Now, to deal with the next part of the theory, we shall begin discussing the stars, and first, in accordance with the logical order, the so-called fixed stars.
To introduce the next book of the Almagest, Ptolemy informs the reader that we will be taking some time to understand the fixed stars. There are two important things to note about this sentence. The first is that Ptolemy is taking extra care to make sure the reader knows we are discussing the fixed stars. This is because the Greek concept of “stars” could include the planets.
The second is why Ptolemy feels that discussion of these is part of the “logical order.” It is because we’re now working towards models for the planets and, while the position of the sun and moon were reckoned with respect to the solstice and the ecliptic1 the planets positions are most readily measured with respect to stars. Thus, before getting to planets, we need to develop a firm understanding of the positions of the stars and this is only useful if those positions are fixed, allowing them to be used as reference points. Ptolemy assures us that they do, stating,
the stars themselves patently maintain the formations [of their constellations] unchanged and their distances from each other the same.
But while the stars are “fixed” to the sphere, Ptolemy wishes to make it clear that we should not apply this terminology to the sphere itself:
We are quite right to call [the stars] “fixed”; but in as much as their sphere, taken as a whole, to which they are attached, as it were, as they are carried around, also [like the other spheres] has a regular motion of its own towards the rear and east with respect to the first [daily] motion, it would not be appropriate to call this [sphere] too “fixed”.
Here, Ptolemy is noting that the celestial sphere has some drift to it, specifically, the precession of the equinoxes in which the position of the vernal equinox slowly drifts eastwards. While I’ve pointed out that this phenomena exists and is part of why Ptolemy’s models can’t be directly applied in present day in numerous posts, this is the first time we’ve encountered Ptolemy discussing it himself. He notes that Hipparchus too was aware of this phenomenon, but calls his estimation of how quickly into question because
he had found very few observations of fixed stars before his own time, in fact practically none besides those recorded by Aristyllos and Timocharis, and even these were neither free from uncertainty nor carefully worked out.
In other words, to determine a rate of precession, one needs to know the ecliptic coordinates of at least some fixed stars in order to see how they’ve changed. As we’ve seen with the mean motions, the longer the gap between measurements, the smaller the error becomes. Unfortunately for Hipparchus, (who lived in the second century BCE), the only figures he had to work with were from astronomers living barely two centuries prior to his own lifetime. Given how small precession is, it would be hard to be certain if the measurements were due to actual precession or simple experimental error. Ptolemy casts doubt on the reliability of the measurements2. However, Ptolemy, living a few centuries after Hipparchus could use Hipparchus’ data to check the figure and he does so, finding it to be in agreement with that which Hipparchus derived.
With the rate of precession known, Ptolemy can then affirm that the positions of the stars has not changed and affirms that they do not and
are seen to be absolutely identical now too.
And being thorough, he also checks to ensure that this isn’t just a phenomena near the ecliptic as Hipparchus had proposed:
This is true not only of the positions of the stars in the zodiac relative to each other, or of the stars outside the zodiac relative to other stars outside the zodiac (which would [still] be the case if only stars in the vicinity of the zodiac had a rearward motion, as Hipparchus proposes in the first hypothesis he puts forward); but it is also true at positions of the stars in the zodiac relative to those outside it, even those at considerable distances.
In short, all stars move together and show the same degree of precession no matter whether or not they’re near the zodiac or not.
[T]o provide a convenient test of the matter, we too will adduce here a few of his observations, [namely] those which are most suitable for easy comprehension and also for those giving an overview of the whole method of comparison, by showing that the configurations formed by stars outside of the zodiac, both with each other and with stars in the zodiac, have been preserved unchanged.
Here, Ptolemy promises to present some of the data collected by Hipparchus as an illustration of how Ptolemy compared Hipparchus’ to his own. This is notable because the data he cites from Hipparchus is not in standard ecliptic latitude and longitude. Rather, both he and Hipparchus would take a taught string and then hold it to the sky, searching for bright stars that fell along this line. While this is crude, it’s also reasonably effective as if any of the stars moved, it would cause one or more of them to fall off the line unless they all moved the same direction and amount (i.e., precession). Ptolemy first presents Hipparchus’ alignments followed by his own, but I’ll split those into separate posts for ease of reference should we need it later.
- I.e., ecliptic coordinates.
- That being said, modern astronomy suggests that Aristyllos’ observations were indeed excellent.