# The Superior planets - Mars

Mars orbits the sun once every 1.9 years. Let t be the time between successive instants when Mars is at its closest to us. In this time, Mars has completed s orbits and Earth (s + 1) hence: t = s * 1.9 = s + 1 from which we can infer that s = 1.1 and t = 2.1 years.

Mars' orbital radius is 1.5 AU so at its closest it is only 0.5AU from us while when it is on the opposite side of the sun it is 2.5AU away from us. Obviously Mars will vary greatly in brightness over the course of 2.1 years.

When you run the simulation of the Earth/Mars system you can verify these statements.

We know that Mars' orbit is larger than the Earth's and therefore the epicycle should be larger than the deferent - but this is not how Ptolemy would have seen things. He imagined the deferents and epicycles to be set into real crystal spheres. Now while it is possible to arrange to have a large sphere rotating about an orbit whose radius is smaller than that of the rotating sphere, it is impossible for two planets to have such an arrangement without the spheres overlapping. Ptolemy would therefore have thought of adding the epicycles together in descending order of size so that there would be clear space inside the system for inner planets. In other words, he visualised the Earth's orbit to be the epicycle! Mathematically, it is, of course, immaterial in which order you add the epicycles together. You can verify this by clicking on the 'Swap' checkbox.

Try an offset of 9% and an equant. Then see if you can do as well using a third epicycle instead of the equant.

(Note that in calculating the real orbit of Mars the eccentricity of the Earth's orbit has been assumed to be zero. Ptolemy also assumed it to be zero as all his epicycles had strict uniform circular motion. What this means, however, is that Ptolemy could not achieve quite as good a fit as is indicated by this program.)