The Latitude and Epoch for the Formation of the Southern Greek Constellations

Rogers J. H. , “Origins of the ancient constellations”, Journal of the British Astronomical Association, cviii (1998), 9–27 and 79–89; Krupp E. C. , Beyond the blue horizon (Oxford, 1991), 124–48 and 205–40; Krupp E. C. , “Night gallery: The function, origin, and evolution of constellations”, Archaeoastronomy: The journal of astronomy in culture, xv (2000), 43–63.

Maunder E. W. , The astronomy of the Bible (London, 1909), 149–61; Maunder E. W. , “The origin of the constellations”, Observatory, xxxvi (1913), 329–34; Crommelin A. C. D. , “The ancient constellation figures”, in Splendour of the heavens (London, 1923), ed. by Phillips T. E. R. and Steavenson W. H. , 640–69; Lundmark K. , “Luminosities, colours, diameters, densities of stars”, in Handbuch der Astrophysik, v/1 (1932), 233; Ovenden M. W. , “The origin of the constellations”, Philosophical journal, iii/1 (1966), 1–18; Roy A. E. , “The origin of the constellations”. Vistas in astronomy, xxvii (1984), 171–97; Frank R. M. and Bengoa Arregi J. , “Hunting the European sky bears: On the origins of the non-zodiacal constellations”, Astronomy, cosmology and landscape, ed. by Ruggles C. L. N. , Prendergast F. and Ray T. (Bognor Regis, 2002), 15–43.

Evershed M. A. , “The origin of the constellations”, Observatory, xxxvi (1913), 179–81; Dicks D. R. , Early Greek astronomy to Aristotle (Ithaca, 1970), 160; Gingerich O. , The great Copernicus chase (Cambridge, 1992), 7–11; Gingerich O. and Welther B. , “Some puzzles of Ptolemy's star catalog”, Sky and telescope, lxvii (1984), 421–3; Krupp , op. cit. (ref. 1), 51–54. Evershed devotes a total of ten sentences to the void question, and her one point is that the southern edge of the constellations might be uncertain, as demonstrated by the change in the length of the River. Dicks gives only one sentence on the void problem, noting that the date estimates are highly unreliable due to the irregular shape of the void and that the southern constellation limits might change with time. Gingerich limits his critique to the one sentence, “While the ingenuity of Ovenden's argument is admirable, I do not find it compelling in the light of the evidence for a relatively recent zodiac and for a system that gradually evolved”. Gingerich and Welther point out that Lundmark's (op. cit., ref. 2) date of 4800 B.C. based on the stars in the Almagest has serious problems with defining the circle of invisibility and that they cannot reproduce Lundmark's date. Krupp gives an extensive review of five voidist papers, but restricts his criticism to a repetition of Dicks's arguments, and ends up concluding only that the true uncertainties are likely larger than advertised by the voidists.

Rogers , op. cit. (ref. 1), 79–83; Gurshtein A. A. , “On the origin of the zodiacal constellations”, Vistas in astronomy, xxxvi (1993), 171–90.

Ridpath E.g. I. , Star tales (New York, 1988); Ridpath I. , “The origin of constellations”. Mercury, xix/6 (1990), 163–71; Witze A. , “Science: Conjuring constellations”, Dallas Morning News, 17 June 1997, see http://almuhit.phys.uvic.ca/∼babul/AstroCourses/P303/Article.htm.

Ovenden, op. cit. (ref. 2).

These criticisms have been collected from the sources cited in ref. 3, discussion on the HASTRO-L listserve group, and from a manuscript in preparation by G. Thompson (titled “The constellation detectives: A history and critique of the use of the Aratean sphere for dating the constellations”). All these criticisms are entirely conceptual. The four technical criticisms in Sections 3.5 to 3.8 are original with myself.

Maunder, op. cit. (ref. 2); Ovenden, op. cit. (ref. 2).

Dicks, op. cit. (ref. 3), 160–3.

See the Appendix for five critical technical errors.

Roy, op. cit. (ref. 2).

Frank and Arregi, op. cit. (ref. 2) say about Roy's saga, “it doesn't have a shred of solid evidence to back it up: It's pure speculation” and “Yet, that theory itself is based more on wishful thinking than actual hard evidence”. Ridpath (“The origin of constellations” (ref. 5), 167) concludes: “So, for now, the theory that the Minoans were middlemen to our constellation system remains nothing more than an appealing idea”.

Quotes and direct references to Aratus are taken from his Phaenomena translated by Mair G. R. , The phaenomena of Aratus (Cambridge, Mass., 1921) as part of the Loeb Classical Series.

Hesiod and Homer also mention individual stars (Sirius, Arcturus) and star clusters (the Pleiades and the Hyades) that are named parts of a constellation. See Condos T. , Star myths of the Greeks and Romans: A sourcebook (Grand Rapids, Mi, 1997), 20–23.

Maunder , “Origin of the constellations” (ref. 2), 330.

Frank and Arregi, op. cit. (ref. 2).

Maunder , “Origin of the constellations” (ref. 2), 330–1.

Frank and Arregi, op. cit. (ref. 2), give a star map in their Figure 5 with about two dozen stars highlighted, and these might identify their key stars. No mention is made of these stars in the text or caption. However, these cannot be their key stars as six of them are inside (even up to ∼6° inside) a circle of radius ∼41° around the south pole of the epoch, in contradiction to their conclusion that the constellation makers could have lived as far north as 43°N.

Schaefer B. E. , “The latitude of the observer of the Almagest star catalogue”, Journal for the history of astronomy, xxxii (2001), 1–42; see also Schaefer B. E. , “Astronomy and the limits of vision”, Vistas in astronomy, xxxvi (1993), 311–62.

This corresponds to a sea level condition. Altitudes at all places in the Fertile Crescent are close enough to sea level that the extinction coefficient will change by only an amount negligible compared to other sources of day-to-day variations. Day-to-day variations in the extinction coefficient range from extremes of 0.17 mag/airmass to over 0.5 mag/airmass, with a median value of 0.27 mag/airmass in winter and 0.37 mag/airmass in summer. The constellation creators were unlikely to have ‘created’ on a hazy night, so the effective extinction at the time of creation is unlikely to be much worse than the median value. Nor are they going to have created based on key stars that are only rarely visible, so the effective extinction will not be much better than the median. In all, the most likely effective extinction is just the median for the site. However, the various limitations in Sections 3.3 and 3.4 force the derived latitudes to be northern limits, so it would be unwise to adopt the median extinction, since then an advocate of a more northerly latitude can always say the derived limit is violated by creators working under good skies. A wiser choice would be to select the best acceptable extinction, since then the derived northern limit could not reasonably be pushed any farther north. I will take the best acceptable extinction as the 10% level of the distribution, which is to say that the extinction is better than that value only 10% of the nights. It is already pushing it too far to think that the creators would select key stars that are only visible 10% of the time, so this limit is very conservative. My recent paper on the Almagest (ref. 20) has examined 27294 extinction observations from the eastern Mediterranean and the Middle East to find average 10% extinction values of 0.22 mag/airmass in winter, 0.25 mag/airmass near the equinoxes, and 0.27 mag/airmass in summer. Now a question arises as to whether to use seasonal extinctions. But the appropriate season for the creation of each constellation is not known. For example, the Altar culminates in dark skies from February mornings to July evenings around 500 B.C. and from January mornings to June evenings in 3000 B.C. This example spans the seasons, so we cannot really pick out the correct seasonal coefficient if we wanted to. For simplicity, I will adopt a uniform extinction coefficient of 0.25 mag/airmass for all seasons. In summer this will be a roughly 5% night, while in winter this will be roughly a 20% night. But in all cases, the adopted extinction will be a conservative limit.

Schaefer B. E. , “Refraction by Earth's atmosphere”, Sky and telescope, lxxvii (1989), 311–13; Schaefer B. E. and Liller W. , “Refraction near the horizon”, Publications of the Astronomical Society of the Pacific, cii (1990), 796–805; also see Schaefer , “Astronomy and the limits of vision” (ref. 20), 314–15.

Meeus J. , Astronomical algorithms (Richmond, Va, 1991), 126–8. A useful source as well as a check for these calculations are the precession tables of Hawkins G. S. , “Astro-archaeology”, Vistas in astronomy, x (1968), 45–88. Proper motion is so small as to be totally negligible in all cases.

This latitude will be 90° plus the star's declination plus the refraction angle minus the extinction angle. To give an example, a V = 1.0 mag star will have an extinction angle of 2.0° for an extinction coefficient of 0.25 mag/airmass, hence have a refraction of 0.3° for a total correction of 1.7° to the south. Further, if the star has a declination of −50° at some epoch, then the latitude limit will be −50° + 90° = 40°N for no atmosphere or −50° + 90° + 0.3° − 2.0° = 38.3°N with an atmosphere. As the key stars get fainter, the refraction correction to the north gets smaller while the extinction correction to the south rapidly gets larger. If there is some gap between the southern edge of the constellation and the north edge of the region of star invisibility, then this gap width must be subtracted from the derived latitude. In the above case, if there was a 3° gap between the southern edge of the constellation and the refracted extinction angle, then the latitude limit will be −50° + 90° + 0.3° − 2.0° − 3.0° = 35.3°N. The voidists have not made the correction for refraction, extinction, or the gap, and hence their latitudes are wrong by many degrees.

All information from the Catasterismi is taken from the translation in Condos, op. cit. (ref. 14).

Here and elsewhere in this paper, I will be using the term ‘Babylonians’ to refer to the single continuous cultural group centred near Babylon in the early first millennium B.C., despite there being a complex succession of empires of various names.

Maunder , “Origin of the constellations” (ref. 2), 330–1.

The one exception is the Southern Fish, which is one of the animals associated with the zodiac. But having such an association for only one of the six southern constellations is not helpful for knowing if all six were made together.

The basic collection of myths from many cultures is given by Gibbon W. M. , “Asiatic parallels in North American star lore: Ursa Major”, Journal of American folklore, lxxvii (1964), 236–50, and by Hagar S. , “The celestial bear”, Journal of American folklore, xiii (1900), 92–103. The idea that the bear is a very ancient constellation is briefly mentioned and supported in the astronomical literature by Gingerich , op. cit. (ref. 3), 10–11; Krupp , op. cit. (ref. 1), 239; and Gurshtein , op. cit. (ref. 4), 171.

Frank R. M. , “Hunting the European sky bears: Hercules meets Harzkume”, Astronomy and cultural diversity, ed. by Esteban C. and Belmonte J. A. (Tenerife, 2000), 295–302.

Frank cites the voidist analysis of Frank and Arregi, op. cit. (ref. 2), to support a date from 2500 to 4000 B.C., but this is really just an unimportant addition to the central thesis.

Wilk S. R. , Medusa: Solving the mystery of the Gorgon (Oxford, 2000).

The setting of the legend is specifically in Argos and Tiryns, while Hesiod mentions the Gorgons in his fragment known as “The Shield of Hercules”, and Gorgon heads appear in Greek architecture as early as the eighth century B.C. The claim by Herodotus that one of Perseus's sons became the eponymous founder of Persia has little relevance as being wishful etymology. The adoption of Perseus by Mithraicism is a later use of the constellation.

Rogers , op. cit. (ref. 1).

Ovenden , op. cit. (ref. 2); with an earlier short presentation and publication in Ovenden M. W. , “The origin of the constellations”, Journal of the British Astronomical Association, lxxi (1961), 91–96.

There will be an ambiguity since such an extension must intersect the pole's circular path at two locations. However, this ambiguity is easy to break since one of the alternatives yields a grossly unreasonable epoch. In this section, I have always chosen the alternative that is closest in time to 1500 B.C. This choice will spread out the derived epochs over a time interval somewhat longer than 13,000 years. The calculated results in Table 4 will not change for any other reasonable choice of a fiducial epoch. Ovenden, op. cit. (ref. 2), does not mention the ambiguity that I just mentioned, instead he discusses the further ambiguity that the indicated date could be any multiple of 26,000 years off in either direction. Ovenden wisely resolves this latter problem by assuming that no subtraction of such multiples is needed.

Roy , op. cit. (ref. 2), 181 himself claims to have found 2300 B.C.

Dicks , op. cit. (ref. 3), 161.

Press W. H. , Flannery B. P. , Teukolsky S. A. , and Vetterling W. T. , Numerical recipes (Cambridge, 1986), 472–5.

Ovenden is repeating the argument presented in Maunder , “Astronomy of the Bible” (ref. 2), 158–9.

This error was also pointed out in Frank and Arregi, op. cit. (ref. 2).

Part of a weak chain of evidence for this proposed change is that a star map drawn in the year 1801 is claimed to have otherwise-lost pre-Hipparchian details. Zero evidence is presented for this astounding claim. To make matters worse, this claim is internally inconsistent for Ovenden, because on this map the Southern Crown is represented to be in the position of the modern Corona Australis.

Roy , op. cit. (ref. 2), Fig. 6; Frank and Arregi, op. cit. (ref. 2), Figs 2 and 3.

Away from the edges of Ovenden's Figure 4, most stars brighter than V = 4.0 are depicted, although Ovenden is missing δ TrA (3.85 mag), η Ara (3.76 mag), ɛ Pav (3.96 mag), α Aps (3.83 mag), and ɛ Cru (3.59 mag). A few stars fainter than V = 4.0 are depicted, and these are always represented with the smallest sized dot.

Two of these four added stars are near the positions of substantially fainter stars, θ TrA and ζ TrA. However, at V = 5.52 and V = 4.91 respectively, these stars should not have been depicted in Ovenden's Figure 4, much less with the larger dots shown.