Post on 05-Jan-2016
JOHANNES KEPLER
1571 to 1630
http://kepler.nasa.gov/johannes
Johannes Kepler–The PhenomenologistHow are things happening?• Mathematical explanation• Reality is the human
explanation• Copernicus did not think his
model represented realityMajor Works:• Harmonices Mundi (1619)• Rudolphian Tables (1612)• Astronomia Nova• Dioptrice
Johannes Kepler (1571–1630)
Euclidean Regular Figures
A regular figure is a closed linear figure with every side and every angle equal to each other.
•For example, an equilateral triangle, a square, an equilateral pentagon, hexagon, and so forth.
There is no limit to the number of regular figures with different numbers of sides.
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a
Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex. Moreover, all its edges are congruent, as
are its vertices and angles.
The Platonic Solids
• Unlike regular figures, their number is not unlimited. There are actually only five possibilities:– Tetrahedron, Cube,
Octahedron, Dodecahedron, Icosahedron
• This was discussed by Plato. They are traditionally called the “Platonic Solids.”
• That there could only be five of them was proved by Euclid in the last proposition of the last book of The Elements.
Coincidence
• 5 planets- Mercury, Venus, Mars, Jupiter, Saturn• 5 Platonic Solids
• Gibbs and Kepler do not believe in coincidences
JOHANNES KEPLER
Kepler tried to fit planetary orbits into a nested system based upon the five perfect geometric solids
( By permission Sternwarte Kremsmünster)
Music of the WorldsHarmonica Mundi
Conic SectionsKepler was the man!
The orbits of the planets are ellipses, with the Sun at one focus of the
ellipse.
It’s the Law!
The line joining the planet to the Sun sweeps out equal areas in equal times as
the planet travels around the ellipse.
The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of
the cubes of their semimajor axes:
It’s the Law!
P2 = a3
Planet a (AU) a3/2 P (yr)
Mercury 0.38 0.24 0.24
Venus 0.72 0.61 0.61
Earth 1.00 1.00 1.00
Mars 1.52 1.88 1.88
Jupiter 5.2 11.8 11.8
Saturn 9.6 29.5 29.5
Why?
• Kepler didn’t care why.• He had found mathematical descriptions for
the motion of the planets.
• Newton supplied the why or perhaps just additional how information.