Summary
In *Mysterium Cosmographicum*, Johannes Kepler argues that the distances of the six known planets from the sun are determined by the five regular solids (cube, tetrahedron, dodecahedron, icosahedron, octahedron) nested within one another. He proposes that the sphere of the Earth is the measure of all, around which a dodecahedron circumscribes Mars, a tetrahedron circumscribes Jupiter, and a cube circumscribes Saturn; inside Earth, an icosahedron inscribes Venus, and an octahedron inscribes Mercury. Kepler admits that a certain thickness must be assigned to the intervening spheres to cover each planet’s greatest and least distances, and that some numbers do not closely fit the observed orbits, which he attributes to erroneous measures of planetary distances. The book also explores the relation between planetary distances and their times of revolution, suggesting that the sun’s moving intelligence forces planets around, weakening with distance. A reader takes away Kepler’s speculative, geometrical model for the cosmos, grounded in his belief that the five regular solids explain the number and arrangement of planets, alongside his early attempt to connect orbital periods to distances.
Key concepts
- Five regular solids — The cube, tetrahedron, dodecahedron, icosahedron, and octahedron, which Kepler uses to determine the spacing of planetary orbits around the sun.
- Nested spheres model — Kepler’s scheme where each regular solid is inscribed or circumscribed by a sphere representing a planet’s orbit, with Earth as the central measure.
- Moving intelligence of the sun — Kepler’s hypothesis that a single force from the sun drives all planets, with the strongest effect on the nearest planets and weakening at greater distances.
- Zodiac division into 360° — A subject Kepler addresses with a subtle reasoning process to account for the zodiac’s division, though the passage calls it “not very intelligible.”
- Planetary distance-period relation — Kepler’s observation that a planet’s orbital period is not simply proportional to its distance, leading him to propose the sun’s weakening virtue as an explanation.
From the book
Astronomy before Kepler → See also Author:Johannes Kepler . 1684853 Kepler 1920 Walter William Bryant KEPLER Pioneers of Progress Men of Science Edited by S. Chapman , M.A., D.Sc., F.R.S. Kepler By Walter W. Bryant Of the Royal Observatory, Greenwich London: Society for Promoting Christian Knowledge New York: The Macmillan Company 1920 CONTENTS. CHAP. PAGE This work was published before January 1, 1931, and is in the public domain worldwide because the author died at least 100 years ago. Public domain Public domain false false← VI. Closing Years Kepler by Walter William Bryant Appendix I.—List of dates Appendix II.—Bibliography → 1684885 Kepler — Appendix I.—List of dates Walter William Bryant APPENDIX I. LIST OF DATES. Johann Kepler , born 1571; school at Maulbronn, 1586;…
Popular questions readers ask
- The text highlights the publication of "Mysterium Cosmographicum" in 1596, well before Kepler's famous laws in 1609 and 1618. How does understanding this chronological order change your perception of Kepler's scientific journey and the evolution of his ideas?
- Given the emphasis on "astronomy before Kepler" and the need to "overthrow" existing theories, what specific assumptions or models do you infer were dominant, and how would Kepler's later work on planetary laws fundamentally challenge them?
- The text notes Kepler joined Tycho Brahe in 1600, followed by Tycho's death a year later. Why might the author deem this brief collaboration so significant as to include it in a concise list of major life events, and how might it have shaped Kepler's subsequent scientific trajectory?
- The book positions Kepler as a "Pioneer of Progress" and a "Man of Science." How does the provided list of his achievements, from publishing "Mysterium Cosmographicum" to the Rudolphine Tables, exemplify the characteristics of a scientific "pioneer" in the historical context presented?
- This excerpt is from a 1920 book about Kepler, listing earlier and contemporary historical accounts in its bibliography. How might the historical context of Bryant's publication (1920) influence the way Kepler's life and contributions are presented, and what value does consulting these older secondary sources offer compared to a modern biography?