Basically, yes: We're kinda "approximating" an integral by summing, but no matter how small we do our summation intervall, unless its infinitesimal (which is what we call "infinitely small" :)) we'll always do a mistake, and those tend to add up.

laugh

Other problems complicate things further: Such as the fact that the differential equations governing their motion are connected (i.e. you need to know the one of A to solve for B and vice-versa), and unlike in a two-body problem, it's not easy to "decouple" them (so that you only get differential equations for stuff that do not depend on each other anymore).

It's actually quite enlightening and a cool bit of cleverness to see how you do that for the two-body problem (Kepler). If you're not afraid of a bit of math, check it out!

Perhaps this post will get me points for originality at least.

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