Finally, in the discussion of Ptolemy’s star catalog, we’ll be moving beyond Grasshoff1.
In this post, we’ll explore a new technique, first considered in the late $1980$’s to use high proper-motion stars to attempt to determine the epoch of the star catalog.
The technique is fairly simple.
By and large, stars do not appear to move relative to one another in a perceptible manner. This is why their motion (known as proper motion) wasn’t discovered until the $1800$s when Edmund Halley compared the positions of stars in his own time to those given by Hipparchus2.
The proposed technique considers a fast moving star among a field of other stars which do not have apparent motion and asks, in what year was its position best described relative to other stars in the same constellation?
The first attempt to apply this method was done in $1989$ by Efremov and Pavlovskaya. There, they attempted to use eight of the highest proper motion stars3 and attempt to determine the best epoch based on their positions given in the star catalog.
Unfortunately, their results were inconclusive. The first six of those stars yielded an extremely wide range from $450$ BCE to $450$ CE. The seventh, ι Per, gave a date of $950$ BCE, and the final one, α Cen, gave no result as the errors in the other, southern, stars was too high to make sufficient sense of the data.
Furthermore, the results seemed to be highly dependent on which stars were picked for comparison pointing to problems reducing the data.
But in $2000$, Efremov tried again, this time with the help of Dambris. This time, they began with ten stars but eliminate the same two from their previous attempt for the same reasons. This time, they came up with an epoch of $53$ BCE $\pm 130$ years. This leans towards suggesting Hipparchus as the author but does not firmly rule out Ptolemy.
They then develop a technique they refer to as the “bulk method” in which they divide the entire catalog into “fast” and “slow” stars and then attempted to perform a similar sort of analysis.
The epoch for this analysis concluded that the epoch of the star catalog was $89$ BCE $\pm 122$ years with a $94\%$ confidence level. This would virtually rule out Ptolemy as the author.
However, the result of this bulk method was swiftly rejected by Dennis Duke. In a response, he attempted to reproduced Dambris and Efremov’s methods and concluded they substantially underestimated the random error in the measurement. This caused them to significantly overestimate their confidence level.
When Duke attempted to reproduce their methods with a more robust statistical methodology, he concluded that “the confidence interval determined is so large that the Hipparchan and Ptolemaic epochs cannot be distinguished.”
Thus, while the methodology is quite interesting, the results are inconclusive.
- Grasshoff’s book does contain one additional chapter. However, it seems to be discussing the philosophical framework in which Ptolemy was operating and how we should judge his actions if he indeed make use of Hipparchus’ work. I’m trying to limit myself to the scientific discussion.
- It’s debatable whether Halley actually discovered proper motion or was simply thrown off by errors in previous astronomers, including Ptolemy.
- α Boo, $\omicron ^2$ Eri, τ Cet, γ Ser, α CMa, η Cas, ι Per, and α Cen.