TL;DR: Dante read a Latin translation of Al-Farghani, who summarized the work of Ptolemy.
Astronomical claims in Purgatory
There is a south celestial pole; the stars near it are not visible from the northern hemisphere; and vice versa:
The planet whose sweet influence strengthens love1
was making all the east laugh with her rays,
veiling the Fishes,2 which she swam above.
I turned then to my right and set my mind
on the other pole,3 and there I saw four stars4
unseen by mortals since the first mankind.5
Dante (c. 1310). Purgatory 1.19–24. Translated by John Ciardi (1957). New American Library.
1. Venus. 2. Pisces. 3. The south celestial pole. 4. It’s not impossible that Dante meant the four stars in Crux (the Southern Cross), as they were known to Ptolemy and recorded in the Almagest, but since Ptolemy treated them as part of the constellation Centaurus, and the name “Crux” was not used until the 16th century, it seems more likely that Dante’s four stars are allegorical inventions, representing the four Cardinal Virtues. 5. Dante puts the Earthly Paradise (the Garden of Eden) on top of Mount Purgatory, so in the southern hemisphere.
When Pisces is rising, as seen from Mount Purgatory, Ursa Major is setting:
As I broke off my gazing, my eyes veered
a little to the left,1 to the other pole2
from which, by then, the Wain had disappeared.3
1. Anticlockwise. 2. The north celestial pole. 3. Ursa Major spans 8h–14h right ascension, while Pisces spans 23h–2h right ascension, so that when Pisces is rising as described in line 21, Ursa Major is setting.
When the sun is rising at Mount Purgatory, it is setting at Jerusalem, since these are antipodes:
The sun by now o’er that horizon’s rim
Was sinking, whose meridian circle stands
With its mid-arch above Jerusalem,
While night, who wheels opposed to him, from sands
Of Ganges1 mounted with the Scales,2 whose weight
Drops in her hour of victory from her hands;
Purgatory 2.1–6. Translated by Dorothy L. Sayers (1955). New York: Basic Books.
1. The Ganges lies to the east of Jerusalem, so that “night” (meaning the antipode of the sun) is rising in the east while the sun is setting in the west. 2. The sun is currently in Aries (as described in Inferno canto 1), so “night” is in Libra, which is opposite; and since the time is shortly after the spring equinox, day and night are of similar length.
The sun moves anticlockwise as seen from the southern hemisphere:
I turned my eyes first downward to the strand,
Then to the sun—and stared to see him go
So that he smote us on the leftward hand.
The sun moves in opposite senses (clockwise and anticlockwise respectively) as seen from Jerusalem and Mount Purgatory, as these are antipodes:
“Come, recollect thyself and work it out—
So: think of Zion and this mountain here
As being so placed on earth that they have got
A separate hemisphere for each, but share
The same horizon; thus, that road ill-tried
By Phaeton the luckless charioteer.1
Must, when it passes Zion on one side
Pass this upon the other, as, if thou
Hast a clear brain, thou wilt be satisfied.”
1. Phaeton was the son of the sun-god Apollo, who tried to drive his father’s chariot, but could not control the horses, as described by Ovid in Metamorphoses books 1–2, so Phaeton’s road here is the path of the sun in the sky.
When the sun is rising at Jerusalem, it is at the meridian at the Ganges, and setting at Mount Purgatory:
As when his earliest shaft of light assails
The city where his Maker shed His blood,1
When Ebro2 lies beneath the lifted Scales3
And noontide scorches down on Ganges’ flood,4
So rode the sun; thus day was nightward winging
When there before us God’s glad angel stood.
1. Jerusalem, where Christ was crucified. 2. A river in Spain, that is, to the west of Jerusalem. 3. Libra, which is setting when the sun is rising in Aries as noted above. 4. Medieval geographers did not know the longitude of the Ganges, so this is not right: the Ganges is about 3½h east of Jerusalem, not 6h as claimed in this passage.
How did Dante figure all this out?
I think the question makes out the difficulties to be greater than they really were. These basic astronomical facts have been known since antiquity:
- the Earth is spherical;
- from the perspective of an observer on Earth, the fixed stars form a celestial sphere that rotates daily about an axis passing through the Earth, so that it and the Earth both have a north pole, a south pole, and an equator;
- from the perspective of an observer on Earth, the sun moves relative to the fixed stars along a great circle (called the ecliptic), taking a year to complete the circle;
- the ecliptic is inclined to the celestial equator by about 23 degrees and intersects it at the equinoxes.
For example, these points all appear in the first book of Ptolemy’s Almagest, written in the 2nd century: the spherical movement of the heavens in 1.3; the spherical Earth in 1.4; the celestial axis passing through the earth in 1.5; the proper motion of the sun and the obliquity of the ecliptic in 1.8; the measurement of the obliquity in 1.12; and the equinoxes as intersections in 1.14.
I’ll give quotations below showing that each of these facts was familiar to Dante. But if you know these facts, then working out the path of the sun through the sky, as seen from Mount Purgatory, is just a matter of geometry. The start of Purgatory is set on Easter Sunday, 10th April 1300, which is about three weeks after the spring equinox (21st March), so the declination of the sun is about 8° north. The latitude of Jerusalem is about 32° north, so that at Jerusalem, the sun appears to the south (since 32° is greater than 8°) and at Mount Purgatory, the sun appears to the north (since −32° is less than 8°). It’s not difficult to see that if it is noon at Jerusalem then it is midnight at Mount Purgatory, and vice versa, so that the two points are twelve hours apart as time of day is reckoned. If you had trouble visualizing this, it would be easy to draw a diagram like this summarizing the geometry:
Dante’s astronomical knowledge
Dante did not, as far as we know, read Ptolemy. But he did read a summary of Ptolemy in the work of the Persian astronomer Al-Farghani (Alfraganus in Latin), whose Elements of Astronomy had been translated into Latin in the 12th century. The evidence for this is set out in Paget Toynbee (1895). ‘Dante’s obligations to Alfraganus in the Vita nuova and Convivio’. Romania 95, pp. 413–432.
In The Convivio, Dante cites Al-Farghani explicitly a couple of times, for example:
Mercury is the smallest star of heaven; for the magnitude of his diameter is not more than two hundred and thirty-two miles, as Alfraganus states it, saying that it is one twenty-eighth part1 of the diameter of the earth, which is six thousand five hundred miles.2
Dante (1307). The Convivio, p. 116. Translated by Philip H. Wicksteed (1903). London: J. M. Dent.
1. On p. 84 of the 1669 edition of Elements of Astronomy, the text is “Mercurii habet partem unam ex diametri terrae partibus 18”, not 28. It seems that Dante’s copy had an error here. See Toynbee, p. 424 for discussion of this issue. 2. Al-Farghani used Arabic miles (about 2 km), not Roman miles (about 1.5 km), so the estimate here for Earth’s diameter is close to the modern value. The confusion of Al-Farghani’s Arabic miles with the smaller Roman miles was one of the mistakes that led Columbus to believe that the East Indies could be reached by sailing west.
Dante also cites Ptolemy (as summarized by Al-Farghani), and the passages quoted below make it clear that he knew the basic astronomical facts I listed above.
This heaven revolves round this centre [that is, the Earth], as we perceive, without break; in the revolution of which there must needs be two fixed poles, and a circle, equally distant from them both, which revolves most rapidly. Of these two poles the one, that is to say this northern one, is apparent to almost all the land which is uncovered; the other, to wit the southern one, is concealed from almost all the uncovered land. The circle which is perceived midway between them is that path of the heaven under which the sun revolves when he goes in company with the Ram or with the Scales.
Convivio, p. 159.
The terminology needs some translation. The “circle, equally distant from them both, which revolves most rapidly” is the celestial equator, as is “the circle which is perceived midway between them [the poles]”. Dante therefore says that the sun is on the celestial equator only at the equinoxes: the spring equinox is in the sign of Aries, “the Ram”, and the autumn equinox is in the sign of Libra, “the Scales”. Dante continues:
I say, then, that the heaven of the sun revolves from west to east, not directly counter to the diurnal movement (that is the movement of day and night), but obliquely against it. So that its mid circle, which lies symmetrically between its poles, whereon is the body of the sun, cuts the circle of the two first poles at two opposite points, to wit, at the beginning of the Ram and at the beginning of the Scales; and it departs from it along two arcs, one toward the north and the other toward the south. And the summits of these arcs depart equally from the first circle, on either side, by twenty-three degrees and a point more; and one summit is the beginning of the Crab and the other is the beginning of Capricorn.
Convivio, pp. 160–161.
Again, some translation is needed. In the Ptolemaic system the heavens were imagined as a concentric set of spheres. The primum mobile was the outermost sphere, rotating daily and carrying the inner spheres with it; but the inner spheres themselves rotated relative to the primum mobile, giving proper motion to the moon, the planets and the sun. So when Dante says that “the heaven of the sun revolves from west to east” he is referring to the motion of the sun along the ecliptic during the year. He says that the ecliptic (the “mid circle” of the sun’s sphere) is oblique to the celestial equator, intersects it at the spring and autumn equinoxes (the beginning of the Ram and at the beginning of the Scales), and that the two circles are inclined by a little more than 23°.
Dante demonstrates that he was able to reason geometrically about the appearance of the heavens, by imagining cities named Maria and Lucia, placed at the north and south poles respectively, and describing how the motion of the sun would appear at each:
And if a man were standing erect in Maria, with his face ever turned to the sun, he would see it ever moving toward his right hand.1 […] And if a man were standing erect at Lucia and ever turning and his face toward the sun, he would see him moving toward his left hand.2 Whereby it may be perceived that these places have one day in the year, six months long, and a night of equal time; and when the one has day the other has night.
Convivio, pp. 161–162.
1. Clockwise. 2. Anticlockwise.