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Historical Astronomy

  • E2-02: MEASUREMENT OF RADIUS OF EARTH

    E2-02
    Demonstrate how the radius of the earth can be measured using trigonometry.

    A disc of radius R with two radial tabs, as shown, is mounted on the optical board and illuminated by a parallel beam of light, as if the earth were being illuminated by the sun. The equatorial tab must have its shadow along the horizontal diameter of the disc. Measure the length b of the upper tab, the length a of its shadow, and the distance S along the surface between the two tabs. By geometry: S/R=a/b, or R=bS/a. Compare the result of this calculation with the direct measurement of the radius R of the disc.

    E2, ofc

    e2-02

  • E2-32: EPICYCLE MODEL - PTOLEMAIC SYSTEM OF PLANETS

    E2-32
    Illustrate the epicycle nature of Ptolemy's model of the solar system
    This device consists of a rotating wooden disc on a stick. Steadily rotate the stick around its end while simultaneously rotating the smaller disc. The dot in the light area on the disc represents a planet.
    OS1

  • E2-37: PLATONIC SOLIDS AND KEPLER

    E2-37
    Visualize the Platonic solids and Kepler's dream for using them to explain planetary orbits.

    There are five three-dimensional Platonic solids. The faces of a Platonic solid are identical regular polygons and all vertex angles are equal. These solids are:

    Name..........Number of faces

    Tetrahedron.......4
    Cube...................6
    Octahedron.........8
    Dodecahedron....12
    Icosahedron........20

    As illustrated in the accompanying transparency, Kepler spent most of his life assuming that planetary orbits were circular and trying to use Platonic solids to deduce their radii. Only much later, after he gave up his dream, did he discover his true laws for planetary motion. Although Kepler's original dream was a failure, much of the same mathematical/geometrical spirit prevails in our modern attempts to explain the fundamental nature of matter via symmetry, group theory, field theory, the geometry of various higher dimensional manifolds, and string theory.

    E2