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From: rdp@teddy.UUCP
Newsgroups: net.physics
Subject: the multi-body problem
Message-ID: <1330@teddy.UUCP>
Date: Mon, 23-Sep-85 12:53:16 EDT
Article-I.D.: teddy.1330
Posted: Mon Sep 23 12:53:16 1985
Date-Received: Wed, 25-Sep-85 12:14:59 EDT
Reply-To: rdp@teddy.UUCP (Richard D. Pierce)
Distribution: na
Organization: GenRad, Inc., Concord, Mass.
Lines: 38

[]

This is quest for some general information.

One often hears that the two-body problem (two bodies interacting
gravitationally) is completely solvable (I guess that means that
one can completely describe the motions and ineteractions of these
two bodies in an isolated system), but when the problem involves any
more tha two bodies (3 or "many"), then there does not exist a known
solution for describing the system completely. About this I have several
questions:

    1.	Why is the three- or many-bodied problem unsolvable? (Note I 
	realize that, given the asccuracy with which we can navigate
	about the solar system, then the problem, while unsolved, is
	approachable with some spectacularily good approximations).

    2.	Do the three-body problems apply for systems where the mass of
	one of the bodies is vanishingly small compared to the others
	(such as in a Voyager/Jupiter/Sun system)?

    3.	Since general relativity seems to approach gravitation not as
	a force acting over a distance, but more as a deformation in the
	geometry of space-time (a wild simplification, I agree), can the
	three- (or many-) bodied problem be solved as a geometry problem?
	In other words, is the difficulty associated with a Newtonian
	view of gravity and the attendant mechanisms, or does general
	relativity suffer the same way?

    4.	Is the solution to all this merely one of computational 
	fortitude? (Has JPL solved the problem simply by brute
	force, or has the brute force merely made their approximations
	less approximate?)

AN ensuing discussion might be of value, unless the answer is really
very simple and obvious, which it does not seem to be.

Dick Pierce


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