Retrograde motion of the planets

This application simulates the apparent retrograde motion that planets exhibit at certain times of the year, as observed from Earth.

The apparent retrograde motion can be simulated using two highly simplified models: the heliocentric model and Ptolemy's geocentric model.

Use Start to run or pause, Restart to return to the configured initial positions, and the Model panel to switch between the two representations. You can also click or tap the canvas to start or pause.

The apparent retrograde motion of a planet occurs when Earth overtakes it in its orbit (both orbiting the Sun in the same direction): as seen from Earth, the more distant planet appears to momentarily reverse its path across the sky. Ptolemy's geocentric model reproduced this effect through epicycles—smaller circles superimposed on the main orbit—without relying on a heliocentric explanation.

Marco P. M. de Souza

Both models are highly simplified. In the heliocentric model, the orbits are assumed to be circular.

The geocentric representation uses Ptolemy's historical model, which is now obsolete. The epicycle is assumed to be circular, and the equant is not taken into account.

In both models, the planets' relative angular velocities are calculated from Kepler's third law. The retrograde motion shown is apparent and results from projecting the line of sight between Earth and the planet onto the celestial sphere.