Prague · 1609

Eight Minutes of Arc Break the Circles

Portrait of Johannes Kepler
Johannes KeplerUnknown painter, 1627 · Strasbourg

A tiny mismatch changes astronomy. The German astronomer and mathematician Johannes Kepler, who worked with Tycho in Prague until Tycho’s death in 1601, inherits his measurements of Mars. For years he tries to fit them with circles, as every astronomer before him had. His best attempt still misses some of them by eight minutes of arc, about a quarter of the Moon’s width. Others might have blamed the measurements, but Tycho’s were too good for that.

These eight minutes alone, Kepler writes in his Astronomia nova, have shown the way to reform all of astronomy. Mars moves not on a circle but on an ellipse, a stretched circle, with the Sun off-center at one of the ellipse’s two foci, and it moves faster when it’s closer to the Sun.

Years later, Kepler’s tables, built on ellipses, foretell that Mercury will pass across the face of the Sun on November 7, 1631. In Paris, the French philosopher and astronomer Pierre Gassendi watches it happen.

Mars on an ellipse with the Sun at one focus, moving faster near the Sun and slower far from it, so that the line from the Sun to Mars sweeps out equal areas in equal times; a circle for comparison Sun Mars Ellipse exaggerated
Drag the slider to move through one of Mars’s years. Mars moves faster near the Sun and slower far from it, so the line from the Sun to Mars sweeps out equal areas in equal times: the two pale areas take it the same time. The dashed circle is for comparison. The ellipse is stretched; Mars’s real one is nearly round.

Criticism of #5798 and #5802 and #5794 by Johannes Kepler​·​#5805 and #5806 and #5807

No arrangement of circles fits Tycho’s measurements of Mars. My best one still misses some of them by eight minutes of arc, far more than Tycho’s errors.

Revision of #5789 by Johannes Kepler​·​#5808​·​Compare with #5798

The Earth is a planet. It spins once a day and goes around the Sun once a year, as the other planets do. Mars moves on an ellipse, a stretched circle, with the Sun at one of the ellipse’s two foci, so that the line from the Sun to the planet sweeps out equal areas in equal times, and the other planets, I expect, move the same way.

The state of the discussion

Kepler’s eight minutes tell against every system built of circles, so Tycho’s system isn’t rationally adoptable anymore. Kepler revises Copernicus’s, and Kepler’s Sun-centered system escapes them, but it still has the two pending criticisms Tycho left Copernicus’s. For now, no system of the world is rationally adoptable.

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Sources:

  • Kepler, Astronomia nova (Heidelberg, 1609), chapter 19 and part IV
  • Kepler, Tabulae Rudolphinae (Ulm, 1627)
  • Gassendi, Mercurius in sole visus, et Venus invisa (Paris, 1632)

Researched and written with the help of AI, from the sources named. AI can make mistakes. Veritula doesn’t claim perfect historical accuracy; the sources are there to check against.

The full discussion

Why Don’t We Feel the Earth Move?

Dennis Hackethal started this discussion 1 day ago.

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The ground feels still, and anyone can see the Sun circle us. Overturning that took two thousand years. It revealed that we ride a planet that spins, circles the Sun, and sweeps around the Milky Way at 230 kilometers a second.


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The discussion as it was in 1609. Chronicle discussions are read-only. Jump to the present
Aristarchus of Samos’s avatar
Aristarchus of SamosHistorical profile​·​#5808​·​1609​·​AI-assisted
3rd of 3 versions​·​revised by Johannes KeplerHistorical profile

The Earth is a planet. It spins once a day and goes around the Sun once a year, as the other planets do. Mars moves on an ellipse, a stretched circle, with the Sun at one of the ellipse’s two foci, so that the line from the Sun to the planet sweeps out equal areas in equal times, and the other planets, I expect, move the same way.

Criticized2
Aristarchus of Samos’s avatar
Aristarchus of SamosHistorical profile​·​#5790​·​about 270 BCE​·​AI-assisted

If the Earth circled the Sun, we would see the stars from different places over the year, so they would seem to shift back and forth. They don’t.

Criticism of #5808
Aristarchus of Samos’s avatar
Aristarchus of SamosHistorical profile​·​#5791​·​about 270 BCE​·​AI-assisted

The stars are so far away that, next to their distance, the Earth’s orbit is like a point. Their shift is far too small to see.

Criticism of #5790Criticized1
Tycho Brahe’s avatar
Tycho BraheHistorical profile​·​#5803​·​1588​·​AI-assisted

Even my instruments, precise to a minute of arc, show no shift of the stars. So they would have to be at least 700 times farther from the Sun than Saturn is, leaving an absurd empty gap in between.

Criticism of #5791
Tycho Brahe’s avatar
Tycho BraheHistorical profile​·​#5804​·​1588​·​AI-assisted

If the Earth spun from west to east, a cannonball fired eastward would fly a different distance than one fired westward with the same force. I’m sure both would fly equally far, so the Earth doesn’t spin.

Criticism of #5808
Claudius Ptolemy’s avatar
Claudius PtolemyHistorical profile​·​#5795​·​about 150 CE​·​AI-assisted

If the Earth spun once a day from west to east, it would outrun everything not standing on it. Clouds, birds, and anything thrown would always seem to drift westward, and we would never see them move east.

Criticism of #5808Criticized1
Claudius Ptolemy’s avatar
Claudius PtolemyHistorical profile​·​#5796​·​about 150 CE​·​AI-assisted

The air might turn with the Earth and carry the clouds and the birds along, so they wouldn’t be left behind.

Criticism of #5795
Claudius Ptolemy’s avatar
Claudius PtolemyHistorical profile​·​#5797​·​about 150 CE​·​AI-assisted

If the air carried them along, they would never seem to move at all. But we see them move in every direction.

Criticism of #5796Criticized1
Nicolaus Copernicus’s avatar
Nicolaus CopernicusHistorical profile​·​#5800​·​1543​·​AI-assisted

The air near the Earth turns with it and carries the clouds along, and whatever rises or falls through the air turns with the Earth too, on top of its own motion. So we see them move every which way, as they would on a motionless Earth.

Criticism of #5797
Claudius Ptolemy’s avatar
Claudius PtolemyHistorical profile​·​#5802​·​1588​·​AI-assisted
2nd of 2 versions​·​revised by Tycho BraheHistorical profile

The Earth stands still at the center. The Moon and the Sun circle it, and the other planets circle the Sun. This explains everything Copernicus’s system does without moving the Earth.

Criticized1
Johannes Kepler’s avatar
Johannes KeplerHistorical profile​·​#5806​·​1609​·​AI-assisted

No arrangement of circles fits Tycho’s measurements of Mars. My best one still misses some of them by eight minutes of arc, far more than Tycho’s errors.

Criticism of #5802
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