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Ptolemy’s Star Catalog

A Stolen Masterwork?

HL Jon Chesey

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Background

Written c150 CE by Claudius Ptolemy
Compilation of 13 books
Comprehensive summary of mathematical astronomy
Was considered the preeminent text on astronomy for ~1,500 years
Books VII – VIII contain a catalog of 1,025 stars which gives description, coordinates, and brightnesses
Catalog is in ecliptic coordinates

Ptolemy’s Almagest was published in the mid 2nd century CE and immediately became the preeminent text on astronomy. It was so comprehensive that scribes virtually stopped copying the work of previous astronomers, making almost all of them lost to us forever. Ptolemy’s work became the primary text for astronomers for the next 1300 years.

The Almagest is actually a compilation of thirteen books. The first two introduced necessary mathematical techniques, producing tables of angles and chords that would be used throughout the rest of the text. The third derived a solar model. The fourth, a lunar model which was then revised in the fifth book based on new discoveries by Ptolemy. The sixth put the solar and lunar and solar models together. Books seven and eight gave a list of over 1,000 stars. The final five books derived models for the five planets visible to the naked eye. In this talk we’ll be concentrating on the star catalog from books seven and eight where Ptolemy gives the celestial coordinates and brightnesses of 1,025 stars.

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Tycho Brahe

16^th century astronomer
Used custom built instruments to acquire the most precise observational data prior to the invention of telescope
Determined that the coordinates in Ptolemy’s catalog were, on average, low by ~1º.

Proposed that Ptolemy had stolen the data from Hipparchus (c150 BCE) and incorrectly adjusted the coordinates

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Ptolemy’s Star Positions

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Ptolemy’s Star Positions
Hipparchus’ Time

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Ptolemy’s Star Positions
Hipparchus’ Time

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Ptolemy’s Star Positions
Hipparchus’ Time
Ptolemy’s Time

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Ptolemy’s Star Positions
Hipparchus’ Time
Ptolemy’s Time
Where Ptolemy Said it was

Now we can understand Tycho’s claim. If Ptolemy had stolen the data for his star catalog from Hipparchus, he would have known he needed to update the coordinates, but using his incorrect value of precession, he would have adjusted the positions incorrectly leaving the stars 1º short of where they should have been. Precisely the amount Tycho determined the stars were off by.

Was this a smoking gun of plagiarism, or simply a cosmic coincidence?

The first question we should ask is whether or not a Hipparchan catalog existed in the first place. After all, there was no copy of one available. Due to the success of the Almagest virtually all of Hipparchus’ writings were lost to history. The only surviving text from Hipparchus was the Commentary on Aratus and Eudoxus.

�Despite most of the works themselves being lost, we do know something about what they were thanks to other authors.

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Did Hipparchus Even Have a Catalog?

[Hipparchus] attempted, what might seem presumptuous even in a deity, viz. to number the stars for posterity and to express their relations by appropriate names; having previously devised instruments, by which he might mark the places and the magnitudes of each individual star. In this way it might be easily discovered, not only whether they were destroyed or produced, but whether they changed their relative positions, and likewise, whether they were increased or diminished; the heavens being thus left as an inheritance to anyone, who might be found competent to complete his plan.

~Pliny the Elder

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Pierre-Simon Laplace

Exposition du System du Mond

Noted Ptolemy’ solar model was inherited from Hipparchus and the value for the length of a year was slightly too long by ~6.5 minutes.
Important because the position of the stars is based on the position of the sun.
Would not have had an effect in Hipparchus’ time but would have compiled by Ptolemy’s leading to an average error of ~1º in the solar position.

The first serious challenge to Brahe’s notion came in 1797 when Pierre-Simon Laplace published his Exposition du System du Monde. In it, he noted that there was a flaw in the solar model Ptolemy developed. Specifically, the value he used for a length of a year was slightly too long - by about 6.5 minutes (a 0.0012% error).

�This becomes important because Ptolemy’s solar model is in fact, Hipparchus’ solar model. While Ptolemy checked Hipparchus’ values in Book III, he did not make any changes. Thus, the date for which the solar model was calibrated was actually during the epoch of Hipparchus. What this meant Ptolemy’s average position of the sun in his own time, was off by just over 1º on average.

Since there isn’t a giant grid affixed to the sky for Ptolemy to measure stellar positions against, he had to first determine the position of something he could see: the sun.

Ptolemy would have used an instrument with two sights. One, he would point at the sun just as it set, and the second, he would align with a bright star that could be seen before the sun completely set. Ptolemy would have calculated the position of the sun using his solar model and then added the difference between the sun and the bright star to determine the star’s coordinates. That bright star could then be measured from to determine the position of other stars.

But because the sun’s position was the first step in determining the positions of stars, any error in the solar model would necessarily transfer to the stellar coordinates.

�This redeemed Ptolemy in the eyes of many historians of astronomy as it offered a very plausible alternative to Ptolemy having used Hipparchus’ data.

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Fingerprints of the Solar Model

Gerd Grasshoff

History of Ptolemy’s Star Catalogue

Plotted the average error of the stars in the catalog as a function of ecliptic longitude.
Compared this to the error from the solar model at the same longitudes.
Showed that they have the same period and amplitude but with a phase shift due to not observing stars directly next to the sun.

This argument was further supported by Gerd Grasshoff in his book published in 1990. There, he looked at the errors in stellar positions as a function of ecliptic longitude. He demonstrated that the errors in position had a distinct sinusoidal pattern. He compared this pattern with the error in the solar model when a second component of the sun’s motion was added in known as the eccentricity.

�On average, the sun moves approximately 1º per day to the east against the background stars. However, it moves slightly more in winter and slightly less in summer. In modern astronomy, we recognize this is due to the earth’s orbit being an ellipse, causing the sun’s apparent motion to be faster when we’re closer in winter and slower when we’re further away in summer. Although Ptolemy incorrectly modeled the orbit as a circle, his model did include an off centered positioning which also allowed for the sun’s apparent position to speed up and slow down - getting ahead of and falling behind the average position. However, because Ptolemy’s model didn’t use an ellipse, the manner in which it did so was a bit off. But more importantly, it was a bit off in the exact same sinusoidal pattern that Grasshoff discovered in Ptolemy’s data.

However, the phase of this pattern was offset. Why? Because Ptolemy would have measured stars some distance away from the sun as any too close to the sun would be lost in its glare, even at sunset.

The fingerprints of the solar model were clearly on the data and thus, offered a plausible explanation for the error in Ptolemy’s data.

�However, just because Ptolemy could have arrived at incorrect results due to the solar model as he would have if he had taken Hipparchus’ data, didn’t mean he did. Since this was Hipparchus’ solar model and he would have observed stars in the same manner, this same pattern of error would have been present in Hipparchus’ data as well.

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Dennis Rawlins

In the Almagest, Ptolemy tells the reader that stellar observations would be conducted with the use of an armillary sphere. This instrument functions by rotating a ring so that it is aligned with the coordinate system being used. In this case, a ring would be aligned with the ecliptic and the stars ecliptic longitude read off this.

However, researcher Dennis Rawlins notes that a misalignment of such an instrument would result in the point of the vernal equinox on this ring shifting along the celestial equator which would also result in an error in ecliptic latitude. For an error of just over 1º in ecliptic longitude, it would produce an error of nearly half a degree in ecliptic latitude near the equinoxes. However, the error would be positive near the vernal equinox (shown here) but then flipped at the autumnal equinox making it negative. This switching between positive and negative errors would produce a sinusoidal error when plotted as a function of ecliptic longitude that Evans did not detect thus making it unlikely that the solar error could be responsible for the 1º error.

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Counting Stars

Hermetic astrological texts were discovered which listed constellations and were attributed to Hipparchus.

Gave support to the existence of his star catalog.

Franz Boll

Some also contained counts of stars for each constellation.

The number of stars in these texts were generally lower than the number of stars for each constellation given in the Almagest.

Toward the end of the 19^th century, many scholars were invested in discovering and reappraising ancient astrological manuscripts. In 1892, Ernst Maas was put in charge of editing a codex from the 8^th century. He discovered that it contained a list of constellations and, based on the language, the text was attributed to Hipparchus. This lent support to the notion that Hipparchus did have a star catalog.

Shortly thereafter, two more texts were discovered. The first was by Alessandro Olivieri in 1898 and the second by Franz Boll in 1901. These texts not only contained the names of the constellations and language associated with Hipparchus, [ANIMATION] but also contained a count of stars in each constellation. And most importantly, [ANIMATION] for most constellations, they counted fewer stars than the Almagest contained.

If these texts summarized a lost Hipparchan catalog, then it would indicate that Ptolemy must have observed at least some of the stars in his catalog. But that did not free Ptolemy from the accusation that he stole some, if not most.

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Noticed that most stars in the Almagest catalog are given with a precision of 1/6 of a degree.
Some have a precision of 1/4 of a degree

Possibly indicative of two different instruments or observers?

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Newton’s Increments in Longitude

Newton argues that the frequency of the various increments does not make sense.

Generally, when observing with an instrument, human bias means the whole number is the most frequent reading taken, followed by a half, …

Newton noticed that the distribution for the increments in longitude don’t follow the expected pattern – stars ending in 40’ are the most common.

Explains this as an effect of Ptolemy using Hipparchus’ coordinates and adding 2;40. This would result in stars that were whole numbers now ending in 40’.

Although the differences in the error sixth and quarter degree stars couldn’t shed any light on the issue, looking at the overall frequency had some interesting clues.

In 1977, R. R. Newton noted that the frequency of the increments in longitude did not make sense.

[ANIMATION]

Due to the oddities of human bias, when reading with an instrument, observers will most frequently read the instrument at the increment for a whole number. The second most common should be a half.

Here is the distribution from around 1200 of my own observing using my quadrant which is graduated into tenths and allows me to estimate between the increments, down to twentieths of a degree. As we can see, the whole number is the most common, followed by a half. Part of the upsurge in these is driven by a reduction in the increments to either side (the .45 and .55 in this case).

[ANIMATION]

However, when analyzing the increments for the longitudes of stars in the Almagest Newton noticed that the whole number was not the most common - Those ending in 40 arcminutes were. And tellingly, the values to either side are reduced.

[ANIMATION]

Newton explains that this would be a natural consequence of Ptolemy having used Hipparchus’ data and adding what he believed to be the correct precession constant of 2;40º. In that situation, the stars that were whole numbers in Hipparchus’ catalog would not all end in 0;40 thereby reproducing the distribution we see here.

Other historians have criticized this noting that, while this explains the values for 30, 40, and 50, the second highest frequency is now 0 which would have been 20 before the addition – not 30 as we should expect. Thus, this transformation explanation does not explain all of the features of the frequency.

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Heinrich Vogt

Assumed that the stellar configurations in Hipparchus’ Commentary on Aratus & Eudoxus was based on the lost star catalog.
Used this to reverse calculate the positions of 122 stars.
Compared the distribution of errors between the supposed Hipparchan stars and the Ptolemaic ones and claimed they did not match.

Ultimately, the question of origin would be most easily answered by having a copy of Hipparchus’ catalog available for comparison. Since that did not exist, historians started considering the one existing Hipparchan text available to them: Commentary on Aratus and Eudoxus.

�This text is largely a criticism by Hipparchus of other philosophers. In particular, Aratus wrote a poem entitled Phaenomena, in which he professed to describe what stars were rising as others culminated (i.e., were at their highest point). Hipparchus found fault with their claims and, in response, decided to correct the information given by Aratus as well as give his own expanded version in an appendix.

For example, Hipparchus tells the reader that the constellation of “Bootes rises simultaneously with the zodiac from the beginning of Virgo until the 27^th degree of Virgo. While Booties is rising, the zodiac culminates from the middle of the 27^th degree of Taurus until the 27^th degree of Pegasus. The first star of Booties to rise is the one in the head, and the last is the one in the right foot.”

�Historians considered that, to create such a work, Hipparchus would likely have performed calculations based on the known positions of stars - likely from his own star catalog. [ANIMATION] Thus, they began to wonder if they could reverse calculate the coordinates from the catalog using the rising/setting/culminating pairs given in the Aratus Commentary.

�The first to claim to do this was Vogt in 1925. [ANIMATION] He published a paper in which he claimed to be able to reverse calculate 881 pieces of numerical data, giving the complete coordinates for 122 stars. So how did they compare to the Almagest?

Vogt first compared the positions for these 122 stars to the ones given by Ptolemy. If the coordinates were the same with the exception of the ecliptic longitude being 2 2/3º higher for Ptolemy, then it would suggest Ptolemy did steal Hipparchus’ data.

[ANIMATION] By and large, Vogt concluded that the coordinates were independent of one another.

�Furthermore, Vogt compared the positions of both the reconstructed stellar positions and the Almagest with those of the actual positions of the stars using modern astronomical calculations to determine the distribution of errors for each of them. [ANIMATION] He found that the distributions were not similar.

However, there were a handful of stars that had similar outlier errors. Among them were τ Ari (Tau Arietis), α Car (Alpha Carinae), ν Boo (Nu Bootis), π Hya (Pi Hydrae), and θ Eri (Theta Eridani). θ Eri was particularly problematic as it was more than 3º off in the same direction from its true location in both catalogues.

Thus, Vogt’s research gave mixed signals. It again indicated Ptolemy was likely to have observed most of his catalog himself, but at least some stars appeared copied.

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Criticism of Vogt

Commentary on Aratus written in 2 parts at different times

Response to Aratus (37º N)
Appendix with values for Rhodes (36º N)

Vogt did not make it clear if he accounted for the different times and latitudes.
Calculations for the same star did not arrive at consistent values.
These errors could easily have changed stars between bins resulting in the distribution of errors not matching Ptolemy’s when it should have.
This undermines Vogt’s conclusions.

While many scholars consider this definitive proof that Ptolemy could not have used Hipparchus’ data, Gerd Grasshoff took issue with the Vogt analysis. The first reason was that one of the variables needed in reverse calculating stellar positions from the rising/setting/culminating descriptions given in the Aratus Commentary is the date. [ANIMATION] Historians have long recognized that different portions of the text were likely written at different times. Vogt was very light on the details of which stars he considered to be from what period making his methods hard to analyze. [ANIMATION]

�A second parameter in the conversion is the latitude of observation. The first part of the Aratus Commentary was a correction of Aratus’ values and meant for a latitude of 37ºN [ANIMATION] while the appendix was for Hipparchus’ own latitude of 36ºN. Vogt is again shy about the exact methods used but only mentions the value of 37º. [ANIMATION]

However, these criticisms are really more of words of caution – Due to Vogt’s lack of clarity, we cannot be sure his methods were applied correctly. But if they were, then these criticisms evaporate.

�But somewhat more concerning, Grasshoff also noted that Hipparchus occasionally listed the same star multiple times - describing its rising or setting with multiple other stars. This resulted in some stars having more than one way by which its coordinates could be calculated - and they didn’t always agree. [ANIMATION] Surely, if this was based on a star catalog, they should.

�The result is that Vogt’s analysis may be prone to error [ANIMATION]. If this was the case, then the distribution of errors that Vogt compared against the Ptolemaic one would be disrupted and may cause it to look different when it should appear similar. [ANIMATION]

But what about going the other way around?

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Ptolemy’s Phaenomena

Grasshoff calculates the errors (vs modern astronomical theory) in the phenomena given by Hipparchus.
He then calculates the same phenomena based on Ptolemy’s star catalog as well as their error.

These errors are compared to determine stars with similar, large errors.
Finds that there are several stars that share a common error.

Instead of trying to calculate the ecliptic coordinates from the phenomena described in the Aratus Commentary to compare to the Almagest, what would happen if we calculated the same phenomena using the Almagest and compared them to the Aratus Commentary?

Grasshoff did precisely this. First, for each of the phenomena Hipparchus described, Grasshoff calculated what the correct values should have been. For example, when Hipparchus tells us that the first star in Bootes to rise does so at the same time as the 27^th degree of Virgo, does it? Or is it actually the 28^th degree of Virgo? If so, then there is a 1º error in the phenomenon described. [ANIMATION]

He then used the coordinates given in the Almagest to calculate the same phenomena, ie., what point on the ecliptic would be on the horizon at the same time as the first star to rise in Bootes. He could then determine the error against the modern astronomical theory from that as well. [ANIMATION]

Next, these errors could be directly compared. If the stars in Ptolemy’s catalog were based on Hipparchus, then there should be a strong correlation between the two that looks like a diagonal line of slope = 1. In other words, a diagonal line from bottom left to top right.

Indeed, there are several stars that show similar, large errors in just this manner. This includes ζ Cas, β Sge, θ Gem*, i Cnc, β Vir, ε Vir, β Sgr, χ Psc, ρ Cet, θ Eri*, α Car*, π Hya*, and α Cen (four of which were stars that Vogt’s analysis had also flagged as suspicious). However, there are also other stars that do not. For example, the one on the far right which has a ~8º error for the Almagest but virtually no error in the Aratus Commentary. This suggests that this star was observed independently.

Thus, this investigation supports the notion that the Almagest catalog is a mix.

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Dating Through Proper Motion

Dambis & Efremov

Analyzed the proper motion of stars to see when they best matched the configuration described in the Almagest.
Specifically looked at fast moving stars.
This test is independent of coordinate systems.

Conclude most coordinates must have come from Hipparchus.

In the 1980’s a new method was proposed. Astronomers had sufficiently accurate data on the motion of stars relative to one another (a phenomenon known as proper motion), that they began considering if they could use this to approach the question of Ptolemy’s star catalog.

The method would essentially look at the fastest moving stars and ask, in what year was their position best described by the position in relation to the other stars in the constellation provided in the Almagest? This approach was free of coordinate systems and thus offered a novel and independent approach.

The first attempt at using this method was in 1989 by Efremov and Pavlovskaya but was flawed due to it being heavily impacted by the choice of other stars in the constellations that were chosen to compare to.

The technique was refined and reapplied in 2000 by Dambis and Efremov. [ANIMATION] It concluded that the best fit point in time was during the era of Hipparchus. It would have been statistically unlikely for Ptolemy to have been the originator for most of his star catalog.

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Response to Dambis & Efremov

Dennis Duke

Reviews Dambris & Efremov’s work and finds that they significantly underestimated the errors.
When accounted for properly, this method cannot distinguish between the epochs of Hipparchus and Ptolemy.

However, the results of Dambris & Efremov were swiftly criticized. Dennis Duke (University of Florida) noted that the amount of proper motion over the 265 years between Hipparchus and Ptolemy for nearly every star in Ptolemy’s catalog was below the precision given in the Almagest. Only three stars would have moved 1/6 of a degree in that time span.

Thus, any hope of teasing out would be swamped by simple instrumental uncertainty, especially since the accuracy of the stellar positions in the Almagest due to instrumental uncertainty is barely accurate to within 1º. When this was taken into consideration, the data was a reasonable fit to either Hipparchus’ time or that of Ptolemy.

Thus, the methodology of attempting to use fast moving stars to settle the question was unlikely to ever succeed.

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Southern Stars

The closer a star is to the horizon, the more it is dimmed by the atmosphere.

Hipparchus observed from a latitude 5º north of Ptolemy so southern stars would have been dimmed more for him than Ptolemy.

The probability that a star of a certain brightness would be included in the catalog drops as the star gets fainter.

Rawlins (1982) asked: For which observer does the number of stars of each magnitude match the expected number after atmospheric extinction?

Concluded it was best for Hipparchus.

Another interesting approach to determine the authorship was to look at stars near the southern horizon.

Light passing through our atmosphere is scattered and, as a result, the more atmosphere we observe the star through, the dimmer it appears. This effect dims stars by about 0.2 magnitudes near the zenith (straight up) but becomes very significant near the horizon as we look through larger amounts of atmosphere as shown in the figure here.

Hipparchus observed from Rhodes in Greece which has a latitude of 36º N while Ptolemy observed from Alexandria which has a latitude of ~31º N.

[ANIMATION]

This means that the same southern star would appear lower on Hipparchus’ horizon than it would for Ptolemy. As a result, it would appear to be dimmer. While Ptolemy claims that the catalog is a complete list of all stars as faint as sixth magnitude, this is obviously not true. Numerous stars brighter than that cutoff are excluded with the probability of inclusion dropping the fainter the star gets.

[ANIMATION]

The probability of inclusion is shown here.

[ANIMATION]

In 1982, Dennis Rawlins attempted to use these facts to determine the authorship of the catalog. Essentially, Rawlins took the list of all possible stars that could have been observed, determined their brightnesses after extinction for each of the two locations, and then applied the probability function to see how many stars of each magnitude would have been included. This could then be compared to the actual number in the catalog to determine which location matched the right answer.

[ANIMATION]

Rawlins determined that the data best supported a latitude matching that of Hipparchus. [ANIMATION]

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Southern Stars - Schaefer

Rejected Rawlins’ conclusions

The inclusion probability Rawlins used was based on a small sample of stars
Rawlins underestimated how much the atmosphere dimmed stars

Recalculated with updated probability function and extinction coefficients

Concludes that Hipparchus could not be the author of the catalog

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Southern Stars - Pickering

Rejected Schaefer’s conclusions

Schaefer’s methods would reject Hipparchus as the author of the only work we know he wrote
Argued that Schaefer’s estimations of the amount of extinction was influenced by post-industrial pollution
Challenged the integrity of Schaefer’s probability function

Attempted to recalculate but determined the inherent uncertainty in the parameters makes the method useless.

The response to Schaefer was swift. The next year, Keith Pickering published a response in which he claimed that Schaefer’s conclusions couldn’t even pass a sniff test. If we attempted to apply Schaefer’s methods to the coordinates of the stars in the only work for which we know Hipparchus was the author, it would claim that he wasn’t. Indeed, the amount of extinction Schaefer predicted would have made some stars described virtually invisible for Hipparchus. Thus, the method must be flawed.

[ANIMATION]

Pickering argued that Schaefer’s value for how much stars were dimmed by the atmosphere were based on observations in the modern world – after industrialization. This wasn’t entirely true as Schaefer had applied four methods to determine a reliable value, and one of them was based on pre-industrial data; But the other three methods firmly were modern.

[ANIMATION]

Furthermore, Pickering criticized Schaefer’s method of attempting to derive the function that would give the probability of a star of a given magnitude being included.

[ANIMATION]

Pickering attempted to correct these issues but found that there was so much inherent uncertainty [ANIMATION] that it was likely impossible to accurately determine the latitude of the observer, largely due to the result depending so heavily on the clarity of the atmosphere. Another dead end.

All of the novel attempts at determining the authorship seemed to be too uncertain to give a clear answer.

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Aratus Latinus

Collection of Aratus’ poems with related material from other authors
Described the positions of the boundaries of Ursa Major, Ursa Minor, and Draco based on their distance from the north celestial pole and east-west direction.

Historically attributed to Eratosthenes

More likely to have been from Hipparchus

Another of the documents examined in the late 19^th century was the Aratus Latinus. This text was the work of Aratus we discussed earlier, translated into Latin, sometime around the 8^th century. However, the text has been interspersed with other material.

Among that other material, there were three passages which contained descriptions of the boundaries of three constellations (Ursa Major, Ursa Minor, and Draco) by giving the positions of the bright stars on their extremities. The passages described the distances of bright stars from the north celestial pole as well as where they fell east and west along the ecliptic.

Historically, these passages were attributed to the 3^rd century BCE astronomer Eratosthenes who is credited with correctly calculating the radius of the Earth.

[ANIMATION]

But beginning in 1900, historians began suspecting it was authored by Hipparchus. Otto Neugebauer supported this conclusion in his 1975 book, History of Ancient Mathematical Astronomy.

Further evidence tied the work to Hipparchus, as it was realized that the co-declination of Polaris, the brightest star in Ursa Minor agreed exactly to the value Hipparchus used according to Ptolemy in another of his works: Geographia.

Could this present another insight into the lost Hipparchan catalogue?

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Codex Climaci Rescriptus

Christian text from the Greek Orthodox St. Catherine’s Monastery in Egypt had overwritten text (palimpsest).
Analyzed beginning in 2017 with multispectral imaging.
Found to contain star-origin myths from Eratosthenes, Aratus’ Phaenomena
And star coordinates.

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Codex Climaci Rescriptus

Corona Borealis, lying in the northern hemisphere, in longitude spans 9¼° from the first degree of Scorpius to 10¼° in the same zodiacal sign. In latitude it spans 6¾° from 49° from the North Pole to 55¾°.

Within it, the star [β CrB] to the West next to the bright one [α CrB] leads [i.e. is the first to rise], being at Scorpius 0.5°. The fourth star [ι CrB] to the East of the bright one [α CrB] is the last [i.e. to rise] ... 10;49° from the North Pole. Southernmost [δ CrB] is the third counting from the bright one [α CrB] towards the East, which is 55¾° from the North Pole.

α

ι

δ

β

The text was found to overlap with the coordinates from the Aratus Latinus, but also included constellation boundaries for a new constellation: Corona Borealis. And the researchers suggest that the remaining constellations may still be hiding in other pages not yet deciphered, or that made their way into other books in St. Catherine’s Monastery.

The researchers again confirmed that these coordinates are most likely given by Hipparchus and, by comparison between the three constellations that were in both this text as well as the Aratus Latinus, the researchers affirmed the two share a common origin.

Thus, they were able to directly compare these coordinates with the ones given in the Almagest to see if they were identical apart from an increase of 2 2/3º in longitude. The authors concluded that the two sources were independent.

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Noel Swerdlow

“I am only too happy that I have never written anything on the subject myself that I might wish to defend.”

Ultimately, the debate over the originality of Ptolemy’s star catalog remains incomplete. Historian of astronomy, Noel Swerdlow famously remarked, “I am only too happy that I have never written anything on the subject myself that I might wish to defend.”

Here, Swerdlow as pointing out that no matter what argument you wanted to make regarding Ptolemy’s star catalog, there seemed to be evidence to favor your position. For those that wish to free Ptolemy of accusations, they can point to the flaws in the solar model accounting for the error as well as the independence of the coordinates from the Aratus Latinus, Codex Climaci Rescriptus, and Vogt’s reconstructed catalog. Ptolemy’s critics can just as easily point to the stars from Vogt’s analysis which share the same significant errors for some stars.

In the end, only by not venturing a confident position can one be free from criticism, Swerdlow tells us.

Until such time as more of Hipparchus’ catalog is recovered, how much, if any, of Hipparchus’ catalog made its way into Ptolemy’s will remain fiercely debated.

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Thank you for attending

Learn more at: JonVoisey.net

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Image Credits

Almagest in Latin: 1515 Printing.
Almagest in Latin with Marginalia: Library of Congress.
Tycho Brahe: Painter unknown. Photo by Jens Mohr. Photo in public domain.
Precession Animation: Nick Anthony Fiorenza.
Pierre Simon-Laplace: Colored engraving by James Posselwhite. In public domain.
Gerd Grasshoff: Faculty Photo – Max-Planck Institute for the History of Science.
Solar Model Error Graph: Gerd Grasshoff, The History of Ptolemy’s Star Catalogue.
Dennis Rawlins: Personal website of Dennis Rawlins
Ecliptic Alignment: Dennis Rawlins, An Investigation of the Ancient Star Catalog
Franz Boll: Photographer unknown. Photo in public domain.
John Dreyer: Photographer unknown. Photo in public domain.
Longitude Increment Distribution: Gerd Grasshoff, The History of Ptolemy’s Star Catalogue.
Heinrich Vogt: Photographer unknown. Photo in public domain.
Error Distributions: Gerd Grasshoff , The History of Ptolemy’s Star Catalogue.
Aratus Commentary (1567): Sophia Rare Books. Work in public domain.
Relationship of Phenomena Errors: Gerd Grasshoff , The History of Ptolemy’s Star Catalogue.
Proper Motion: Richard Pogge, Ohio State University.
Dennis Duke: Faculty Photo – Florida State University.
Atmospheric Extinction: Casey Reed, Sky & Telescope.
Bradley Schaefer: Faculty Photo – Louisiana State University.
Magnitude vs Declination: Bradley Schaefer, The Latitude of the Observer of the Almagest Star Catalogue.
Keith Pickering: Contributor Photo – Academia.edu
Aratus Latinus: Warburg Institute Iconographic Database.
St. Catherine’s Monastery: Photo by Joonas Plaan, Creative Commons 2.0.
Codex Climaci Rescriptus: © Museum of the Bible, 2021. Image shared under Creative Commons BY-SA 4.0 license, 2022. All conditions apply.
Corona Borealis: Stellarium.
Noel Swerdlow: Photo by Van Urfalian, Caltech.
Astronomer Copernicus: Conversation with God, Jan Matejko (1872)

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