Principia VS CKAN-meta

Principia is extremely impressive, they document all their math here: https://github.com/mockingbirdnest/Principia/tree/master/doc...

One interesting detail is that the source code makes extensive use of non-ASCII identifiers, for mathematical symbols and for the names of mathematicians. One of the two primary contributors is also an active contributor to Unicode

Principia has n-body

I haven’t read all of it, but the Principia source code has a comprehensive units system and makes effective use of Unicode: https://github.com/mockingbirdnest/Principia/

https://github.com/mockingbirdnest/Principia/blob/master/ast... is a decent example of both:

    // We compute the mean rate (slope) of the mean anomaly M(t), the mean

Modded KSP is a good option. It's available for purchase from https://www.kerbalspaceprogram.com/ , and Linux is supported (I've run it on Linux and it worked fine). You will want to use the Realism Overhaul mod, https://github.com/KSP-RO/RP-0/wiki . You will also need the Principia mod, https://github.com/mockingbirdnest/Principia . If you're interested in pursuing the KSP option, maybe ask over at r/RealSolarSystem too.

Yeah, RP-1 puts an overhauled career mode on top of Realism Overhaul and Real Solar System, and then I added Principia to make the orbits more realistic.

Two recommendations for KSP1 mods, if you want progression from the base game and to learn a ton about real spacefaring history:

RP-1: Realistic progression career using the real solar system, real part configurations, etc. Start in 1951 and build your space program. Forum Page: https://forum.kerbalspaceprogram.com/index.php?/topic/190040... Wiki: https://github.com/KSP-RO/RP-0/wiki

Principia: N-body orbital mechanics. Actively developed, works with the stock solar system & Real Solar System. A truly stunning achievement. https://github.com/mockingbirdnest/Principia

Install Principia for N-body physics. You want things to get serious, right?

> 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...

> It's not like you need to update orbits nearly as often as part physics. The max time warp is 100000x, and at that speed if you updated orbits every 10 game seconds that would only be 400 calculations per tick, per craft. So without that simplification you might need a smaller cap on satellite swarms, or a max speed of 10000x, but time warp would still be well inside the realm of "possible".

KSP's most well-known n-body physics mod does precisely this. 1 integration step is performed every frame by default, but during warp an integration step is performed every 10 in-game seconds for vessels and every 35 minutes for bodies [0].

> You could probably get processor use really low by using an exact curve for the most influential object and a very slowly updated offset for other influences.

The Keplerian curve no longer applies once you introduce additional influences, though, so it doesn't really matter how (in)frequently updates are applied for those other influences.

The approximation wouldn't be very good farther away from a body as well, as the difference in effect between the "most influential" and less-influential bodies would be smaller.

[0]: https://github.com/mockingbirdnest/Principia/issues/2247#iss...

The vanilla KSP physics aren't realistic, only the nearest/most influential body exerts gravity on the spaceship. With the Principia mod[0], more realistic and complex maneuvers[1] can be simulated.

"Orbit Type Diagrams"[3][4] show the fractal-like complexity of three or n-body problems[5][6]

[0] https://github.com/mockingbirdnest/Principia

[1] https://www.youtube.com/watch?v=l3PCCJZzVvg

[3] https://www.semanticscholar.org/paper/Crash-test-for-the-res...

Yes it is marked as compatible with KSP 1.10.1 in CKAN, and no, getting it manually is not the right way for RSS/RO/RP-1.

Yes and no. The way CKAN works is that there are tens of thousands of metadata files, one for each mod release. It contains all the necessary data CKAN needs to know about the mod, like installation instructions, dependencies, compatibility, version number...