2010: The year we make contact" http://2010odysseyarchive.blogspot.com/2014/12/
I've had to resort to simpler means myself, which means faking it. I use OpenSimplex noise on the surface of a sphere, and from this I can find the gradient of the noise field tangent to the surface of the sphere, rotate this vector 90 degrees about an axis passing through the center of the sphere -- which is equivalent to some kind of spherical curl of the noise field -- which gives me a non-divergent velocity field. Because incompressible fluid flows are also non-divergent, there's a strong but superficial resemblance -- it looks like fluid flow, even though it is just an arbitrary process. Into this field, I dump a bunch of colored particles and let them flow around, painting alpha blended, slowly fading trails behind them onto the surface of a cube to be used later as textures of a cubemapped sphere.
Results looks like this: https://duckduckgo.com/?q=gaseous-giganticus&t=h_&iax=images...
This program is open source, it's here: https://github.com/smcameron/gaseous-giganticus