In the XVI century, the German astronomer Johannes Kepler (1571-1630) tried to find a relation among the five regular platonic solids and the six planets known in his time: Mercury, Venus, Earth, Mars, Jupiter and Saturn. Kepler thought the two numbers were connected: the reason there were only six planets was because there were only five regular solids.

Johannes Kepler (1571-1630) Mysterium Cosmographicum Mysterium Cosmographicum Inner Section Close Up Model Exhibited in The Technisches Museum, Vienna, Austria 10 Euro Silver Commemorative Coin
Pictures: Wikimedia Commons and Sam Wise.

In 1596, in his work Mysterium Cosmographicum, Kepler established a model of the solar system where the five platonic solids were inserted one inside another, separated by a series of inscribed spheres. He realized that the ratios among the planets orbits' radii could match the ratios among the spheres' radii. His model, however, was not supported by the experimental data from the astronomers Tycho Brahe (Danish, 1546-1601) and Nicolau Copernicus (Polish, 1473-1543). Indeed, his model was entirely disapproved by posterior discoveries of the planets Uranus and Neptune: there are no additional platonic solids that determine their distances to the Sun. However, from his research, new solids were discovered (that, nowadays, are named after him), the perception that the orbits of the planets are not circles but ellipses, and the three laws of the planetary motion.

The applet below shows an interactive model of the Kepler's model. To rotate the scene, you have to place the mouse pointer over the left area of the applet and then, keeping the mouse left button pressed, drag it. To enlarge/shrink the scene, you have to place the mouse pointer over the left area of the applet and then, keeping the mouse right button pressed, drag it. Doing the same operation with the mouse middle button translates the scene. To fit the scene on the window, click on the left area of the applet and, then, press the “f” key.



Please, check if your navigator is blocking the access to the applet. To install the JAVA language in your computer, please, access the link http://www.java.com/.



Creative Commons License

Responsible: Humberto José Bortolossi.
Idealization and Programming: Mariana Figueira Lacerda de Menezes and Humberto José Bortolossi.
Revision: Mariana Figueira Lacerda de Menezes and Humberto José Bortolossi.
English version: Carlos Eduardo Castaño Ferreira and Igor Bromonschenkel Brandão.
Graphical library: JavaView – Interactive 3D Geometry and Visualization.

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