Dante and the early astronomers . a diurnal motion like thestars, as well as their own proper motions, each sethad to be provided with a sphere which moved exactlylike the great all-enclosing star-sphere. Thiis, the sun had one sphere turning like the star-sphere, and within this was a second, on which thesun was fixed, which turned round in a year, in awest-to-east direction. The sun, carried along by thecombined motion, travelled through the sky with thedaily and yearly motions, as we see them. The planetary spheres were much more difficult toarrange. Eudoxus used four spheres for each, andt
Dante and the early astronomers . a diurnal motion like thestars, as well as their own proper motions, each sethad to be provided with a sphere which moved exactlylike the great all-enclosing star-sphere. Thiis, the sun had one sphere turning like the star-sphere, and within this was a second, on which thesun was fixed, which turned round in a year, in awest-to-east direction. The sun, carried along by thecombined motion, travelled through the sky with thedaily and yearly motions, as we see them. The planetary spheres were much more difficult toarrange. Eudoxus used four spheres for each, andthese had in every case to be carefully adjusted tothe very different periods and amplitudes of the 90 EUDOXUS. planetary oscillations. It must be confessed that thescheme failed with the difficult case of Mars, and wasnot quite satisfactory with Venus, but it represented re-markably well the movement-—so far as then known—of Sun and Moon, Saturn, Jupiter, and Mercury. Itwas certainly a feat for those days, whether we consider. Fig. 19. The spheres of the sun in the system of Eudoxus. The outer sphere turns on its axis A A in a day and night; the inner onits axis a a in a year, in the opposite direction. it merely as the solution of a mathematical problem,or as an embodiment of astronomical knowledo^e. Theperiods of the planets as known to Eudoxus, statedin round numbers only, are given in the following are taken from Simplicius, who describes thesystem of Eudoxus, but as in the so-called Papyrus EUDOXUS. 91 oi Eudoxus the synodical revolution of Mercury isgiven as 116 days, the same as the modern value,Eudoxus may have had much more exact data. Itwill be seen that his synodic period for Mars is theonly one which is totall}^ wrong, and the large erroris difficult to explain. ModernSynodic Period. Value. 110 days 116 days 19 months 584 ,, 8 months, 20 days 780 „ 13 months 399 „ 13 months 378 ZodiacalPeriod.^ 1 year 2 years30
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