Sylvanus G. Morley reports that the Maya achieved a high degree of astronomical accuracy.
Sylvanus G. Morley, The Ancient Maya, 3rd ed. (Stanford, CA.: Stanford University Press, 1956), 257–58
ASTRONOMICAL OBSERVATORIES
It may be asked how the ancient Maya achieved such a high degree of astronomical accuracy without the instruments upon which modern astronomers depend. However, if the lines of sight are sufficiently long, accuracy to within less than a day’s error may be achieved in fixing the synodical or apparent revolution, as opposed to sidereal or true revolution, of many of the heavenly bodies. Maya temples are sufficiently high to obtain clear lines of sight from their summits to distant points on the horizon. A pair of crossed sticks was set up inside the temple on top of a pyramid. From this as a fixed observation point, the place where the sun, moon, or planets rose or set was noted with reference to natural feature on the horizon. When the heavenly body under observation rose or set behind this same point a second time, it had made one complete synodical revolution.
Although the three known Maya codices have no representations of observatories, pictures of them are found in the Mexican codices. Figure 30a shows an observatory from the Codex Bodley. In the doorway of a temple is a pair of crossed sticks, and looking out through them is the head of a man. In Figure 30b, also from the Codex Bodley, an eye appears in the notch made by a pair of crossed sticks in the temple doorway. Another picture in the Codex Bodley shows an eye between two crossed sticks, a star descending into a notch, and two observers (Fig. 30c); the projection at the left of the platform represents a pair of crossed human legs and a celestial eye. With such simple instruments as crossed sticks, the ancient Maya probably also predicted eclipses and the heliacal risings and settings of the Morning and Evening Stars.