J OHANNES K EPLER 1571 to 1630 .
-
Upload
phillip-cook -
Category
Documents
-
view
214 -
download
0
Transcript of J OHANNES K EPLER 1571 to 1630 .
![Page 1: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/1.jpg)
JOHANNES KEPLER
1571 to 1630
http://kepler.nasa.gov/johannes
![Page 2: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/2.jpg)
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)
![Page 3: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/3.jpg)
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.
![Page 4: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/4.jpg)
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.
![Page 5: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/5.jpg)
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.
![Page 6: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/6.jpg)
Coincidence
• 5 planets- Mercury, Venus, Mars, Jupiter, Saturn• 5 Platonic Solids
• Gibbs and Kepler do not believe in coincidences
![Page 7: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/7.jpg)
JOHANNES KEPLER
Kepler tried to fit planetary orbits into a nested system based upon the five perfect geometric solids
( By permission Sternwarte Kremsmünster)
![Page 8: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/8.jpg)
Music of the WorldsHarmonica Mundi
![Page 9: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/9.jpg)
Conic SectionsKepler was the man!
![Page 10: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/10.jpg)
![Page 11: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/11.jpg)
The orbits of the planets are ellipses, with the Sun at one focus of the
ellipse.
![Page 12: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/12.jpg)
![Page 13: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/13.jpg)
It’s the Law!
![Page 14: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/14.jpg)
The line joining the planet to the Sun sweeps out equal areas in equal times as
the planet travels around the ellipse.
![Page 15: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/15.jpg)
![Page 16: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/16.jpg)
The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of
the cubes of their semimajor axes:
![Page 17: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/17.jpg)
It’s the Law!
P2 = a3
![Page 18: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/18.jpg)
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
![Page 19: J OHANNES K EPLER 1571 to 1630 .](https://reader035.fdocuments.us/reader035/viewer/2022070403/56649f325503460f94c4ee33/html5/thumbnails/19.jpg)
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.