Kepler can compare the three known distances of Mars from the sun considered in chapter 41 with the distances Mars would assume were its motion circular. To calculate its expected distance, Kepler creates a circular orbit corresponding to the eccentricity determined in chapter 42. This is the same orbit that he used in chapter 43. Here are the results of his comparison:
What could occaision these differences? Observational error? Not with Tycho’s data. How about incorrectly using the apparent sun rather than the mean sun? Nope, that would cause Mars to be closer on one side and farther on the other, but, now, Mars is too close on both sides of the orbit.
“Clearly, then, [what is to be said] is this: the orbit of the planet is not a circle, but comes in gradually on both sides and returns again to the circle’s distance at perigee. They are accustomed to call the shape of this sort of path ‘oval’.”
Other Oval Evidence
These distances are not the only reason to conclude that “the path of the planet through the ethereal is not a circle.” Kepler has also the evidence of chapter 43: applying area-time to the proposed circular path results in motion that is too swift near the apsides and too slow in the middle longitudes. But were the planet brought inwards in the middle longitudes, it would be made swifter there and correspondingly slower near the apsides, correcting the error!
Therefore, the times, when they are abstracted from the plane and adjusted upward and downward, will be accumulated at aphelion and perihelion in much the same manner as, if one were to squeeze a fat-bellied sausage at its middle, he would squeeze and squash the ground meat, with which it is stuffed, outwards fromthe belly towards the two ends, emerging above and below beneath his hand.
Sitting on an egg
How exactly does Kepler propose to make the egg-shaped orbit? His first proposal is in the next chapter: