Tag: precession

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Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel

Having reviewed Vogt’s work, Grasshoff now turns to dissecting Gundel’s. As a reminder, Gundel discovered a $15^{th}$ century set of hermetic writings that contained a list of stars that was dated to the time of Hipparchus, potentially making it the first direct evidence of a Hipparchan star catalog.

But what Gundel’s analysis lacked is any exploration of how this related to  whether or not Ptolemy stole Hipparchus’ data. In this post, we’ll explore Grasshoff’s analysis of that topic. However, before doing so, Grasshoff works to ensure that we have the best possible understanding of the hermetic catalog before comparing the hermetic catalog to Ptolemy’s. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel”

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Scholarly History of Commentary on Ptolemy’s Star Catalog: Gundel, Pannekoek, and Peter & Schmidt (1936-1968)

In the last post, we explored the 1925 paper by Vogt that attempted to reverse engineer entries from the presumed Hipparchan star catalog. Assuming that the coordinates derived were actually representative of such, Vogt demonstrated that Ptolemy was unlikely to have based his catalog on that of Hipparchus.

Continuing in the theme of defending Ptolemy, we’ll explore three more texts which come to Ptolemy’s defense: a book by Gundel (1936), a paper by Pannekoek (1955) and a paper by Petersen & Schmidt (1968). Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Gundel, Pannekoek, and Peter & Schmidt (1936-1968)”

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Scholarly History of Commentary on Ptolemy’s Star Catalog: Vogt – 1925

In our last post we had established that it was impossible for Ptolemy to have stolen all of his data from Hipparchus as indirect evidence of the number of stars that would have been included in Hipparchus’ catalog indicate that Ptolemy’s catalog had around $200$ stars that Hipparchus’ presumptive catalog did not. Furthermore, we cited Dreyer and Fotheringham who both showed that errors in the determination of the position of equinoxes and solstices would have resulted in the $1º$ error at the heart of the accusation against Ptolemy, eliminating the need for Ptolemy to have used Hipparchus’ catalog.

Thus, while it’s not necessary that Ptolemy took all of his data from Hipparchus, the possibility remains that he took some. But to determine that, we’d need more information about Hipparchus’ presumed catalog which is what we’ll explore in this post looking at an important 1925 paper by Vogt. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Vogt – 1925”

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Scholarly History of Commentary on Ptolemy’s Star Catalog: 137 CE – 1918 CE

I’m going to take a bit of a break from direct progress on the Almagest as we get to the star catalog. This is because there is, what I feel to be a fascinating and important discussion surrounding its legitimacy and I want to explore the history of this discussion, even though almost all of it is outside the range of the SCA period1. Namely, the discussion is whether or not Ptolemy’s star catalog is legitimate, one which he took the measurements himself, or if Ptolemy stole the data from an astronomer that came before him and tried to update it, but failed due to an incorrect value for the rate of precession.

Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: 137 CE – 1918 CE”

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Almagest Book VII: On the Rate of Precession from Other Greek Astronomer’s Observations

In the last post, we showed how we can determine the rate of precession if we know how much a star has changed its declination over a long period. In it, we used a baseline of $265$ years, corresponding to the time between Hipparchus and Ptolemy.

Next, Ptolemy wants to increase that baseline further and turns to the observations of three other Greek Astronomers: Timocharis, Agrippa2, and Menelaus. However, these astronomers did not give the position of the stars in equatorial coordinates. Rather, they described occultations of various stars by the moon. Thus, Ptolemy turns to the lunar model to determine the positions of these stars and instead of finding a change in declination, is able to directly compare the ecliptic longitude of them over time. Continue reading “Almagest Book VII: On the Rate of Precession from Other Greek Astronomer’s Observations”

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Almagest Book VII: On the Rate of Precession from Hipparchus’ Observations

In the last post, Ptolemy concluded that the motion of the fixed stars over time, known as precession, happens about the poles of the ecliptic. He determined this by stating that the longitude of stars with relation to the ecliptic remained consistent over a long interval of time but varied with respect to the celestial equator. That post concluded with Ptolemy’s promise that we would be able to determine rate of that precession using the same data he presented previously.

It is particularly [easy to demonstrate] from the differences in declination found for those stars near the equinoctial points.

Continue reading “Almagest Book VII: On the Rate of Precession from Hipparchus’ Observations”

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Almagest Book VII: On the Poles of Precession

From the above, it has become clear to us that the sphere of the fixed stars, too, performs a rearward motion along the ecliptic, of approximately the amount indicated. Our next task is to determine the type of this motion, that is to say, whether it takes place about the poles of the equator or about the poles of the inclined circle of the ecliptic.

Now that Ptolemy has determined that precession does indeed happen at a rate that agrees with Hipparchus, he now asks whether that precession is happening in the same direction as the ecliptic or the celestial equator.

Continue reading “Almagest Book VII: On the Poles of Precession”

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Almagest Book VII: On Precession

At the beginning of the last chapter, Ptolemy noted that the celestial sphere appears to have a rearward motion of its own known as precession of the equinoxes. This motion means that the position of the sun in the zodiacal signs slowly increase in advance as time passes. In particular, the sun was at the beginning of Aries in Ptolemy’s time, but since then has advanced such that today it lies near the beginning of Pisces.

We can see this mainly from the fact that the same stars do not maintain the same distance with respect to the solstical and equinocital points in our times as they had in former times: rather, the distance [of a given star] towards the rear with respect to [one of] the same points is found to be greater in proportion as time [of observation] is later.

Continue reading “Almagest Book VII: On Precession”

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Almagest Book VII: Hipparchus’ Star Alignments

Ptolemy lays out the arrangements described by Hipparchus by going through stars in various constellations:

Stars in Cancer. [Hipparchus] records that the star in the southern claw of Cancer [α Cnc], the bright star which is in advance of the latter and of the head of Hydra [β Cnc], and the bright star in Procyon [α CMi] lie almost on a straight line. For the one in the middle lies $1 \frac{1}{2}$ digits to the north and east of the straight line joining the two end ones, and the distances [from it to each of them] are equal.

First, we should discuss the identification of the stars. The designations of the stars in the brackets are the modern Bayer designations first created in $1603$. For Ptolemy’s part, he described the positions of the stars based on how they should appear in the representation of the constellation. For example, we see him here describing α Cnc as the “southern claw of Cancer”. However, because the depiction of the figures in constellations is somewhat subjective, this leads to some ambiguity in which stars are which, making assessing the validity of Ptolemy’s statements somewhat difficult. Continue reading “Almagest Book VII: Hipparchus’ Star Alignments”