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Ancient Theories of the Sun:
3.
Eccentric and Equant Model Applet Select from the Details menu. e is distance between the center (+) and the Earth, which is equal to the distance between the center and the equant point, both measured in units of the radius. For e=0 the equant point and the Earth coincide with the center. Select the time interval. Uncheck the box to remove the equant point (setting it to the center).

Apogee
A P
Perigee

 In addition to the eccentric position of the Earth there is an equant point - which is opposite to the Earth and sees the planet or the Sun move at a uniform angular speed (angle α) on the black circle (radius r) around the center (+). rMin=r-e, rMax=r+e eccentricity=(rMax-rMin)/(rMax+rMin)=e/r  Diagram computed by e=1/60

The results are in very good agreement with my Seasons Applet

 The following diagrams are showing the between the precise heliocentric longitude (computed by my Planet applet) and the value from the eccentric and equant model:  The following diagram is showing the between the precise distance of the Sun (computed by my Planet applet) and the value from the eccentric and equant model (e=1/60): Web Links Hipparchus: Orbit of the Sun (Wikipedia) Gemini Elementa Astronomiae, editit C. Manitius (PDF, Greek/German) Des Claudius Ptolemäus Handbuch der Astronomie (Übers. Karl Manitius) Books James Evans: The History and Prctice of Ancient Astronomy, Oxford University Press, 1998, Chapter Five: Solar Theory. Hugh Thurston: Early Astronomy, Springer, Berlin/New York 1994. Jean Meeus: Astronomical Tables of the Sun, Moon and Planets. 2nd ed., Willmann-Bell, Richmond 1995. Updated: 2012, Jul 15