Kepler
Why don't planets move in perfect circles?
That time, that place
Kepler came to Prague as Tycho's assistant. Tycho parted with his data grudgingly and the two quarreled often. Only after Tycho's sudden death did Kepler get hold of the twenty years of observations. The planet assigned to him was Mars.
Why this question
He labored for years to fit Mars into a circle. It very nearly worked. It missed by eight minutes of arc — less than a quarter of the Moon's diameter.
Once, that would have been written off as observational error. Now it could not be. Kepler knew Tycho's data were not sloppy enough to produce such a gap. If he trusted the data, the circle had to go.
What was found
He gave up the circle. Mars travels an ellipse, and the Sun sits not at its middle but at one of two special points called a focus.
And he gave up something else. Planets do not move at a steady speed — faster near the Sun, slower far from it. What stays constant instead is the area swept out by the line from Sun to planet in equal times.
Two things unquestioned for two thousand years, the perfect circle and the uniform speed, discarded together. Over eight minutes of arc.
Heavenly bodies trace perfect circles at unvarying speed
Tycho's Mars observations, and eight minutes of arc that would not go away
A decade later he found the third law linking period and distance. Newton starts from here