Johannes Kepler

An astronomer who changed the model when precise observations refused to fit beautiful circles. Originally a theology student, Kepler became a mathematics teacher and calendar maker in Graz and began working with Tycho Brahe in Prague in 1600. Tycho’s observations could reach a few arcminutes, and the famous discrepancy Kepler refused to ignore in his Mars model was about eight arcminutes. After years testing combinations of circles and epicycles, he adopted an ellipse and published the first two laws in 1609. In 1619 he stated that the square of a planet’s period is proportional to the cube of its orbit’s semimajor axis. Newtonian mechanics later explained these relations, but the history is better read as a chain from Copernican models through Tycho’s data and Kepler’s calculations to Newton than as one man shattering two millennia of dogma. Kepler also took a major role in the legal defense of his mother Katharina after accusations beginning in 1615; she was released in 1621.

This is a thought experiment about influence, not a verified historical fact.

Beginners compare planetary positions on circles and ellipses. Intermediate learners experiment with equal areas in equal times. Advanced learners test the period–semimajor-axis law on a log plot. Experts connect residuals in Mars observations, the ellipse equation, and Newton’s inverse-square law as different levels of mathematical explanation.