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Posted by Ken S. Tucker on November 26, 2006, 3:40 pm
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Jonathan Silverlight wrote:
> >
> >David Williams wrote:
> >> -> Dave, you're missing the fun. One can set-up a
> >> -> system such that a pea in orbital relation with a
> >> -> pair of cabbages will eventually acquire escape
> >> -> velocity, and be emitted.
> >> -> That's an analogy to an unstable isotope or
> >> -> particle that *transmutes* via emission.
> >> -> Regards
> >> -> Ken
> >>
> >> The questioner has already, he says, experienced too much of this fun.
> >> He said that he couldn't set up a stable arrangement with more than
> >> three stars. I tried to show how this is possible.
> >
> >But it's not possible.
> >IIRC, there's no Newtonian stable solution even
> >with 3 bodies, the solution is chaotic.
> >The net energy - is of course - conserved, however,
> >the system takes a path where 2 of the bodies
> >orbit more and more closely and supply kinetic
> >energy to the third which acquires the escape,
> >by sucking kinetic energy from the orbital energy
> >of the remaining pair. There is no such thing as
> >a stable *static* arrangement in our universe,
> >it's all dynamic.
> >Ken
> >
>
> There are dynamically stable situations of three or more equal masses -
> Klemperer Rosettes (the thing Larry Niven mis-spells in Ringworld :-)
> <http://en.wikipedia.org/wiki/Klemperer_rosette>
> I recall reading an article a few years ago in "Astronomy" or "Sky and
> Telescope" about a star that is thought to have been ejected from a
> close triple system.
Jon I must agree with you and dow,
in a perfect universe with an ideal configuration
a gazillion "symmetrical" configurations will
remain stable, (I'm using Newton, GR screws
things up with so-called g-radiation).
But using the greatest supercomputer, you can't
achieve mathematical perfection because you
will always have a limited number of digits.
Let's suppose an n>2 body stable configuration
to start, and 1 friggin asteriod passes threw that
system, in and out but deflected. That asteriod
has now induced a bit of chaos that will break-
down the systems stabilty, in my understanding,
which will eventually decay to an n-1 system, by
eliminating one particle from the original n body
system.
I've argued with Dave (dow) that I find the neutron
~15 minute decay is induced by a neutrino, where
the spin is still conserved.
I think this is a good discussion because principles
that apply to gravitationally bound systems may also
apply in sub-atomic particle decays. That in turn may
provide us some insight into the structure of particles.
Thanks guys
Ken
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