Dante and the early astronomers

by M. A. Orr

Two half photographs of the Sun, taken at Kodaikanal Observatory. The smaller was taken two days before apogee, the larger on the day of perigee.

Instead, he worked very hard at the moon, and added another periodical irregularity to those already known. Perhaps his feelings were somewhat mixed when this happened, his pride and pleasure in his important discovery being counter-balanced by the consciousness that it would still further complicate his lunar theory. Our satellite is acted upon by ourselves as well as by the sun, so that she suffers many perturbations, for Earth, though so small compared with the sun, is comparatively near. Ptolemy’s discovery was a difference in her speed at full and new, as compared with her intermediate phases, and this periodic difference is called by modern astronomers the “evection.” It was already known that her nodes, or the points at which she crosses the ecliptic, are in constant retrogressive motion, just like the equinoctial points, where the sun crosses the equator; but the moon’s crossing points, instead of taking thousands of years to circle the zodiac, run round in about eighteen years. This was discovered early, because observations were chiefly made during eclipses, and at these times the moon is always at a node, that is to say, she is crossing the ecliptic, the sun’s path; otherwise the eclipse could not happen. It was also known that she has a varying speed in the zodiac, and that her apogee, where the motion is slowest, instead of being apparently fixed, like that of the sun, also runs round the zodiac, but with a direct motion, and in a period of about nine years.

We need not enter into all the details of Ptolemy’s arrangements for the moon, which are exceedingly complicated, but it is interesting to note that he does not explain her varying velocity by an eccentric, as with the sun and the planets. She has an eccentric, but Ptolemy needed it for representing his own discovery, the evection, so he gave her an epicycle, using it in quite a different way from the epicycles of the planets. This epicycle also revolved while moving on the eccentric, but in the opposite direction, and there was so little difference in speed between the two motions that it never brought the moon to a stop, nor reversed her direction, but simply increased and retarded her motion alternately during her monthly revolution. Thus, when the moon was at M, in what Ptolemy called the upper apsis (or arc) of her epicycle, or as we should say in her apogee, the motion on the epicycle was contrary to her motion on the eccentric, and made it seem slower. When the epicycle had travelled halfway round the eccentric, it had also made nearly half a revolution on its own axis: consequently the moon was at M¹, near the lower apsis, or perigee, and the motion on the eccentric seemed to be accelerated.

Fig. 34. The moon’s epicycle and deferent.

The slight difference in speed between the two motions accounted for the continuous displacement of the apogee in the zodiac, as may be seen from the diagram. For suppose that when in apogee at M the moon is seen from Earth among the stars in the middle of Taurus. At the return of the epicycle to this place next month, she has not yet quite completed a revolution on her epicycle but is at M², and will not be in apogee until the centre of her epicycle is advanced 3° further in Taurus. After some time (five months), apogee does not occur until the moon is in Gemini, and it will be nine years before it occurs again in Taurus.

These are the leading features of the system by which Ptolemy represented the motions of the planets, the sun, and the moon. He is uncomfortably conscious that it may strike us as very complicated, and in his last book he makes a kind of apology. We must remember, he says, that we are not dealing with earthly machines which jar and wear, but with celestial bodies which have no weight, cause no friction, and are eternally the same. Delambre somewhat cruelly retorts that he need not have wasted time in writing such rubbish, but have been content to put his results into tables.

But what true astronomer could be content with tables and nothing more? He must try to understand their significance. Nearing the end of his great work, which had cost so much labour, and was so brilliant a success within its limits, Ptolemy allows us to see in this little paragraph that he felt he had but touched the hem of Nature’s veil, and longed in vain to lift it. The circles which he manipulated so skilfully were only mathematical abstractions to him:[53] what was the reality behind? What were the stars? whence came their unwearied strength, their eternal calm? The power of Egypt, of Assyria, and of Persia had declined, Greece was now laid low, and it was the day of Rome, but still Venus pursued her ancient path among the little stars of Aquarius, and when all faded in the solemn dawn, the sun arose in his ancient majesty. Then Ptolemy looked at his circles and triangles, and felt how inadequate they were; yet it was the nearest approach he could make to truth.