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This is the method used by the early Greek astronomers and others prior to the Copernican Revolution to explain why the planets occasionally move westwards relative to the stars ("retrograde motion") instead of their usual eastward motion ("direct motion"). They believed that the planet, here represented by a blue dot, rotates on a circle, called the "epicycle", shown in red here. The center of the epicycle rotates on a larger circle, here colored magenta, called the "deferent".
For this initial display, the rotation of the deferent has been stopped by setting the "rotation ratio" to 0. This is the ratio of the angular velocity of the deferent to that of the epicycle. To display, press the "Start" button.
To set the epicycle in motion around the deferent, increase the rotation ratio (the ratio of the angular velocities of the deferent to epicycle) from 0, and adjust the rate ("fast","medium" or "slow"), which governs how fast the planet's positions are drawn. To determine how the planet rotates, press "clockwise" or "anticlockwise".
To change the size of the epicycle, adjust "Size ratio", which is the ratio of the diameters of the deferent to the epicycle.


Some celestial objects rotate in such a way that their rotational periods are related to their orbital periods. This is the situation for the Moon, whose rotational and orbbital periods are equal. This is why we never see its far side! To see this, turn on the "Moon" button.
Mercury orbits the Sun synchronously, rotating twice every 3 orbits. To view this, turn off the Moon button and set up an anticlockwise rotation with a rotation ratio of 1.5.