
PtolemyCopernicusTycho
General Description
The Ptolemy/Copernicus/Tycho EJS Model illustrates the relationships
between the systems of planetary astronomy developed by Claudius
Ptolemy, Nicholas Copernicus, and Tycho Brahe. The model presents a
simplified version of all three systems, showing the motions of the
Sun/Earth and two planets (one inferior, one superior). The model is
initially set to model the planets Venus and Mars. In addition, the
apparent motion of the sun and two planets across the sky is displayed
in another window.
This model can be used to illustrate the essential geometric
equivalence between these three system. In particular, it shows that
the Earth's orbit (in the Copernican system) becomes the orbit of the
sun in the Ptolemaic and Tychonic systems, and also appears as the deferent of
Venus and epicycle of Mars in the Ptolemaic system. The orbit of
Venus about the sun (in the Copernican and Tychonic systems) becomes
the epicycle of Venus in the Ptolemaic system. The orbit of Mars
about the sun (in the Copernican and Tychonic systems) becomes the
deferent of Mars in the Ptolemaic system.
Note that the version of the Ptolemaic system shown has been scaled so
that the deferent of the inferior planets, and epicycle of the
superior planet, are the same size as the sun's orbit. The Ptolemaic
system does not set the absolute size of the planetary orbits, just
the relative sizes of the deferent and epicycle, so scaling the system
in this way is mathematically legitimate (although Ptolemy never would
have done it, since it causes the orbits of the planets to overlap
with that of the sun).
Comparison Frame
- Display Options Menu
- Show Sky View: show the Sky View Frame.
- Show Venus: show the inferior planet and its associated lines/circles.
- Show Mars: show the superior planet and its associated
lines/circles.
- Show Lines to Earth: show lines connecting Earth to the other
bodies.
- Show Lines to Sun: show lines connecting the Sun to other
bodies.
- Show Ptolemaic System: show the Ptolemaic system.
- Show Copernican System: show the Copernican system.
- Show Tychonic System: show the Tychonic system.
- Controls
- Play/Pause: start or stop the simulation.
- Step: advance by one time step.
- Reset: reset the simulation to its initial state.
- R_v: radius of the inferior planet's orbit (Earth/Sun
orbits has radius of 100).
- omega_v: angular speed of inferior planet's orbit
(Earth/Sun orbit has angular speed 1).
- R_m: radius of the superior planet's orbit (Earth/Sun
orbits has radius of 100).
- omega_m: angular speed of superior planet's orbit
(Earth/Sun orbit has angular speed 1).
- Visual Elements
- Orange point/circle/lines: the Sun, its orbit (Ptolemaic and
Tychonic), and the Earth-Sun line.
- Blue point/circle: the Earth and its orbit (Copernican).
- Yellow point/circle/lines: the inferior planet,its orbit
(Copernican and Tychonic) or epicycle (Ptolemaic), and the
lines connecting it to Sun and Earth.
- Red point/circle/lines: the superior planet, its orbit
(Copernican and Tychonic) or deferent (Ptolemaic), and the
lines connecting it to Sun and Earth.
- Magenta circle: Ptolemaic epicycle for the superior
planet. This is really a mirror image of the Earth/Sun orbit.
Sky View Frame
- Visual Elements
- Orange disk: the Sun.
- Yellow disk: the inferior planet.
- Red disk: the superior planet.
- Background: shows the constellations along the ecliptic with
symbols.
Todd K. Timberlake (ttimberlake@berry.edu)