Seeking the Sidereal: Observable Planetary Stations and the Ancient Maya Record

Lounsbury F. , “Maya numeration, computation, and calendrical astronomy”, in Dictionary of scientific biography , xv, 759–818; Justeson J. , “Ancient Maya ethnoastronomy: An overview of hieroglyphic sources”, in Aveni A. (ed.), World archaeoastronomy (Cambridge, 1989), 76–129; Milbrath S. , Star gods of the Maya (Austin, 1999); Aveni A. Skywatchers: A revised and updated version of Skywatchers of Ancient Mexico (Austin, 2001).

Lounsbury F. , “The base of the Venus Table in the Dresden Codex, and its significance for the calendar-correlation problem”, in Aveni A. Brotherston G. (eds), Calendars in Mesoamerica and Peru: Native American computations of time (BAR International Series, 174; Oxford, 1983), 1–26.

Bricker H. Bricker V. , “Classic Maya prediction of solar eclipses”, Current anthropology , xxiv (1983), 1–23.

Bricker V. Bricker H. , “The Mars Table in the Dresden Codex”, in Andrews E. W. (ed.), Research and reflections in archaeology and history: Essays in honor of Doris Stone (Tulane University Middle American Research Institute, Publ. 57; New Orleans, 1986), 51–80; Bricker H. Bricker V. , “More on the Mars Table in the Dresden Codex”, Latin American antiquity , viii (1997), 384–97.

Bricker V. Bricker H. , “The Seasonal Table in the Dresden Codex and related almanacs”, Archaeoastronomy , no. 12 (1988), S1–62.

Aveni A. Hartung H. , “Maya city planning and the calendar”, Transactions of the American Philosophical Society , lxxvi/7 (1986); Bricker H. Bricker V. , “Astronomical references in the Throne Inscription of the Palace of the Governor at Uxmal”, Cambridge archaeological journal , vi (1996), 191–229.

For example, Dütting D. Aveni A. Schramm M. , “The 2 Cib 14 Mol event in the inscriptions of Palenque, Chiapas, Mexico”, Zeitschrift für Ethnologie , cvii (1982), 233–58; Aveni A. , Conversing with the planets (New York, 1993); Schele L. Miller M. , The blood of kings (Fort Worth, 1986).

Aveni A. , “Is harmony at the heart of things?”, Wilson quarterly , Winter 2001, 54–65.

Cf. Milbrath , op. cit. (ref. 1), for a summary.

Bricker H. Bricker V. , “Zodiacal references in the Maya codices”, in Aveni A. (ed.), The sky in Mayan literature (Oxford, 1992), 148–83.

Bricker H. Bricker V. , op. cit. (ref. 6).

Milbrath , op. cit. (ref. 1), chap. 7.

See Aveni , Skywatchers (ref. 1), 87–91.

Bricker V. Bricker H. , “Astronomical references in the Water Tables on pages 69 to 74 of the Dresden Codex”, in Boone E. (ed.), Mesoamerican manuscript studies in honor of Mary Elizabeth Smith (Tulane University Middle American Research Institute, Publ. 69; New Orleans, in press [ms. 1998]).

For example, if Mars passed 0° longitude just before first stationary, it would pass a second time while in retrograde and a third time following second stationary. The two prograde passages would be separated by a very short period. How this period might be handled in discerning repeatable patterns of ESIs is discussed in ref. 19.

Stahlman E.g. W. Gingerich O. , Solar and planetary longitudes for years −2500 to +2000 by 10-day intervals (Madison, 1963), and Hinkley R. , BRES1M [a computer software package for historical research in astronomy] (Richmond, 1989).

Specifically, we found the 500-year pattern to be: 7-8. 7-7-8-7-8. 7-7-8-7-8.7-7-8. 7-7-8-7-8. 7-7-8-7-8. 7-7-8-7-8. 7….

Bricker H. Aveni A. Bricker V. , “Ancient Maya documents concerning the movements of Mars”, Proceedings of the National Academy of Sciences , xcviii (2001), 2107–10.

As during the very short period in question the planet does not travel all the way around the sky, one cannot consider this interval to be a sidereal period ( Bricker H. Aveni Bricker V. , op. cit. (ref. 18), 2107). We have chosen to include it with the next interval following it (both underlined) to form a LESI. The following examples are taken from the actual intervalic record: …695 542 285 419 709…: 285 + 419 = 704;. …705 136 548 706…: 136 + 548 = 684;. …702 549 140 705…: 140 + 552 = 692;. …706 130 548 705…: 130 + 548 = 678.

Bricker H. Aveni Bricker V. , op. cit. (ref. 18), 2108.

Though the sequences always consist of five long and three short ESIs, about every 2 ½ centuries one of the SESIs undergoes a slow increase at the expense of a slow decrease in an adjacent LESI over a half century, after which the two intervals, in effect, change places.

More precisely, if we define 5 LESI + 3 SESI as an empirical sidereal module M, then M = 2921.5^d = 5S + 1.9^d = 8E — 0.5⁵, where S = the synodic period of Venus and E = the length of the tropical year. Moreover, M = 13P + 0.4^d, where P = the heliocentric sidereal period of Venus. For a more detailed treatment of the commensurations among S, P and E for the planets, see Aveni , Skywatchers (ref. 1), 87–90 and Table 7.

In fact the pattern is quite erratic. Two sequences covered 94+ of the 500-year period: A 5–6 sequence, which occurred 18 times and a 5-6-6 sequence which occurred 11 times. The commensurations for the most common sequence are: 5S + L + 6S + L = 4748.4^d = 13E + 0.3^d. The planetary mean daily motion acquired from data in Stahlman Gingerich ( op. cit. (ref. 16)) by means of linear interpolation proved adequate, except for the case of Mercury which necessitated use of a more precise source ( Hinkley , op. cit. (ref. 16)).

The near equivalence of the LESIs of Mercury and Venus is an artifact of their direct (so to speak) link to the movement of the Sun along the ecliptic, Mercury never being more than 26° and Venus more than 46° distant in longitude from the Sun. They complete these periods in somewhat more than a year as a result of expending time in retrograde motion, thereby lengthening the mean daily motion. For the rare SESI, which lacks the retrograde loop, the mean daily motion for both planets is much higher and consequently each completes its cycle in less than a year.

Bricker V. Bricker H. , op. cit. (ref. 4); Bricker H. Bricker V. , op. cit. (ref. 4).

Bricker V. Bricker H. , op. cit. (ref. 5), S14.

Bricker V. Bricker H. , op. cit. (ref. 14); see also Bricker H. Aveni Bricker V. , op. cit. (ref. 18).

Bricker H. Aveni Bricker V. , op. cit. (ref. 18), 2109, Table 1.

See Aveni , Skywatchers (ref. 1), 89, Table 7.

11,681.4^d = 15S — 17.1^d. 17,172.2^d = 22S + 14.4^d. 28,853.6^d = 37S — 2.7^d. 11,681.4^d = 32E — 6.4^d. 17,172.2^d = 47E + 5.8^d. 28,853.6^d = 79E — 0.5^d.

We note that the 11,681.4 days contained in the pattern described above is equivalent to 20 mean synodic periods of Venus with an error of approximately three days (583.92^d × 20 = 11,678.40^d); the appearance of the glyph for Venus in the captions to the UWT offers strong presumptive evidence of a Maya concern with the relationship between the cycles of Venus and Mars, but as we have yet been unable to detect a patterned, cyclical relationship, this notation may have been only historical.