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

[John Mallinckrodt <ajm@csupomona.edu>]

Ludwik,

You wrote:

> OK, let me ask two different questions. Suppose I am able to perform a
> described experiment, somewhere far away from any galaxy.
>
> 1) Is it true that the closed system of my three stars will start
> rotating as described ?
> 2) Is it true that the described circular motion will continue, cycle
> after cycle ?


Imprecise language often results in a lot of misunderstanding and  
"speaking past each other."  So, I assume you mean to perform  
"the" [previously] described experiment.  If so, then, of course, the  
stars will "start rotating as described"; the description itself  
specifies that fact.  They certainly would not do it spontaneously as  
your language seems to imply.  The only slightly more interesting  
fact is your point #2, that they'll continue indefinitely to orbit  
along the same circular trajectory about the motionless central  
star.  I say "only slightly more interesting" because the initial  
conditions were, after all, chosen explicitly to insure that outcome.

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.

> ... Would it be desirable to present this kind of gedankening to
> students of introductory physics course, or at least to a group of
> selected students, to promote critical thinking and learning?

I certainly think so and have done so for years.  Asking students to  
find the period of a system of, say, three identical stars of mass M  
forming an equilateral triangle of side D with each following a  
circular path centered on a fourth star of mass, say, 2M is, IMO, a  
wonderful way to test students' abilities to

1. do some geometry,
2. resolve some vectors,
3. apply Newton's law of gravity,
4. apply Newton's second law,
5. apply the formula for centripetal acceleration,
6. and, generally, to think and work carefully.

Moreover, following up that exercise with questions about a) what  
would happen if the speeds were (symmetrically) too small or too  
large or, indeed, b) what would happen if there were any asymmetry in  
the initial conditions are excellent ways to test for conceptual  
understanding and physical intuition.

John Mallinckrodt
Cal Poly Pomona