SirNitram wrote:300 billion(Roughly..) based on the Episode II ICS. The math for this is a few posts back, but it really changes very little.
It'd change things, but not drastically. I can try to keep it in mind if I need to redo the calcs, though.
Works, though I'd throw in consideration that each system would have between hundreds and tens of thousands of objects that need to be considered. That'll push the whole thing up orders of magnitude, though this is fine for conservative things.
Now that I think about it, a very probable optimization would be that each star system is considered as a whole when doing the gravitational calcs. Hazards within a star system would only need to be considered when a ship gets near one.
One consideration: Wouldn't you need 3 64 bit numbers per object? For it's position in a XYZ grid?
Already considered.

The 7 numbers I said that were required are: x, y, and z coords for position, x, y and z vectors for velocity, and the mass of the system.
I can't really comment on the accuracy here; Big O notation to me is something to do with a cartoon.

But yea, one would have to know the positions throughout the jump, and the 5 minute thing is broadly correct. If there's more, well, we don't know.
Big O notation isn't too bad, though deriving one from some arbitrary algorithm can be a pain. Just imagine how the number given would be graphed if it were a function and you'll get an idea as to how many more CPU cycles are required as the data increases. (x axis is amount of data, y axis is CPU cycles.)
As for proving that it's O(n^2)... take 4 objects and compare their gravitational influences... It'll take you 16-4=12 calculations. Take 8 and do the same thing. 64-8=56 calcs. So 300 billion stars would require (300 billion)^2 - 300 billion calcs... n^2 - n estimates to n^2.
If you can imagine ways to cut down on the calculations where the resulting inaccuracies won't affect the end results, then you might be able to reduce the workload a bit, I dunno how much as of yet, though. And, like I said, we're neglecting a lot of other calcs, and we don't know how often the graviational influences have to be recalculated during the processing, if at all.
Later...