Re: [Phys-l] Binary star question

[John Denker <jsd@av8n.com>]

On 12/29/2007 06:47 AM, Savinainen Antti wrote:

> I have a problem with one detail in quite a simple exercise. 
> It goes like this. Two stars are revolving in circular orbits 
> around their common center of mass. The masses are given and it 
> is told that their mutual distance remains constant (this distance also given). The period is asked; with the above mentioned 
> assumption they have the same periods. 
>
> Now this is not hard to do and I have no problems with solving 
> the exercise. I just can't see why their mutual distance remains
> constant. I suspect it follows from a conservation law (angular momentum?). 

Before asking why something is true, we should ask whether
it is true.

The statement that the distance remains constant is either
tautological or false.
 -- If we are told that for this problem the distance is 
  constant /by hypothesis/ then that's true /by hypothesis/.  
  It's true for this problem, but not in general.
 -- If the problem asserts that in nature the eccentricity
  is always zero, then it's just wrong.  You can have any
  eccentricity you want, from zero on up.  
     e = 0             circle
     e in (0,1)        ellipse
     e = 1             parabola
     e > 1             hyperbola


The physics here is well known.  Keplerian orbits.  An obvious
way to set up a highly eccentric orbit is to start with two
stars far apart, nearly at rest (i.e. verrry small angular 
momentum) and then just let go.  The result is a verrry thin 
ellipse.