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On Dec 30, 2007, at 1:25 PM, John Mallinckrodt wrote:
Imprecise language often results in a lot of misunderstanding
and "speaking past each other." . . . By the way, I am willing
to absolutely guarantee that you will not find a system like this
anywhere in this universe. First, it would require a perfect
realization of the initial conditions. Any single deviation, no
matter how minor from those conditions would entirely
obliterate any semblance of orbital perfection. Furthermore,
even if you could realize those perfect initial conditions (and
you couldn't), external perturbations would still entirely
obliterate the orbital perfection.
The issue is not orbital perfection; it is persistence of the average
state of motion; one circle after another. Tiny osillations (random or
periodic) of distances between the stars would not matter to me.
I do not think that tiny oscillations will obliterate the system (three
identical stars at the rotating diameter).
The system is gravitationally bound.
The binding energy is 1.25*G*M^2 / R. That is
equal to work an outside agent would have to do to completely separate
three mutually-attracting particles. Is it OK to think the to
“obliterate” means to “put particles infinitely far away from each
other?”
In the case of three stars of solar mass (m=2e30 kg) orbiting a circle
whose diameter is 200 AU (R=100 AU = 1.5e13 m), the binding energy
would be about 2e37 joules. Where would the energy needed to obliterate
the system come from?
I suspect that my interpretation of the term
“obliterate” is wrong. We are probably again speaking past each other.
Do you agree, John, that my hypothetical system will not disintegrate
spontaneously into three no-longer-interacting particles?
That what I had in mind in using the term "stable."