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coining back from any given position to the same positionagain, relatively to the Sun. For Mars , therefore, the orbitalperiod is 687 days, the synodic period 780 days. For Jupiter ,the two periods are respectively 4333 and 399 days ; forSaturn , 10759 and 378 days. These figures, according to theCopernican theory, involve an important distinction betweenthe cases of those planets whose orbits are exterior to that ofthe Earth, and that of the inferior planets Mercury and Venus ,viz., that it is the Earth which has to catch them up, insteadof their overtaking it. Moreover, it is the fact of the Earth ’smoving so much more quickly round the Sun than Jupiter orSaturn (or any planet still further away), that enables it todo so in their case, as the last two sets of numbers indicate,in a little more than a year; although it requires more thantwo years in order to overtake Mars , whose angular velocity isonly somewhat more than one-half of its own.
It may also be easily understood, as a consequence of thesame theory, that, the orbits of these planets round the Sun being outside that of the Earth , they may be seen, in thecourse of any such period, at any angular distance from theSun , between it and the exactly opposite part of the heavens;and that they will not, like Mercury and Venus , simplyappear to oscillate within a short distance on opposite sidesof their great ruler. It is, moreover, evident that, as theyalternately come nearer to and depart further from the Earth ,their apparent paths seen from it must, according to theCopernican theory , bear a general resemblance to the series ofcurved loops drawn by Cassini in Fig . XXIV.; the successiveportions being described in their respective synodic periods,which also agree with the times assigned for their descriptionby the ancient astronomers as the result of the combination ofthe cycles and epicycles of the Ptolemaic theory.
Thus far, then, the hypothesis of Copernicus is found to agreein general with the chief results of observation. But we havenot yet shown how exactly it explains that which we think tobe the most peculiar part of all the movements involved in theapparent paths of the planets. We refer to their stations, andto their alternately direct and retrograde motion amongst the