Kepler Breaks the Circle and Finds the Ellipse

What happened

Johannes Kepler, a German mathematician who became Tycho Brahe's assistant in 1600 and inherited his observational data after Tycho's death in 1601, was assigned the notoriously difficult problem of calculating the orbit of Mars. Kepler, like nearly every astronomer before him, initially assumed planetary orbits had to be built from perfect circles, since Renaissance thinkers still held the circle as the universe's divinely ordained shape. He struggled for years trying to reconcile Tycho's precise observations with a circular path for Mars and could not make them agree. Abandoning the circle, Kepler found that an ellipse, a stretched-out oval, with the Sun positioned at one focus rather than the center, fit the data. In Astronomia Nova, published in 1609, Kepler set out what became his first law, that planets move in ellipses with the Sun at one focus, and his second law, that a line from the planet to the Sun sweeps out equal areas in equal times, meaning a planet moves faster when nearer the Sun. A decade later, in Harmonices Mundi (1619), he added a third law relating each planet's orbital period to its distance from the Sun.

How we know

Kepler's own published works, Astronomia Nova and Harmonices Mundi, survive and have been translated and studied continuously; MacTutor's biography of Kepler traces the specific sequence, from his early belief in circular orbits through Tycho's data to his discovery of the elliptical orbit, citing Kepler's own account in his books.

Sources

• MacTutor History of Mathematics, University of St Andrews. Johannes Kepler · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
• NASA Earth Observatory. Planetary Motion: The History of an Idea That Launched the Scientific Revolution · Reputable sourceearthobservatory.nasa.gov · The domain "earthobservatory.nasa.gov" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)