> Ah, so the force vector is constant/infrequently updated, not the position of the second body. My apologies for the misunderstandin
That's fine, glad we got it cleared up.
> I'm honestly a bit curious what an that would look like. For example, what would an orbit around the Earth-Moon L1 look like? What would an Earth -> Moon low-energy transfer look like?
> I feel like depending on the system you might need to update the "fixed" force vector relatively frequently to get anywhere close to approximating n-body results, which basically sounds like regular integration.
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.
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. So instead of doing a moderately complex calculation every 10 seconds, you'd do two of them every 1000 seconds, an estimated 50x CPU savings.
If you're not very close to anything, there's no benefit over just running an n-body calculation every 1000 seconds. But the hard-to-handle case is orbits that are low enough to need rapid updates, but high enough that it's noticeably wrong to use an ellipse. And it's easy to end up with a lot of things in those orbits.
> Wouldn't that arguably be where the most significant errors would be, as that's where the relatively unphysical constant force vector would have the most significant influence?
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.
As you get further and further away from the most influential mass, this system gets closer and closer to simply being an n-body simulation with a timestep of how often you update the force vector.
