Epitome of Copernican Astronomy

Summary

The Epitome Astronomiae Copernicanae is the textbook Kepler wrote so that his reformed astronomy could be taught in schools as the old astronomy of spheres had been. It appeared in instalments between 1617 and 1621, while Kepler was district mathematician at Linz and was also defending his mother against a charge of witchcraft, and it is set out as a long series of questions and answers, the form in which Lutheran students learned both the catechism and elementary astronomy. The title promises Copernicus, but the contents are Kepler's own. The first three books cover the doctrine of the sphere that every university arts student had studied: the shape and size of the earth, the daily rotation, the circles of the heavens and the risings and settings of stars, now explained from a moving earth. Book IV, the first of the two parts printed in the Great Books, is a celestial physics. Kepler asks why there are six planets, why their distances and periods stand in the ratios they do, and what moves them. He keeps the nested regular solids of his youthful Mysterium Cosmographicum and the harmonic proportions of the Harmonice Mundi as the archetypal plan of the world, and he restates his third law, that the squares of the periodic times are as the cubes of the mean distances, offering a physical reason for it. The sun, he argues, rotates on its axis and sends out an immaterial moving power that sweeps the planets round, weaker with distance, while a magnetic polarity in each planet, an idea borrowed from William Gilbert, draws it alternately nearer to and farther from the sun. Book V turns from causes to computation: it constructs the elliptical orbit, defines the mean, eccentric and true anomalies, and shows how the law of equal areas yields a planet's place, admitting that the resulting equation can be solved only by approximation. The closing books apply the theory to the apparent motions of the planets, the moon and the stars. The Epitome is where Kepler extended to every planet, and to the moon, laws he had first won from the orbit of Mars alone. Its physical causes did not survive Newton, but its ellipses and areas did, and for a generation it was the fullest account of the new astronomy in print. It also shows a Lutheran mathematician arguing that the order he found in the heavens was evidence of a Creator who works by number, weight and measure. No public-domain English translation was available for the library, so this record is a summary without quotations.

Plot or Argument

• Books I-III: The doctrine of the sphere from a moving earth

  The traditional first-year material of astronomy, the earth's roundness and size, the celestial circles, day and night, the seasons and the rising and setting of stars, is taught again in catechism form, but every phenomenon is explained by the earth's daily rotation and annual motion rather than by a turning heaven.

• Book IV, Part 1: The plan and proportions of the world

  Kepler defends the sun's central place and the immensity of the fixed stars, and gives his archetypal reasons for the number and spacing of the planets: the five regular solids nested between the planetary spheres and the harmonic ratios of their extreme motions. He likens the sun, the sphere of fixed stars and the space between to the Persons of the Trinity, a comparison he had first made in 1596.

• Book IV, Parts 2-3: Celestial physics

  The planets are moved by a power issuing from the rotating sun, so that more distant planets move more slowly; the third law is restated and explained by assumptions about each planet's size and matter. A magnetic disposition in the planetary body, modelled on Gilbert's terrestrial magnet, accounts for its approach to and retreat from the sun along an ellipse. The moon's motions receive the same kind of physical treatment, with the earth as its mover.

• Book V: Computing an elliptical orbit

  The geometrical part: how the ellipse is constructed from the eccentric circle, how the sun stands at one focus, how the eccentric and true anomalies follow from the mean anomaly by the law of equal areas, and why this problem admits no exact geometrical solution but only calculation by successive trial.

• Books VI-VII: Apparent motions

  The physical orbits are turned into what an observer on the moving earth sees: the stations and retrogradations of the planets, the theory of the moon and of eclipses, and the slow motion of the sphere of fixed stars. These books prepare the user for the Rudolphine Tables that Kepler was then completing.

Characters

• Nicolaus Copernicus, authority named in the title

  Polish canon whose De revolutionibus (1543) set the sun near the centre; Kepler honours him while replacing his circles and epicycles with ellipses and physical causes.

• Tycho Brahe, source of observations

  Danish astronomer whose precise naked-eye observations Kepler inherited in Prague in 1601 and on which every orbit in the Epitome ultimately rests.

• William Gilbert, source of the magnetic hypothesis

  English physician whose De Magnete (1600) treated the earth as a great magnet; Kepler extends the idea to explain why planets vary their distance from the sun.

• The student, questioner

  The implied learner whose questions organise the book, often raising the objections of Aristotelian physics and of common sense that Kepler then answers.

Lessons

• A catechism for the heavens

  Kepler chose the question-and-answer form of school textbooks, the same form Lutheran children used for Luther's Small Catechism. The choice shows his ambition: he wanted the new astronomy not merely published for experts but taught, memorised and defended by ordinary students, and he anticipated their objections by putting them into the questions.

  • What does the question-and-answer form allow Kepler to do that a continuous treatise would not?
  • Kepler's questions often voice objections from Aristotle or from common sense. Why might a teacher put the strongest objections into the student's mouth?
  • What would be gained and lost if your physics textbook were written as a catechism?

• Asking why, not only where

  Earlier astronomers, including Copernicus, mostly sought geometrical models that predicted positions. Kepler insisted that astronomy should give physical causes: something must move the planets, and that something should explain why distant planets are slower and why orbits are ellipses. His particular causes, a solar moving power and planetary magnetism, were wrong, yet the demand that the heavens obey the same kind of physics as the earth outlived them and prepared for Newton.

  • How does Kepler explain the fact that Saturn moves more slowly than Mercury?
  • Can a scientist be right to look for a cause even when the cause he proposes is mistaken? Use Kepler's magnetic hypothesis as your example.
  • Newton later replaced Kepler's solar power with universal gravitation. What did Newton keep from Kepler?

• Archetypes and data side by side

  Book IV places Kepler's earliest speculation, that God spaced the planets by the five regular solids, beside laws derived from years of calculation on Tycho's data. Kepler did not treat these as rival methods: he believed the Creator designed the world by geometry and harmony and that careful observation would reveal that design. Students can discuss which parts of his system rested on evidence and which on expectation, without assuming that faith and calculation must pull apart.

  • Which claims in Book IV could be tested against observation, and which could not?
  • Kepler abandoned circles when Tycho's data on Mars disagreed by eight minutes of arc, yet kept the regular solids. Why might he have treated the two differently?
  • How does Kepler's belief that God works by number shape what he looks for in the heavens?

• A problem that will not close

  Book V shows that once orbits are ellipses traced according to the area law, finding a planet's position at a given time leads to an equation that cannot be solved by ruler and compass. Kepler says so plainly and offers calculation by successive approximation. The admission is a lesson in intellectual honesty and an early sign of how much of modern science would depend on numerical methods rather than exact construction.

  • State the law of equal areas in your own words and draw a diagram showing where a planet moves fastest.
  • Why does the area law make the position of a planet hard to calculate?
  • Is an answer reached by approximation less true than one reached by exact construction?

Context

The Epitome belongs to the decades when Copernican astronomy moved from a mathematical hypothesis to a contested claim about the real world. Galileo's telescopic discoveries (1610) had made the old system harder to defend, and in 1616 the Roman Congregation of the Index suspended Copernicus's book until corrected. Kepler, a Lutheran outside Rome's jurisdiction, nonetheless saw his own textbook placed on the Index soon after its first part appeared. Most university teaching still followed Ptolemy or Tycho Brahe's compromise system, in which the planets circle the sun while the sun circles a motionless earth.

Composition

Kepler planned the Epitome as a teaching book from about 1615. Books I-III appeared first (1617, with a title page dated 1618), Book IV in 1620 and Books V-VII in 1621. Work was interrupted by Kepler's journeys to Württemberg to defend his mother, Katharina, who was tried for witchcraft and released in 1621, and by the publication of the Harmonice Mundi (1619), whose third law the Epitome incorporates.

Reception

The Epitome was reprinted at Frankfurt in 1635 and, with the Rudolphine Tables (1627), became the principal route by which astronomers learned elliptical orbits. Kepler's solar force and magnetic fibres found few followers, but the ellipse and the area law were gradually accepted after the tables proved more accurate than their rivals, notably in predicting the transit of Mercury of 1631. Newton derived Kepler's three laws from universal gravitation in the Principia (1687). Books IV and V, translated by Charles Glenn Wallis (1939), were chosen for the Great Books of the Western World (2nd ed., 1990), volume 15, alongside Ptolemy and Copernicus.

Comparisons

• New Astronomy and The Harmony of the World

  The Astronomia Nova records the struggle with Mars that produced the first two laws, false starts included, and the Harmonice Mundi finds the third law among musical ratios. The Epitome presents the results without the struggle, generalised to all the planets and arranged for teaching, so reading them together shows the difference between discovery and exposition.

• On the Revolutions of the Heavenly Spheres

  Copernicus moved the centre to a point near the sun but kept uniform circular motion, epicycles and a sphere-carrying cosmos; Kepler places the sun itself at the focus, removes the epicycles and asks what physically moves the planets. The Epitome's title claims continuity, but Book V is a quiet demolition of the machinery of De revolutionibus.

• Almagest

  The Almagest set the pattern for astronomical textbooks for fourteen centuries, and the Epitome deliberately follows its order from the sphere to the planets. Where Ptolemy treats his models as calculating devices, Kepler insists the orbit is a real path produced by real forces.

• On the Magnet (De Magnete)

  Gilbert's experiments with the terrella persuaded him that the earth is a magnet and that magnetism might explain its rotation. Kepler borrows the idea to give each planet a magnetic axis that keeps a fixed direction in space, so that it is alternately attracted toward and repelled from the sun.

• Principia

  Newton showed that an inverse-square attraction toward the sun yields Kepler's ellipses, equal areas and harmonic law, while discarding Kepler's solar moving power. The Epitome supplied the laws Newton had to explain and the conviction that the heavens obey physics.

Quotes

Creative Prompts

• Classroom

  Draw an ellipse with two pins, a loop of string and a pencil, mark the sun at one focus, and divide the orbit into four regions of equal area. Use the drawing to explain to a younger student where a planet moves fastest and why.

• Dialogue

  Write a short question-and-answer catechism, in Kepler's manner, that teaches a ten-year-old why we do not feel the earth moving. Let the student's questions raise the best objections an Aristotelian could make.

• Essay

  Kepler kept his theory of nested regular solids while discarding the circles every astronomer before him had assumed. Write an essay judging how a scientist should decide which of his convictions to abandon when the evidence turns against him.

Further Reading

• Kepler, Max Caspar, trans. C. Doris Hellman

  The standard biography, by the editor of Kepler's collected works; covers the Linz years, the witchcraft trial and the writing of the Epitome.

• Kepler's Physical Astronomy, Bruce Stephenson

  A careful study of Kepler's celestial physics, including the solar force and magnetic hypothesis developed in the Epitome.

• The Sleepwalkers, Arthur Koestler

  A vivid and opinionated narrative of astronomy from Pythagoras to Newton with a long section on Kepler; best read alongside more cautious historians.