On May 15 of 1618 Kepler realized that the 3/2 power of an orbit's size tells you its period he kept a diary and recorded how he came to his ideas and when the insight occurred and what if felt like he says he had a premonition of it in March of that year and couldnt believe it and suppressed the idea and it came back to him on 15 May and he realized it really was true. In the 1618 book "Harmony of the World" where he published this idea he says a propos of this or some related idea: "Since I have attested it as true in my deepest soul, and since I contemplate its beauty with incredible and ravishing delight,..." He thought of it as the 3/2 power. The Latin for 3/2 is "sesqui" and he said that the period was the "sequipotence" of the mean distance from sun. I checked the Latin text of "Harmonice Mundi" We tend to rephrase this as "period squared proportional to semiaxis cubed" but that was not how he wrote it--he said one was 3/2 power of the other. Perhaps details like that dont matter. It works out in earth years and AU. What do you know about that period 1600-1620. Shakespeare, King James Bible translation, the Defenestration of Prague (where two Catholics were pushed out of a window---but they fell into the castle moat and just got wet). Later the religious controversy in central Europe got bloodier. Do you think Kepler was doing science (or something more basic) when he discovered this? Or was it a crackpot idea that just happened to be right? Kepler wrote poetry in Latin--I guess this was normal at the time. He taught the Virgil course at the first place he was hired. They hired him as a mathematicus but happened to need someone to teach classical Latin poetry so they had him do that the first semester. I do not think that "the scientific method" had been worked out or that people around Kepler had a clear idea of scientist. I think they did have a clear idea of what a mathematician was supposed to do, however. Mathematicians were supposed to cast horoscopes for people. Later in Kepler's life the Emperor in Prague hired him as official court mathematicus and his main duty was to do the horoscopes. Sometimes we think we know what it was like and we really dont. To me, thinking back, Kepler does not seem to be a scientist as we expect them to be. He doesnt think like one or talk like one or act like one. He was very intense though. They had witch burnings in those days and Kepler's mother almost got burned. Her aunt was, but she got off. They wanted to burn her but there was some legal difficulty so they just kept her in jail for a while trying to get a confession.