Epicycle calculations for Mars, illustration. Epicycles were complicated mathematical constructs used to explain geocentric orbits before heliocentric models simplified the calculations. An example of such a calculation was the orbit of the planet Mars (bottom right) as seen from Earth (centre). Across top is the observed path of the planet through the sky, tracing retrograde motion (dotted lines). The main diagram shows the Earth and Mars in relation to mathematical constructs called a deferent (large red circle) and an epicycle (smaller red circle). The centre of the deferent is named the equant point (yellow dot), while the centre of the epicycle rotation is marked with a green dot. It was the combined effect of epicycle and deferent motions that was used to explain the observed retrograde motion loops.