Principia

Ωt_dt / Δt³; The advantages are concise notation plus compile–time guarantees that the units work out. I don’t care much for C# in general (or C++ for that matter), but I like the results here. Sounding out the Greek names occasionally used as release names is always fun too.

miliar 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...

e initial pitchover? I feel like they wouldn't be powerful enough in most cases to pull it off. > The velocity vectors are similar to the vertical flight phase but because the gravity acts on the same vertical plane it makes the spacecraft change it's pitch without additional input from the engines, tasking them with the only job of increasing the speed of the spacecraft. Technically, it's a combination of gravity and aerodynamic forces that cause the pitch to change. Gravity causes the velocity vector to turn, but doesn't exert a (noticeable) torque. It's aerodynamic forces that work on the rocket to (hopefully) keep it aligned with the velocity vector. This is why some rockets have fins at their base - additional drag at the base ensures that the aerodynamic forces keep the rocket pointed the right way. Rockets without enough drag near their base or too much drag at their nose will tend to flip right around with interesting consequences. ---- That being said, it's one thing to read about orbital mechanics, but it's hard to beat hands-on experience for really wrapping your head around things. As mentioned in the article, Kerbal Space Program is one frequently-recommended way to go about this, and does a fairly good job with the basics. Not to say that the basics aren't much; you can get quite far with "just the basics", and arguably they'll work just fine for the most common mission profiles. KSP does use a simplified gravitational model, though, taking into account the gravitational forces of only a single body at a time, which means it's missing some more interesting features of full n-body dynamics, such as Lagrange points and low-energy transfers. If you're interested in those, consider trying the Principia mod, which adds n-body dynamics, non-uniform gravitational fields, and more [0]. There's also the Realism Overhaul mod if you wish to work with more realistic rockets and celestial bodies [1]. [0]: https://github.com/mockingbirdnest/Principia [1]: https://forum.kerbalspaceprogram.com/index.php?/topic/155700...

roduce 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...