Re: [OT] Hints for an algorithm - avoiding O(n^2)

["Robert I. Eachus" <rieachus@comcast.net>]

Jano wrote:

> I had never stopped to think about it, but if I understand you 
> correctly, that means that the Moon's orbit has a zig-zag path. Nice :)

Not even that.  No zigs, no zags.  If you draw a set of lines 
perpendicular to the Moon's path around the Sun (from a heliocentric 
view), at any point in its orbit, the points where the lines cross will 
be inside the Sun or very near.  It is only from a geocentric point of 
view that the Moon and Earth seem to orbit a common point.  (And that 
point is actually about one Earth radius from the Earth...)

> I'll look further into your Runge-Kutta suggestion, thanks.

I wish I could recommend a good book on how to implement Runge-Kutta, 
but your choice is probably a book about how the algorithm works, or one 
about how to use some math library that implements it.  It isn't that 
hard to implement, but be sure to use double precision unless you are 
really careful.

-- 
                                           Robert I. Eachus

"The only thing necessary for the triumph of evil is for good men to do 
nothing." --Edmund Burke