Re: Circular orbits, and other stuff

["A. R. Marlow" <marlow@loyno.edu>]

> ...
> Let me try to consider a very massive star and a single small planet. We 
> know that an orbit is circular if the initial v=0.5*m*r^2  (in a typical 
> problem) has no radial component. The same planet is at rest in the frame 
> of reference whose one axis is always directed from the star to the planet.
> How this be explained?  By saying that a centrifugal force 0.5*m*v^2, "due 
> to rotation"  happens to be equal to the centripetal force G*M*m/r^2 "due 
> to gravity". The net force is zero and that is why the planet is at rest.
> ...

  Let me emphasize that I am answering here from a purely pedagogical
point of view -- i. e., if a mature physicist decides to call
accelerations forces for her own purposes, I have no objection  --  but
for teaching purposes would it not be better to state what is actually
going on?  We are choosing a noninertial accelerating frame so that the
*acceleration* of the frame (relative to inertial frames)  cancels the
*acceleration* (and the velocity also in the given case) of the planet.
 No additional force enters the picture, and you get your calculational
advantages just as quickly.  Why invent a fictional force that has no
third law counterpart?  The only motivation I could conceive has been
referred to by another poster as a possible "mystical" quest to make
Newton's 2nd law applicable where it is not applicable.  Introducing
forces with unreal properties cannot help but confuse students.

> I am not saying the second explanation is better. I am saying it is not
> heretical. One way of deciding which model is better, in the long run, is
> to compare efforts needed to calculate ellipticities, for example, when
> the initial condition is changed by doubling the speed. But that is not
> the issue.

All the calculational advantages are present without inventing any
fictitious force.
>

A. R. Marlow                          E-MAIL:  marlow@loyno.edu
Department of Physics, Box 124        PHONE:   (504) 865 3647  (Office)  
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