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Re: Astronomy - History



On Thu, 26 Sep 1996, Leigh Palmer wrote:

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.

Al did indeed produce an ellipse,
What evidence do you have to support this claim, since I am quite sure
that in principle it is not possible. You can make an oval, but the
constraint on an ellipse is that the total distance from one focus to the
circumference to the other focus is a constant as you move around the edge.
I suggest the figure looks like an ellipse, but does not satisfy the
mathematical criterion for one.

If you use the epicycle model you can produce a number of figures, some
with retrograde occuring close to the center, and others far from the
center, depending on the relative directions of rotation of the planet on
the epicycle and the epicyle on the deferent..the circle the epicycle
turns on. As I recall if the rotation rates are the same, then for one
direction you get an eccentric...the circle is shifted, and for the other
direction you get an oval....

but of course an ellipse was *not* the
goal (known or unknown) of the ancient astronomers. They were modelling
a geocentric cosmology. They had to produce a trajectory which looped
back on itself to model the appearances. Al's construction (which is an
ellipse by my reckoning) does not do that because his angular speeds are
equal and opposite in sign, two attributes which differ freom Ptolemy's.

Leigh