Ancient astronomers: Hipparchos, Hero and Geminos

Different from today, people writing in antiquity usually did not date their work. A typical introduction of a biographical Wikipedia page is: "Little is known about the life of ...". Therefore more indirect hints are used to place these persons on the historical time line (which is relative and could be misdated). One kind of hint is the mentioning of famous predecessors or contemporaries. Another method especially applicable to astronomers is the retrocalculation of some unique observations which would pin the person to the astronomical time line (which is absolutely dated).

Our 232-hypothesis implies that the historical time line and the absolute astonomical time line are not correctly synchronized in antiquity. Therefore we would expect to find some irregularities in the written history of that time. Note e.g. the emergence of a Theon, who is an expert of astronomical literature and lives in Egypt, in a dialogue by Plutarch.

Geminos was a Greek astronomer and mathematician. Recently, a complete English translation of Geminos' only surviving work "Introduction to the Phenomena" has been published (ref. 1). Geminos wrote the "Introduction" as a textbook for beginning students of astronomy. The book is nowadays considered to be written in the first century BC, that means the period between Hipparchos and Ptolemy. Geminos mentions  Hipparchos as a forerunner, but he does not mention Ptolemy. But Geminos also mentions Hero of Alexandria as a forerunner, which seems to be a problem. The following is a direct citation from section 6 of the introduction of the new publication:

One minor problem with dating Geminos to the first century BC involves his mention of Hero of Alexandria in fragment 1. The dating of Hero has been controversial, with suggested dates from the middle of the second century BC to the middle of the third century AD.  In Dioptra 35, however, Hero mentions a lunar eclipse observed simultaneously in Alexandria and Rome. Although Hero does not mention the year of the eclipse, he is detailed about its other circumstances: 10 days before the vernal equinox, 5th seasonal hour of the night at Alexandria. Neuge­bauer (ref.2) has shown that these circumstances were satisfied by only one lu­nar eclipse between about -200 and +300, namely that of March 13,  AD 62. If Hero used an eclipse of recent memory, we must place him in the second half of the first century AD. Thus, if the dating of Geminos to the first century BC is correct, we must suppose that Proklos or a later copyist interpolated the name of Hero in fragment 1.

Hipparchos was a Greek astronomer and mathematician said to have lived about RomBC 190 to 120, because Ptolemy attributes to him astronomical observations in the period from -146  to -126 in his Almagest. Some of these observations are stated as made in Rhodes. Some earlier observations since -161 might also have been made by Hipparchos. As mentioned above, Geminos names both Hipparchos and Hero as forerunners, which means that Hero even could have been contemporary with Hipparchos. This has been considered by historians, and this makes the dating of Hero controversial. But maybe we should instead dispute the dating of Hipparchos in the Almagest, as discussed in our introduction to "Ancient history".

If Hero would be fixed on the absolute astronomical time line, while Hipparchos and Geminos are placed on the relative historical time line, our 232-years shift would make Hipparchos and Hero contemporary living in the second half of the first century AD, while Geminos would have lived in the second half of the second century AD and had both as forerunners.

Although he wrote at least fourteen books, relatively little of Hipparchos' direct work survived into modern times. However, there are a few observations probably made by Hipparchos himself, which are mentioned by later authors and are detailed enough to give us a possible dating.

The solar eclipse
The first observation is a solar eclipse used by Hipparchos to determine the size and distance of sun and moon. Cleomedes writes:

Once when the Sun was wholly eclipsed in the Hellespont, it was observed in Alexandria to be eclipsed except for the fifth part of its diameter.

We are looking for a solar eclipse which is total in the Hellespont region and of magnitude 0.8 in Alexandria, occurring during the active time of Hipparchos as an astronomer. There are five matching eclipses in the time span -199 to 200 (ref. 3).

The eclipse of -128 Nov. 20 is regarded by many as the most likely match for this observation. It is total in the Hellespont and has a magnitude of 0.79 in Alexandria. But, it comes very late in Hipparchos' active life.

We might now redate Hipparchos by 232 years towards our time according to our hypothesis. If this is right he most likely has been active as an astonomer between 70 to 105. One of the eclipses matching his observation is within this time span: on 71 Mar. 20. If this is Hipparchos' eclipse, he would have observed it when he was 29 years old.

The lunar eclipse
The second observation is a lunar eclipse described by Pliny as follows:

He also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth. (ref. 4)

We are looking for a total lunar eclipse visible in Greece or Asia Minor, where the moon is setting eclipsed exactly at sunrise.
This is a typical midwinter observation. The nearer to winter solstice the better and longer the observability, probably also enhanced by refraction near the horizon line. The frequency of such an occasion is about 1 to 4 per century.

Toomer (ref.5) argued that this must refer to the large total lunar eclipse of -138 Nov. 26, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast.

If Hipparchos has lived 232 years nearer our time (42 to 112) as redated above he could have observed the large total lunar eclipse of 65 Jan. 11 when he was about 23 years old, i.e. five years before his observations gained reputation.

1. James Evans & J. Lennart Berggren, Geminos's Introduction to the Phenomena, Princeton University Press 2006. read here
2. Neugebauer 1938; with results summarized in Neugebauer 1975, 846.
3. Nasa Eclipse Web Site
4. translation H. Rackham (1938), Loeb Classical Library 330, p.207
5. G.J.Toomer (1980): Hipparchus' Empirical Basis for his Lunar Mean Motions, Centaurus (24), pp. 97-109.