Maya Observations of Very Long Periods of Venus

Teeple John E. , “Maya astronomy”, Contributions to American archaeology , i, no. 2 (Carnegie Institution of Washington, Washington, D.C., 1930), 29–116, esp. pp. 94–98; Thompson J. E. S. , A commentary on the Dresden Codex (Memoirs of the American Philosophical Society, xciii; Philadelphia, 1972); “Maya astronomy”, Philosophical transactions of the Royal Society of London , A cclxxvi (1974), 83–98; Lounsbury Floyd G. , “Maya numeration, computation and calendrical astronomy” in Dictionary of scientific biography, ed. by Gillispie C. C. , xv (New York, 1978), 759–818.

Aveni Anthony F. Gibbs Sharon L. and Hartung Horst , “The Caracol Tower of Chichen Itza: An ancient astronomical observatory?”, Science, clxxxviii (1975), 977–85.

Gibbs Sharon L. , “Mesoamerican calendrics as evidence of astronomical activity”, in Native American astronomy, ed. by Aveni A. F. (Austin, Texas, 1977), 31–35.

Aaboe Asger , “Scientific astronomy in Antiquity”, Philosophical transactions of the Royal Society of London, A cclxxvi (1974), 21–42.

Teeple , “Maya astronomy”, 96.

Lounsbury , “Maya numeration, computation and calendrical astronomy”, 788–9.

Thompson , “Maya astronomy”, 87; but cf. his earlier Commentary, 64, where he describes it only as an “ideal correction”.

Calculations of various periods are based on angular velocities obtained by taking derivatives of Newcomb's expressions for the mean longitude of the Sun and Venus, relative to equinox of date, given in the Explanatory supplement to the astronomical ephemeris … (London, 1961), 98 and 113. Periods relative to the sidereal reference-frame use velocities corrected by Newcomb's expression for the rate of precession in longitude, ibid., 169.

Among the approximations to the Venus Synodic Period based on integral numbers of 260-day Sacred Almanacs, with their errors, are: 301 vsp / 676 sa / 175,760 days, −0.33d; 362 vsp / 813 sa / 211,380 days, +0.46d; 61 vsp / 137 sa / 35,620 days, +0.80d; 240 vsp / 539 sa / 140,140 days, −1.13d; 122 vsp / 274 sa / 71,240 days, +1.59d.

The exact value varies from 91,478 days/156.66 vsp / 250.46 years in a.d. 500 to 91,496 days/156.69 vsp / 250.51 years in a.d. 1500. The slow drift of Venus's heliacal risings through the year and along the ecliptic is described in pp. 31–33 of Severin Gregory M. , “The Paris Codex: Decoding an astronomical ephemeris”, Transactions of the American Philosophical Society, lxxi, no. 5 (1981). Severin does not, however, go on to consider the length of this period or the periodic changes in the azimuth of heliacal rising that it implies.

The choice of 317, rather than the more precise 313, for the approximation provides an obvious challenge to this hypothesis. Two possible explanations are suggested. Although 313 is closer than 317 to 313.36, the Venus phenomena of the 317th period occur nearer in the year to the phenomena of the 314th period than do those of the 313th period. This ritual/astrological factor may have been important. A numerological/practical constraint may also have operated: Given the Maya preference for elegant numerical coefficients, note that 313 vsp is 703 × 260 and the decomposition into prime factors of 703 gives 19 × 37, while 317 vsp is 712 × 260 and 712 equals 2⁵ × 3 × 7. In either event, it appears that precision was not the primary concern of the Maya.

The great sidereal period is almost constant, varying by only one day from 87,266 days/149.45 vsp / 238.93 tropical years in a.d. 500 to 87,265 days/149.45 vsp / 238.92 tropical years in a.d. 1500.

Lounsbury Floyd G. . “Some problems in the interpretation of the Mythological Portion of the Hieroglyphic Text of the Temple of the Cross at Palenque” in Robertson Merle G. (ed.), Proceedings of the Tercera Mesa Redonda de Palenque, v (Austin, Texas, 1980), 99–115; I would like to thank Dr Lounsbury for bringing this paper to my attention. Closs Michael P. , “Venus in the Maya world: Glyphs, gods and associated astronomical phenomena”, in Robertson Merle G. (ed.), Proceedings of the Tercera Mesa Redonda de Palenque, iv (Palenque, Chiapas, Mexico, [n.d.]), 147–65; see esp. p. 151.

These errors reflect extrapolations implying Maya knowledge of the Great Tropical Revolution with an accuracy of one part in two thousand.

Lounsbury , “Maya numeration, computation, and calendrical astronomy”, 808; Mathews Peter and Schele Linda , “Lords of Palenque—the glyphic evidence”, in Robertson Merle G. (ed.), Proceedings of the Primera Mesa Redonda de Palenque, Part I (Pebble Beach, Calif., 1974).

The discrepancy between the Palenque intervals and modern calculations may stem from limitations in our understanding of the astronomical phenomena corresponding to specific events in a particular god's life or from the numerological constraints that limited the Maya's choice of intervals. On numerology at Palenque see Lounsbury F. G. , “A rationale for the initial date of the Temple of the Cross at Palenque”, in Robertson Merle G. (ed.), The Art Iconography and Dynastic History of Palenque, Proceedings of the Segunda Mesa Redonda de Palenque (Pebble Beach, Calif., 1976), 211–24.

All three sets of data that I examined, from the Codex Dresden, from Palenque, and from a group of inscriptions at Bonampak, contained this Great Venus Period. The Bonampak data came from newly transcribed inscriptions mentioned by Floyd G. Lounsbury, “Astronomical knowledge and its uses at Bonampak, Mexico”, paper presented at the iau/iuhps Archaeoastronomy Symposium, Queen's College, Oxford, 4–9 September 1981. The relevant dates were omitted from the published version of Lounsbury's paper, so discussion of the Bonampak results must await publication of these inscriptions.

Freeman P. R. and Elmore W. . “A test for the significance of astronomical alignments,” Archaeoastronomy , no. 1 (JHA, x (1979)), S86–96. Preliminary results of such an analysis using 406 intervals at Palenque were presented before the Historical Astronomy Division of the American Astronomical Society, Boston, January 1983.