Aristotle had done ancient and medieval astronomers a considerable service by drawing a line between physics and the mathematical sciences, including astronomy, in a way that could be interpreted to mean that astronomers need not search for Aristotelian “causes” for celestial motions. By Ptolemy’s day, it had become routine to invent devices such as the epicycle and equant that yielded reliable predictions, without any need to explain what might cause the planets to move in the manner prescribed by those devices. In fact, to declare that Ptolemy either did or did not think the planets literally move in the way these mechanisms had them moving would be to misunderstand him. In the absence of any remote chance of conclusive direct evidence one way or the other, there was much to be said for not belaboring that question–maybe for not even realizing the possibility of such a question. A man who worried about whether his mathematical system represented literal reality was an exception. This was not an intellectual situation confined to the ancients. A similar mind-set exists today at the leading edge of theoretical physics. (Kitty Ferguson, Tycho and Kepler)
Ptolemy couldn’t get his geocentric model to work right with his observations of the skies. Why did some planets appear to move backwards sometimes? Why do planets change their speeds? He scratched his head and went to work fudging the equations to make it work, because it simply had to work. There wasn’t any other viable option (nevermind that pesky Aristarchus…crazy sun centered fool!).
But Kepler knew better. Kepler was a Copernican. He knew that the earth was just another planet warlbling her way along some invisible path around the sun. What Kepler meant to figure out was how to work the math that really and truly described what was happening in the sky, not just fudged numbers.
Was Kepler a crazy maniacal bulldog who hated Brahe’s fame/weath/success and ultimately poisoned Brahe with mercury in order to steal his observations? Or was Kepler a mild mannered–if perhaps slightly abrasive–fellow, who waited patiently for old Brahe to decide to hand over the observations, coincidentally dying a few short days later? I’m afraid we shall never know. What we do know is that Kepler obsessed and guessed and checked and took long walks and stayed up all night and made tables and pictures and wrote chapters and ignored his wife for years and years, whittling away at his theories, before finally solving Ptolemy’s problem of planets that go backward and change speeds. (I won’t try to rehash all that math gnashing for you. If you’re interested, there’s a great math gnash rehash here). I’ll just give you the short skinny:
Kepler ultimately discovered that planets travel in ellipses rather than in circles. They speed up when they are closer to the sun, because of the sun’s gravitational pull. Because the planets don’t travel at the same speeds, some planets may “lap” each other, so to speak, which causes Ptolemy’s problem of planets that appear to be moving backwards.
That may sound rather anticlimactic but please rest assured this seemingly simple deduction was perfectly outrageous in the early 1600’s (even Copernicus had his planets traveling in perfect little o’s). Kepler’s discovery reformed all of astronomy, eventually leading to the formation of the laws of planetary motion. These laws, along with Newton’s mathematical theories, gave rise to a new generation of modern astronomy and physics.
From the time Kepler first began working with Tycho’s data at Benatky, he chose to let the tight constraints of mathematical/geometrical logic and precise observations be his primary guides and to give them, for a while, precedence over the [ancient Greek] ideas of symmetry and harmony. Kepler was setting a precedence still followed in science, where symmetry, harmony and logical beauty are not the most important criteria for judging whether a theory is correct. (Kitty Ferguson, Tycho and Kepler)
ps. Kepler really was the Imperial Mathematician for Rudolph II. One of his jobs was to do astrological readings for the Royalty.
pps. His mom was arrested and taken to jail when she was 74 years old, accused of being a witch by some meddling neighbors. Kepler and his lawyer wrote up a 126 page legal brief to try and get her acquitted, but it was his mother’s own verbal defense in the presence of a bailiff and a torturer which ultimately saved her. The neighbors were charged 10 florins (about a dollar and a half) for the false report.