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?
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.