Re: [Phys-l] A numerical simulation of orbiting

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

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." I will try not to use this term 
again because it already has several meanings. The term "persistent" 
seems to be better.
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/