Astronomy 1609

Astronomia Nova (New Astronomy)

Johannes Kepler

The planets ride ellipses around the Sun — fast when near, slow when far.

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In depth · the introduction

For two thousand years everyone knew the heavens ran on perfect circles. Eight minutes of arc — and one stubborn man who trusted his data — proved them wrong.

The big idea

Kepler discovered the real shape of a planet's path. It is not a circle but an ellipse — a circle gently squashed — and the Sun does not sit at the centre but a little to one side, at a point called a focus.

He found a second, subtler rule as well. A planet does not move at a steady pace: it speeds up as it swings close to the Sun and slows down as it drifts away. The exact version is lovely — the line joining a planet to the Sun always sweeps out the same amount of area in the same amount of time.

How it came about

The story turns on data. The Danish astronomer Tycho Brahe had spent twenty years measuring the planets by eye, more accurately than anyone in history, and he took on the young Kepler as an assistant. When Tycho died in 1601, Kepler inherited the priceless Mars observations — after a quarrel with Tycho's heirs over who owned them.

Kepler then spent some five years in what he called his 'war on Mars.' His best circular orbit was wrong by just eight minutes of arc — about a quarter the width of the full Moon. He could easily have shrugged it off. Instead he trusted Tycho's measurements over two thousand years of tradition, threw out the circle, and found the ellipse. He published the result in 1609 as the Astronomia Nova — the 'New Astronomy.'

Why it mattered

Kepler replaced a 2,000-year-old assumption with two exact, testable laws — and turned astronomy from a tale of spinning crystal spheres into something a single force might explain. Three generations later Isaac Newton showed that one law of gravity produces Kepler's ellipses and his area rule automatically. Kepler's curves were the clue; Newton's gravity was the answer.

A way to picture it

Imagine a runner on an oval track with a lamp standing at one focus. Every minute, the runner must paint the same amount of floor in the pie-slice between themselves and the lamp. Near the lamp that slice is short and fat, so to cover its area the runner has to sprint; far from the lamp the slice is long and thin, so the same area is swept while barely moving. That is exactly how a planet races when it is near the Sun and crawls when it is far.

Where it sits

Half a century earlier, Copernicus (1543) had dared to put the Sun at the centre — but he kept the old perfect circles, stacked with epicycles to fit the sky. Kepler kept Copernicus's Sun and fixed the shapes. At the very same moment Galileo's new telescope was revealing moons and phases that pointed to a Sun-centred system. The line runs straight on to Newton's Principia (1687), elsewhere in this Library, which finally explains why Kepler's laws are true.

The original document

Original source text

Johannes Kepler · Astronomia Nova · Prague 1609 · on the motions of Mars, from the observations of Tycho Brahe

The full title

New Astronomy, Based upon Causes, or Celestial Physics, Treated by Means of Commentaries on the Motions of the Star Mars, from the Observations of Tycho Brahe, Gent. The whole work is staged as a ten-year campaign against a single planet, Mars — the one whose orbit is eccentric enough to give the old circles away.

The eight minutes of arc

Kepler's best circular model — his 'vicarious hypothesis' — matched Tycho's Mars oppositions to within about eight minutes of arc, far better than any astronomy before it. But Tycho's naked-eye positions were trustworthy to roughly two minutes, so the eight could not be blamed on the observer. Kepler would not look away:

Now, because they could not have been ignored, these eight minutes alone will have led the way to the reformation of all of astronomy, and have constituted the material for a great part of the present work.

The second law — equal areas

Tracking how the planet's speed changes along its path, Kepler found that the straight line from the Sun to the planet sweeps out equal areas in equal intervals of time. The planet hurries when it is near the Sun and dawdles when it is far. He reached this area rule before he had pinned down the orbit's true shape.

The first law — the ellipse

After proposing and discarding an egg-shaped 'oval,' Kepler concluded that the orbit is an ellipse, with the Sun placed not at the centre but at one of its two foci. Two thousand years of stacked circles fell away.

[ … ]

A celestial physics

Kepler insisted the planets are driven by a physical cause spreading from the Sun — a 'celestial physics,' not mere geometry. His proposed mechanism, a sweeping quasi-magnetic influence weakening with distance, was wrong; but the conviction that one force from the Sun governs every orbit pointed straight at Newton.

Johannes Kepler · Imperial Mathematician to Rudolf II · 1609