Re: Astronomy - History

[Joseph Bellina <jbellina@saintmarys.edu>]

On Thu, 26 Sep 1996, Al Bachman wrote:

>    Two questions and a comment re: Planetary orbits
> 1) How does one determine the orbit of a superior planet, eg Mars, from
> visual observations? A reference will do.
> 2) Any references for a technical description of the Ptolemaic Model, with
> numerical values?
There has been lots of work on Ptolemy and ancient astronomy in general, 
of course you could get brave at look at Ptolemy himself.  You might want 
to start with anything by Owen Gingerich.


> 3) One can produce an ellipse by using one epicycle, see below. Is this
> well known? Is there any relationship to the Ptolemaic Model?
>    Consider an epicycle (small circle) of radius r, whose center moves
> on the the larger circle (of radius R) at the angular speed W.
>    Point P moves on the epicycle a the angular speed -W.
>    If one starts with the epicycle at +R on the X-axis, and P at R+r on
> the X-axis, P will trace out an ellipse whose semi-major axis is R+r and
> semi-minor axis, R-r.
>    An interesting result is that the line from the CENTER to P will trace
> out equal areas in equal times.
>    Of course, moving from the center to a focus destroys this relationship.
Are you sure you have indeed produced an ellipse, in the mathematical 
sense, or just a shape which is generally elliptical.  Kepler's problem 
what that try as he may, he could not account for the appearance of the 
orbit of Mars with sets of circles, and in the end had to use a 
non-circular device, the ellipse.  This suggests that ellipses cannot be 
made from constructions of circles...but as has happened the the past, I 
could be wrong.

cheers

joe bellina