The Astronomical Events of the Parapegma of the Antikythera Mechanism

Freeth T. Bitsakis Y. Moussas X. Seiradakis J. H. Tselikas A. Mangou H. Zafeiropoulou M. Hadland R. Bate D. Ramsey A. Allen M. Crawley A. Hockley P. Malzbender T. Gelb D. Ambrisco W. Edmunds M. G. , “Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism”, Nature , cdxliv (2006), 587–91. For this paper there is substantial “Supplementary information” available at http://www.nature.com/nature/journal/v444/n7119/suppinfo/nature05357.html. Also: Wright M. T. , “The Antikythera Mechanism reconsidered”, Interdisciplinary science reviews, xxxii/1 (2007), 27–43.

Freeth T. Jones A. Steele J. M. Bitsakis Y. , “Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism”, Nature , cdliv (2008), 614–17. For this paper there is substantial “Supplementary information” available at http://www.nature.com/nature/journal/v454/n7204/suppinfo/nature07130.html. Also: Evans J. Carman C. C. Thorndike A. S. , “Solar anomaly and planetary displays in the Antikythera Mechanism”, Journal for the history of astronomy, xli (2010), 1–39; and M. T. Wright private communication.

de Solla Price D. , “Gears from the Greeks: The Antikythera Mechanism — A calendar computer from ca. 80 B.C.”, Transactions of the American philosophical Society, n.s., lxiv/7 (1974) (reprinted New York, 1975).

C1-b is part of the front plate which has been broken, detached and stuck inverted on side 1 (ref. 1) of Fragment C.

Price was the first to link the letters of the alphabet inscribed in order along the zodiac dial with the letters at the beginning of the lines of the parapegma text. See Price , “Gears” (ref. 3), 18.

Lehoux D. , Astronomy, weather, and calendars in the ancient world: Parapegmata and related texts in classical and Near Eastern societies (New York, 2007).

Price , “Gears” (ref. 3), 49.

This observation was also publicly announced by Freeth T. Anastasiou M. in their oral presentations in the XXIII ICHST (International Congress of History of Science and Technology) Ideas and Instruments in Social Context, 28 July — 2 August 2009, Budapest, Hungary.

Evans J. , The history and practice of ancient astronomy (New York, 1998), 191.

Schoch C. , “The ‘arcus visionis’ of the planets in the Babylonian observations”, Monthly notices of the Royal Astronomical Society , lxxxiv (1924), 731–4; Schaefer B. E. , “Predicting heliacal risings and settings”, Sky and telescope, lxx (1985), 261–3; Schaefer B. E. , “Heliacal rise phenomena”, Archaeoastronomy, xi (1987), 19–33; Schaefer B. E. , “Astronomy and the limits of vision”, Vistas in astronomy, xxxvi (1993), 311–61; Robinson M. , “Ardua et astra: On the calculation of the dates of the rising and setting of stars”, Classical philology, civ (2009), 354–75; Alcyone software (Lange, R.), available at http://www.alcyone.de/.

Nawar S. , “Sky twilight brightness and colour during high solar activity”, The Moon and the planets, xxix (1983), 99–105.

Koomen M. J. Lock C. Packer D. M. Scolnik R. Tousey R. Hulburt E. O. , “Measurements of the brightness of the twilight sky”, Journal of the Optical Society of America, xlii (1952), 353–6.

Freeth , “Decoding” (ref. 1), 587.

Duffett-Smith P. , Astronomy with your personal computer (New York, 1990).

Ptolemy , Almagest VII, 5; Toomer G. J. , Ptolemy's Almagest (London, 1984).

The total apparent magnitude of the Pleiades was calculated by finding the brightness of each of the ten stars from its apparent magnitude m and by adding these values of brightness. From the total brightness value, the total apparent magnitude of Pleiades was calculated. The mean equatorial coordinates of the Pleiades, thus the mean right ascension α and the mean declination δ, were calculated correspondingly as a mean value of the ten right ascension values of the ten stars, α, and as a mean value of the ten declination values of the ten stars, δ.

The autumn equinox taking place when “Libra begins to rise” was first publicly reported by T. Freeth in his oral presentation in Budapest “The parapegma of the Antikythera Mechanism” (ref. 8). The presentation was reflecting work by A. Jones, T. Freeth and Y. Bitsakis, work which is currently in preparation. In this work, the plate C1-b was adjusted to other fragments of the Mechanism and the lines of the zodiac statement and the autumn equinox were reconstructed revealing that the two events take place at the first degree of the zodiac sign of Libra. The presence of lines in the parapegma referring to equinoxes and solstices remained unknown until then.

Evans J. Berggren J. L. , Geminos's Introduction to the Phenomena (Princeton, 2006), 231–40.

Meton is said by a scholiast to Aristophanes to have observed on the Pnyx, a small hill in Athens. See Toomer G. J. , “Meton”, Complete dictionary of scientific biography , ix (Detroit, 2008), 337–40. Theophrastus (De signis I, 4) says that matters (“signs” to be understood) concerning the solstices were observed by Matriketas at Methymna from Mount Lepetymnos, by Cleostratus in Tenedos from Mount Ida, and by Phaeinos at Athens from Mount Lycabettos. See Sider David Brunschön Wolfram Carl , Theophrastus of Eresus On Weather Signs (Leiden and Boston, 2007), 60–3.

Price , “Gears” (ref. 3), 13. and Freeth , “Calendars” (ref. 2), 614.

Freeth , “Calendars” (ref. 2), Supplementary Information, p. 17.

Tousey R. Koomen M. J. , “The visibility of stars and planets during twilight”, Journal of the Optical Society of America , xliii (1953), 177–83 (Tables I and Fig. 1, p. 177).

Blackwell H. R. , “Contrast thresholds of the human eye”, Journal of the Optical Society of America, xxxvi (1946), 630.

For an explanatory and very thorough analysis of the true and visible events, how they are related, their annual cycle, as well as the understanding of this cycle already at the time of Autolycus of Pitane (320 b.c.), see Evans , op. cit. (ref. 9), 190–7.

For the Greek text of Ptolemy's Phaseis see Heiberg J. L. , (ed.), Claudii Ptolemaei Opera quae exstant omnia, ii: Opera astronomica minora (Leipzig, 1907), 1–67. Jones A. , “Provisional translation of Ptolemy's phaseis“is available at http://www.classicalastrologer.com/Phaseis.pdf.

The geographic latitude where the longest day has a length of 14 hours was calculated using the equation: Cos H _δ = — Tan φ tan δ, where H _δ is the hour angle of the Sun at sunset and δ its declination on the longest day. For 14 hours day length, H _δ = 7h and for the longest day δ is equal to the obliquity of the ecliptic ε. For a.d. 130, ε was calculated using the equation provided by the Astronomical Almanac for the Year 2012:

ε = 84381″.406–46″.836769 · T — 0″.0001831 · T² + 0″.00200340 · T³ — 0″.576 · 10⁻⁶ · T⁴ − 4″.34 · 10⁻⁸ · T⁵ = 85244″.1177 = 23°.67892.

where T is the time in Julian centuries since the ephemeris epoch of 2000. The day length of 14 hours was found to correspond to φ = 30.55°N = 30° 33′N.

The events missing are: The α Leonis (Regulus) mr, the α Tauri (Aldebaran) ms, the α Virginis (Spica) mr and er, the β Aurigae mr, the α Cygni (Deneb) mr, the β Geminorum (Pollux) mr, the α Librae mr and er and the α Scorpii (Antares) ms.

Koomen , “Measurements” (ref. 12). Nawar, “Sky” (ref. 11).

That θ Eridani should be problematical is perhaps not surprising. This star is characterized by anomalously large errors in longitude in both Ptolemy's star catalogue in the Almagest and in Hipparchus's Commentary on the phenomena of Eudoxus and Aratus. See Grasshoff Gerd , The history of Ptolemy's star catalogue (New York, 1990), 97, 215–16.

Heiberg , Claudii (ref. 25).

The entries for which there is conflict between the two principal manuscripts are: The α Aurigae (Capella) mr, the α Lyrae (Vega) er, the α Boötis (Arcturus) mr, ms and er, the β Leonis (Denebola) ms, er and es, the α Tauri (Aldebaran) mr and es, the α Orionis (Betelgeuse) mr, ms, er and es, the β Orionis (Rigel) mr, er and es, the α Canis Majoris (Sirius) es, the α Piscis Austrini (Fomalhaut) mr, ms, er and es, the θ Eridani (Acamar) mr, the α Carinae (Canopus) mr, er and es, the α Centauri (Rigil Kent) mr and er, the α Persei (Mirfak) mr, er and es, the β Aurigae (Menkalinan) es, the α Cygni (Deneb) er, the α Coronae Borealis (Alphecca) mr, the α Geminorum (Castror) mr and ms, the β Geminorum (Pollux) ms and es, the α Andromedae (Alpheratz) mr and es, the γ Orionis (Bellatrix) mr, er and es, the α Hydrae (Alphard) mr, ms and es, the β Librae (Zubeneschamali) mr and ms, the ε Orionis (Alnilam) mr and es, the α Librae (Zubenelgenubi) ms, the α Scorpii (Antares) er and es and the α Sagittarii (Alrami) ms.

Nawar , “Sky” (ref. 11), Tables I(a) and I(b), p. 101. Nawar works in terms of S10 units. For the conversion of S10 to candle/foot², see Nawar S. , “Solar activity and atmospheric attenuation effects on the visibility of stars and planets during twilight”, Moon and the planets, xxix (1983), 107–16.

Koomen , “Measurements” (ref. 12), Tables I and II, p. 354.

Tousey Koomen , “The visibility” (ref. 22).

Nawar , “Sky” (ref. 11).

Schaefer , “Astronomy” (ref. 10), 314. The same formula is reported by Meeus J. , Astronomical algorithms (Richmond, 1998), 106.

Schaefer , “Astronomy” (ref. 10), 315.

Schaefer , “Predicting” (ref. 10), 261.

Schaefer , “Astronomy” (ref. 10), 315–19.

Schaefer , “Astronomy” (ref. 10), 317.

Freeth , “Calendars” (ref. 2), 616.

Ptolemy , Almagest VII–VIII; Toomer , Ptolemy's Almagest (ref. 15).

Evans Berggren , Geminos's Introduction (ref. 18).

Koomen , “Measurements” (ref. 12).

Nawar , “Sky” (ref. 11).

Ptolemy , Phaseis (ref. 25), II, 67.