From: Henry Spencer <henry@zoo.toronto.edu>
Newsgroups: sci.space.science
Subject: Re: Kepler Rosettes
Date: Fri, 15 Aug 1997 01:00:11 GMT

In article <5suv1c$793@hornet.my>, Timothy C. Eisele <tceisele@mtu.edu> wrote:
>Lurker (gt7035b@prism.gatech.edu) wrote:
>...Changes in either mass or position
>of as little as 1% made the whole structure fall apart in less
>that three orbits (by "fall apart", I mean some of the bodies were
>ejected, and all of them ended up in radically different orbits.
>Collisions were also frequent.)  I never tried it with a large body
>off to one side, but that probably wouldn't do the structure any good
>either.  All in all, "marginally stable" is probably a better description
>than "very stable".

A general rule of thumb for multi-body problems is that, with the
exception of some special cases like the Trojan points and the Rosette,
multi-body systems are stable only if they are arranged as a hierarchy of
approximately-two-body systems.

For example, there are quadruple stars, but such a system is normally two
close double stars far apart, so that each pair is approximately a single
body in the overall system, and each pair's internal motion is nearly
unaffected by the presence of the other pair.

Multi-body systems which don't meet this criterion have a strong tendency
to eject bodies until they *do* meet it.  In the simplest case, the usual
fate of a randomly-initialized three-body system is that one of the bodies
gets ejected and the other two settle down as a two-body system.

For example, the solar system is approximately a collection of two-body
systems, because the Sun dominates each planet's motion very thoroughly;
to a good approximation, each Sun-planet two-body system is unaffected by
the presence of the others.  When this stops being true, e.g. when an
asteroid wanders into a resonance with Jupiter, the usual result is
conspicuous instability, e.g. the asteroid usually ends up being ejected
from the solar system by a close Jupiter encounter.
--
Committees do harm merely by existing.             |       Henry Spencer
                           -- Freeman Dyson        |   henry@zoo.toronto.edu