Epitome of Copernican Astronomy

Overview

The Epitome of Copernican Astronomy is about two hundred and fifty pages, published in three instalments between 1618 and 1621, and it is a textbook. Kepler wrote it in question and answer form, for students, and its purpose was to replace the standard introductory manuals that still taught Ptolemy.

That form is a gift to a modern reader. Kepler’s other major works are extraordinary and very hard: the Astronomia Nova of 1609 records his six-year fight with the orbit of Mars in something close to real time, including the failed attempts, and the Harmonies of the World of 1619 embeds the third law in a system of musical ratios and Platonic solids. The Epitome is where he lays the finished system out in order.

What he is presenting is not really Copernicus. The title is loyal, and the content is a rebuilt astronomy: elliptical orbits, non-uniform motion, the sun physically responsible for driving the planets, and the moon and the satellites of Jupiter brought under the same laws. Copernicus would not have recognised most of it.

Note the standing of the author. Kepler was an astrologer by trade, cast horoscopes for a living, believed the cosmos was built on musical harmonies, spent years defending his mother against a charge of witchcraft, and produced the most rigorously data-driven work of his century.

The argument

Books I to III: the earth as a planet. Kepler begins where a textbook has to, with the sphere, the horizon, the celestial circles and the apparent motions, and then argues for the earth’s rotation and revolution. The arguments are largely Copernican and the presentation is clearer than Copernicus managed. He also discusses the size of the universe, and is more willing than most to face how large the absence of stellar parallax forces it to be.

Book IV: the physics. This is the part with no precedent. Kepler asks why the planets move at all, a question Ptolemy did not need to ask, since spheres simply turned, and Copernicus did not ask either.

His answer is that the sun is the source. It rotates, and it emits something, a species or immaterial power, which sweeps round with it and pushes the planets along. Because this power spreads out through space it grows weaker with distance, so planets further out are driven more slowly. He draws on William Gilbert’s work on magnetism, and supposes the planets are magnets whose orientation makes them alternately drawn toward and pushed from the sun, producing the elliptical shape.

Almost none of this is right. The force does not push tangentially, it is not magnetic, and the falloff is wrong. What matters is the shape of the enterprise. Kepler is proposing that a physical cause acting at a distance and diminishing with distance governs the heavens, and that celestial and terrestrial physics are one subject. That is the programme Newton completed.

Book V: the laws. Here the three relations appear together and are applied generally.

First, that each planet moves on an ellipse with the sun at one focus. The ellipses are very nearly circular, which is why the error had gone unnoticed for so long, and the whole discovery rests on Kepler’s refusal to accept an eight-minute discrepancy in Tycho Brahe’s Mars observations. He says himself that those eight minutes led the way to a reformation of astronomy.

Second, that the line from the sun to the planet sweeps equal areas in equal times. This is the more radical of the two. Uniform motion had been the unquestioned assumption of celestial mechanics; the area law says a planet speeds up near the sun and slows further off, and gives the exact rule.

Third, that the square of a planet’s period is proportional to the cube of its mean distance. This ties the planets into a single system: knowing the period of any planet tells you its distance relative to the others. It also encodes, though Kepler could not see it, an inverse-square law.

Books VI and VII apply the same treatment to the moon and to the satellites Galileo had found around Jupiter, and Kepler insists the same laws govern them, which is the first claim that the system is general rather than a description of our planets.

How to read it

Read Book IV and Book V. That is the physics and the three laws, and it is where everything new lives.

Understand the second law properly, because it is the one usually misremembered. It does not say a planet moves at constant speed; it says the opposite, and gives the rule by which the speed varies.

Read some of the Astronomia Nova if you want to see the work rather than the result. Kepler narrates his own errors, including the moment he built a model that fitted to within eight minutes of arc and threw it away because eight minutes was more than Tycho’s observations could be wrong by. It is one of the finest records in existence of what scientific integrity actually costs.

Keep the wrong parts in view rather than skipping them. Kepler’s physical mechanism is mistaken, his harmonies are a numerological fantasy, and he arrived at three correct laws while looking for a music of the spheres. That combination is not an embarrassment to be explained away; it is the most interesting thing about him.

Read it between Copernicus and Newton. In that sequence you can watch a geometrical model become a physical theory, and see exactly which question Newton inherited.

Questions it raises

• Kepler abandoned the circle because of eight minutes of arc. When is a small discrepancy noise, and when is it the whole story?
• He asks what makes the planets move. Why had nobody needed to ask before, and what changed?
• The three laws are correct and the physics behind them is wrong. What does that say about the relation between laws and explanations?
• Kepler was looking for harmonies placed in the world by a geometer God. Would he have found the laws without that motive?
• The third law relates every planet’s period to its distance. What does it mean for a system to have a law that connects its parts like that?
• Newton derived these laws from a force. Does that make Kepler’s laws explained, replaced, or merely re-described?