[deepsun]

My biggest problem with trajectories in KSP was that they flip non-continuously once the trajectory passes through a sphere of influence. I believe it would be much clearer and easier if trajectories were continuously changing but just marked once they pass through a SoI.

[teraflop]

If I'm correctly understanding what you mean, I'm fairly sure that's a deliberate optimization/design choice.

In the real world, a spacecraft or other object in orbit around Earth is also being constantly influenced by other celestial bodies, especially the sun and moon. Over short timescales this causes the spacecraft's orbital parameters to slowly drift; over longer timescales, it means the long-term position and fate of an object is chaotic and unpredictable. The behavior near the "boundary" between two spheres of influence is just a situation where these perturbations are more noticeable.

KSP only implements two-body physics, so a spacecraft is only affected by the gravity of one celestial body at any given time. This allows you to put something in orbit and know that it will stay there without you needing to constantly check on it and perform stationkeeping.

It's also the key simplification that makes "time warp" possible, since two-body orbits have closed-form solutions. To implement time warp with many-body physics, you would need to either keep the integration step size the same and drastically increase the amount of computation, or increase the step size and suffer from extreme inaccuracy, causing objects to crash or fly off into space.

[Dylan16807]

> It's also the key simplification that makes "time warp" possible, since two-body orbits have closed-form solutions. To implement time warp with many-body physics, you would need to either keep the integration step size the same and drastically increase the amount of computation, or increase the step size and suffer from extreme inaccuracy, causing objects to crash or fly off into space.

It makes things nicer at extremely high time warps, but it's not necessary. 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".

Edit: 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.

[aw1621107]

> 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...

[Dylan16807]

> 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.

It depends on how well you can simplify the math. I would imagine that instead of an n body calculation it's lot simpler to calculate the influence from one body plus one unchanging vector, but I've never tried it.

> 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.

Not a problem because if you're not close to anything then your orbit won't be chaotic.

[aw1621107]

> I would imagine that instead of an n body calculation it's lot simpler to calculate the influence from one body plus one unchanging vector, but I've never tried it.

I think what you describe could either be Euler's three-body problem (two fixed point masses and a particle) [0], or the restricted three-body problem (two point masses and a particle) in a rotating/pulsating reference frame. The former does have exact solutions, and I don't believe the latter does, though I'm admittedly not familiar with the literature. I'm also not sure how easy/hard it is to evaluate the exact solution, and how the difficulty compares to proper n-body integration.

That being said, I think using Euler's three-body problem would result in losing some potentially useful n-body effects. For example, centrifugal/centripetal forces would be missing compared to a restricted three-body problem in a rotating reference frame, so Lagrange points might not be present. There might be other effects I'm not aware of as well.

> Not a problem because if you're not close to anything then your orbit won't be chaotic.

I'm not sure I understand why being farther away from something would result in less chaotic trajectories? If anything, I'd expect more interesting orbits due to the lack of one dominating influence.

[0]: https://en.wikipedia.org/wiki/Euler%27s_three-body_problem

[Dylan16807]

> I think what you describe could either be Euler's three-body problem (two fixed point masses and a particle) [0], or the restricted three-body problem (two point masses and a particle) in a rotating/pulsating reference frame.

Even simpler, though, because only one of the masses needs to have a location. The other one is effectively at a fixed direction and distance, far enough away that you can ignore relative motion.

> I'm not sure I understand why being farther away from something would result in less chaotic trajectories? If anything, I'd expect more interesting orbits due to the lack of one dominating influence.

I'll rephrase. The gravitational vector on the craft won't be shifting very fast, so you can get away with a quite big timestep.

[db48x]

I found Principia’s code to be quite nice to read too; I recommend it next time you have a lazy Sunday afternoon.

[Groxx]

When you do that, you have to start specifying what reference-point you're looking from. And then regardless of what you choose, you get these awesomely-weird spiraling / spirograph-ing orbits in some cases, e.g. like Principia shows https://www.youtube.com/watch?v=eU-kLLeE7n0

The non-continuous flip lets them keep orbits exclusively centered around the you're-most-likely-orbiting-this thing, which makes them all look "normal" and the same. Though I would like to be able to see either option in the stock game - they both have their uses.

[lamontcg]

There's I think 5 different ways to handle rendering of orbits once the vessel goes through an SOI that KSP supports.

[loa_in_]

If you mean the seam between Surface and Orbit frames of reference, then it's unavoidable. One measures velocity with the surface velocity vector added and one doesn't. The surface velocity vector is the linear velocity of ground due to planet rotation around it's own axis