

CopernicanSystem
General Description
This simulation illustrates Copernicus' system of planetary motions. The entire system is centered on the center of Earth's uniform, circular orbit. Sun is placed near, but not at, this center point. The orbit of each planet (other than Earth) consists of a deferent circle, centered on a point some distance from the center (at the eccentric point). Attached to this deferent is the center of a much smaller circle, the epicycle (or epicyclet). The radius of the epicycle is 1/3 the eccentricity of the deferent. The planet moves along the epicycle at a constant angular speed equal to twice the angular speed along the deferent. This model produces retrograde motion and changes in brightness that are always properly correlated with the location of Sun. In this simulation the planet is assumed to move in the plane of the ecliptic, so its latitude is always zero.
The parameters are initially set to model the orbit of Mars. The user can select orbits for Mercury, Venus, Mars, Jupiter, Saturn, or a user-defined orbit. Parameters for the Mercury, Venus, Mars, Jupiter, and Saturn orbits are taken from Copernicus' De Revolutionibus Orbium Coelestium. The simulation can also display simplified orbits that do not use the eccentric and epicycle.
The top window shows the elements of the model. The bottom window shows the view from Earth.
Orbit Frame
- Orbit Options Menu
- Show Zodiac in Background: show the signs of the zodiac around the orbit.
- Show Planet's Orbit: show a line tracing the planet's path (full model) or a circle representing the planet's orbit (simplified model).
- Show Sky View: show the view of an observer on Earth.
- Show Lines: show lines connecting important points.
- Show Center Points of Circles: show points at center of Earth's orbit, eccentric point, and center of epicycle.
- Show Deferent: show the deferent of the planet's orbit (full model).
- Show Epicycle: show the epicycle of the planet's orbit (full model).
- Show Earth's Orbit: show Earth's circular orbit.
- Show Line of Sight: show arrow indicating position of planet, as observed from Earth, against the background stars. This vector is always parallel to the Earth-planet line but it starts at the center because the stars are MUCH farther away than indicated by the zodiac symbols in the Orbit Frame.
- Select Planet Menu: the user may select orbits for Mercury, Venus, Mars, Jupiter, Saturn, or a user-defined orbit.
- Controls
- Play/pause: play or pause the simulation.
- Step: advance the simulation by one time step.
- Reset: reset the simulations to its initial state.
- Erase Trace: clear the trace of the planet's orbit.
- Time Step: the size of the time step used in the simulation. Increase this value to make the simulation run faster, decrease it to make the simulation run slower.
- Use Simplified Orbits: use orbits with no eccentric/epicycle.
- Visual Elements
- Blue disk: Earth.
- Red/yellow disk: the superior(red) or inferior (yellow) planet.
- Green circle: the deferent of the planet's orbit.
- Magenta circle: the epicycle of the planet's orbit.
- Green point: the eccentric point, which is the center of the deferent.
- Various lines connecting the elements listed above.
- Red/yellow trace (or circle): trace of the planet's path, or circle representing planet's orbit.
- Red/yellow arrow: line of sight vector showing where planet appears against the background stars as seen from Earth.
- Zodiac symbols: symbols show the locations of the zodiacal constellations as seen from Sun.
Sky View Window
- Visual Elements
- Red/yellow disk: the superior (red) or inferior (yellow) planet.
- Orange disk: the sun.
- Background showing zodiacal constellations and symbols.
- Show Zodiac in Background: checkbox to show zodiac constellations and symbols in background. The alternative is a black background.
Orbit Parameters (for User Defined orbit)
- Deferent/Orbit Radius: distance from Earth to center of epicycle (or planet), in astronomical units (AU). The radius of Earth's orbit is 1 AU.
- Deferent/Orbit Angular Speed: the angular speed with which the center of the epicycle (or planet) moves as seen from the eccentric point.
- Epicycle Radius: distance from the center of the epicycle to the planet (in AU).
- Epicycle Angular Speed: the angular speed with which the planet moves around the epicycle.
- Eccentricity: the distance from center of Earth's orbit to the center of the deferent/orbit (in AU).
- Longitude of Apogee: direction (in degrees east, or counterclockwise, from vernal equinox) toward the eccentric point from center of Earth's orbit.
- Use Linked Values for Epicycle: sets radius of epicycle to 1/3 eccentricity and angular speed on epicycle to twice that on deferent.
Todd K. Timberlake (ttimberlake@berry.edu)