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From: bill@utastro.UUCP (William H. Jefferys)
Newsgroups: net.physics
Subject: Re: the multi-body problem
Message-ID: <100@utastro.UUCP>
Date: Thu, 24-Oct-85 09:44:14 EST
Article-I.D.: utastro.100
Posted: Thu Oct 24 09:44:14 1985
Date-Received: Thu, 31-Oct-85 02:41:36 EST
References: <1330@teddy.UUCP> <218@redwood.UUCP> <10781@ucbvax.BERKELEY.EDU>
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Organization: U. Texas, Astronomy, Austin, TX
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> I think that multi-body systems can become chaotic in the sense
> that small perturbations can grow to macroscopic size. Thus it is
> impossible to predict the exact state in the future even with an
> arbitrarily small delta-t iteration.

Absolutely correct.  It's even true for n=3.  It is the real reason why 
the three body problem is not solvable (although this fact  was not 
appreciated until recently).

Note that for a system to be chaotic, the small perturbations have to
grow exponentially fast.  In the two-body problem, for example, a
small error in the initial conditions eventually produces a
macroscopic perturbation, but it only grows linearly.  The two-body
problem is not chaotic.

-- 
Glend.	I can call spirits from the vasty deep.
Hot.	Why, so can I, or so can any man; But will they come when you
	do call for them?    --  Henry IV Pt. I, III, i, 53

	Bill Jefferys  8-%
	Astronomy Dept, University of Texas, Austin TX 78712   (USnail)
	{allegra,ihnp4}!{ut-sally,noao}!utastro!bill	(UUCP)
	bill@astro.UTEXAS.EDU.				(Internet)