What Did Johannes Kepler Discover? The Three Laws That Broke the Perfect Circle

Johannes Kepler discovered that the planets move around the Sun in ellipses, not perfect circles, and he summed up their motion in three laws: each orbit is an ellipse with the Sun at one focus; a line from a planet to the Sun sweeps out equal areas in equal times; and the square of a planet's orbital period is proportional to the cube of its average distance from the Sun. The first law appeared in Astronomia nova in 1609 and the third in Harmonice Mundi in 1619. Decades later, Isaac Newton used these laws as a key piece of evidence for his theory of gravity.

That is the textbook answer. The human story behind it, involving poor eyesight, religious exile, a famous Danish astronomer and a mother accused of witchcraft, is even more remarkable.

A sickly child who looked up

Kepler was born on 27 December 1571 in Weil der Stadt, a small free imperial city in what is now southern Germany. His father, Heinrich, was a mercenary soldier who left the family when Johannes was about five. His mother, Katharina, was a healer who worked with herbs.

As a boy he caught smallpox, which left him with weak vision and damaged hands, a cruel handicap for a future astronomer. Yet the sky caught his imagination early. At six he saw the Great Comet of 1577, later recalling that his mother took him to a high place to look at it. At nine he watched a lunar eclipse and remembered that the Moon appeared quite red.

From future pastor to Copernican

Kepler was a bright scholarship student and in 1589 entered the Tübinger Stift, the Protestant seminary at the University of Tübingen. He planned to become a Lutheran minister.

There, the mathematics professor Michael Maestlin taught him both the traditional Earth-centred system of Ptolemy and the Sun-centred system of Copernicus, and Kepler became a convinced Copernican. At the time this was still a minority view. His religious independence also cost him: his beliefs conflicted with the official Lutheran confession, and he was never ordained.

In 1594, aged 22, he took a job teaching mathematics and astronomy at a Protestant school in Graz, and in 1596 he published his first major book, Mysterium Cosmographicum.

Exile, and a meeting with Tycho

In 1600 the Catholic Archduke Ferdinand ordered Protestants in Graz to give up their faith or leave. Kepler refused to convert and was forced out.

Fortunately, he had a new contact. In February 1600 he had met Tycho Brahe, the Danish nobleman whose observatory had produced a long, careful record of planetary positions. Tycho put him to work on the orbit of Mars. Their negotiations broke down that April, and only after a reconciliation did Kepler bring his family to join Tycho. It was an uneasy partnership, but it changed astronomy.

Tycho died on 24 October 1601. Just two days later, Kepler was appointed his successor as imperial mathematician to Emperor Rudolf II in Prague. Now he had something no one else had: Tycho's data.

The war on Mars

Kepler, like almost everyone before him, assumed that planets must move in circles. Circles were considered perfect, and perfection seemed to belong in the heavens. But Tycho's observations of Mars simply would not fit a circular orbit.

Mars was a lucky choice. Among the planets, its orbit is one of the most stretched-out, more eccentric than any except Mercury, so the error of a circle shows up clearly. After years of calculations, Kepler accepted what the numbers were telling him. The orbit was an ellipse, with the Sun not at the centre but at one of its two foci.

He published this in Astronomia nova, "New Astronomy," in 1609. The idea that a planet speeds up when closer to the Sun and slows down when farther away, now called the second law, also came from this work, although its modern form was stated later, in his Epitome of Copernican Astronomy.

A new star and a harmonious universe

In October 1604 a brilliant new star appeared in the sky; today we know it was a supernova. Kepler observed it carefully and argued that, because it showed no parallax, it lay far beyond the planets. That was a direct challenge to the old belief that the heavens never change.

In 1612 he moved to Linz in Austria. There, in 1618, he found a relationship between how long a planet takes to orbit the Sun and how far away it is, and he published it in Harmonice Mundi, "The Harmony of the World," in 1619. This third law tied all the planets together in a single mathematical pattern.

Defending his mother

While Kepler was uncovering the order of the cosmos, his family was caught in the chaos of his age. In 1615 his mother, Katharina, was accused of witchcraft in Leonberg. Kepler defended her through letters to the authorities and in person. She was imprisoned from 1620 to 1621 and questioned under the threat of torture, but she refused to confess. She was released on 4 October 1621 and died about six months later.

It is a sobering reminder that the Scientific Revolution happened alongside witch trials, religious wars and plague. Kepler also cast horoscopes for the emperor; the line between astronomy and astrology was not yet drawn the way it is today.

Last works and legacy

In 1627 Kepler published the Rudolphine Tables, a catalogue of planetary positions based on Tycho's observations and his own laws, and presented them to Emperor Ferdinand II. He also worked out his own table of logarithms. He died in Regensburg on 15 November 1630, aged 58.

His laws found their deepest explanation more than half a century later. In 1687 Newton's Principia showed that orbits obeying Kepler's first two laws require a force pulling towards the Sun that weakens with the square of the distance, and proposed gravitation as that force. Kepler described how the planets move; Newton explained why.

Learn with Kepler: five useful English phrases

Kepler's story is perfect for learning English expressions about persistence and discovery:

Phrase	What it means	Example
to crunch the numbers	to do a lot of calculations	We crunched the numbers before deciding.
the data doesn't add up	the information does not fit the theory	Her story didn't add up.
back to the drawing board	to start again after a failure	The test failed, so it's back to the drawing board.
a breakthrough	an important discovery after long effort	The vaccine was a major breakthrough.
to stand on the shoulders of giants	to build on earlier people's work	Every scientist stands on the shoulders of giants.

Try this: Describe a problem you solved only after several failed attempts. Write three English sentences using back to the drawing board and a breakthrough. Kepler spent years fighting Mars before the answer came; your own small "Mars problem" is great material for practising English.