Newsgroups: comp.arch
Path: utzoo!henry
From: henry@utzoo.uucp (Henry Spencer)
Subject: Re: Seeing the future
Message-ID: <1988Nov28.195846.921@utzoo.uucp>
Organization: U of Toronto Zoology
References: <1984@eos.UUCP> <28200245@mcdurb> 
Date: Mon, 28 Nov 88 19:58:46 GMT

In article  jeff@lorrie.atmos.washington.edu (Jeff L. Bowden) writes:
>
>What is the n-body problem?

Given n objects in space, considering each as a point mass affected by no
forces other than gravity (for simplicity's sake), predict their positions
and velocities in the future given initial positions and velocities.

For n=1, it's trivial.

Newton solved n=2.

Doing n=3 algebraically is incredibly hard, and common wisdom hath it that
it is impossible.  Not true; there is a little-known but valid solution 
using somewhat exotic infinite series.  (It *is* provably unsolvable using
"finite" mathematics.)  Unfortunately the infinite-series solution is of
no practical use:  it converges too slowly.  There are useful algebraic 
solutions for some very restricted special cases of n=3.

For practical n=3 work, and any work for n>3, one must use iterative
numerical approximations.  Making them efficient for large n is hard.
Hence the interest in the new approach.
-- 
Sendmail is a bug,             |     Henry Spencer at U of Toronto Zoology
not a feature.                 | uunet!attcan!utzoo!henry henry@zoo.toronto.edu