Re: Circular orbit


PD wrote:

> However, the OPs point is well-taken. Regardless of the *magnitude* of
> the force at r=0 (and it's infinite, not zero), an orbit that is
> tangent to the force center is asymptotically radial as it approaches
> that force center. Since the force is also radial, where does the
> particle get any azimuthal velocity after passing through the force
> center?
>
> Perhaps what I'm missing is that it is a *one-time-only* circular
> orbit, and once it passes through the force center, it proceeds along a
> straight line, like a rounded "P"?

First, replace the singularity by using a mass shell, so
that the g-field in the shell is zero, then specify the mass
in mass shell does not interact to disrupt the particles
orbital motion, (let Moses part the way).

Next, (this is a GR context), let the CS rotate, then I think
the particle would orbitally trace a figure "8" through the
center of the shell in any arbituary CS.
(You can create that by scrapping across your least
favorite phonograph record).

So Paul, I think you get a figure 8, not a "P".
Ken

.

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