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*From*: John Mallinckrodt <ajm@csupomona.edu>*Date*: Sun, 30 Dec 2007 10:25:55 -0800

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

**Follow-Ups**:**Re: [Phys-l] A numerical simulation of orbiting***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**References**:**[Phys-l] two questions***From:*"Anthony Lapinski" <Anthony_Lapinski@pds.org>

**Re: [Phys-l] [tap-l] two questions***From:*William Beaty <billb@eskimo.com>

**[Phys-l] Sharing a problem for students***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] Sharing a problem for students***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] Sharing a problem for students***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] Sharing a problem for students***From:*"Bob Sciamanda" <trebor@winbeam.com>

**Re: [Phys-l] Sharing a problem for students***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**[Phys-l] A numerical simulation of orbiting***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] A numerical simulation of orbiting***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] A numerical simulation of orbiting***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] A numerical simulation of orbiting***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] A numerical simulation of orbiting***From:*Ludwik Kowalski <kowalskil@mail.montclair.edu>

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