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Return to Eudoxus Homocentric Spheres
We can construct a standard version of the Eudoxan model for Venus. Keep in mind, however, that this is pure speculation. These are the considerations that should go into any reconstruction, even if not all of them become part of the actual model we use.
No version of Eudoxan models can account for the discrepancy between the two profoundly different invisibility periods, since the curve is essentially symmetric. At least, one would have to adjust the center of the hippopede, which would require more spheres. A 1 1/2 sign curve seems reasonable as it will capture the most important feature, the maximum elongation from the sun.
Assume that the poles of spheres 2 and 3 are 1 1/2 signs (45 degrees) apart, i.e., that the angles between the equators are 1 1/2 signs. Hence, the loops are each 1 1/2 signs in length. The maximum latitude will be 9.74 degrees, but in the wrong part of the cycle. It should be clear from the diagram that there is no retrograde motion on this model.
Right click here to download a Quicktime™ of EudoxusVenus45Hippopede.mov (File Size: 1.1 megs)
If, as most readers since the 6th century CE have assumed, a primary purpose was to account for retrograde motion, we can construct a model with retrograde motion. However, it will be deficient in its elongation, here 5 signs (150 degrees) and its maximum latitude will be 68.6 degrees or about 2/3 right angle.
Right click here to download a Quicktime™ of EudoxusVenus150Hippopede.mov (File Size: 1.1 megs)
Some modern readers have been sceptical about this assumption. Alan Bowen thinks that the primary purpose of the model was to account for latitude variation. I have suggested that invisibility periods were an important consideration. However, it is possible that the only purpose of the models for Venus and Mercury was to account for elongation.