Re: [Phys-l] Fun orbital problem

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

On Jan 2, 2008, at 10:48 AM, John Mallinckrodt wrote:

> Apropos of nothing in particular, here's a fun problem whose solution
> may raise more questions in your mind:
>
> Three particles interact only gravitationally, follow circular
> orbits, and remain at all times collinear.  The radii of two of the
> orbits is unity.  What is the radius of the third?

I simulated such system with I.P., which ignores perturbations. The 
result was as realistic as a pencil standing permanently on its sharp 
tip. But it was still a result. Only two stars were on the common 
circular orbit, the third was in the center. I also simulated a system 
of three stars sharing a circular orbit. But they  did not remain 
collinear. I do not know how to answer the above question.
_______________________________________________________
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/