Ancient Maya documents concerning the movements of Mars

A large part of the pre-Columbian Maya book known as the Dresden Codex is concerned with an exploration of commensurate relationships among celestial cycles and their relationship to other, nonastronomical cycles of cultural interest. As has long been known, pages 43b–45b of the Codex are concerned with the synodic cycle of Mars. New work reported here with another part of the Codex, a complex table on pages 69–74, reveals a concern on the part of the ancient Maya astronomers with the sidereal motion of Mars as well as with its synodic cycle. Two kinds of empiric sidereal intervals of Mars were used, a long one (702 days) that included a retrograde loop and a short one that did not. The use of these intervals, which is indicated by the documents in the Dresden Codex, permitted the tracking of Mars across the zodiac and the relating of its movements to the terrestrial seasons and to the 260-day sacred calendar. While Kepler solved the sidereal problem of Mars by proposing an elliptical heliocentric orbit, anonymous but equally ingenious Maya astronomers discovered a pair of time cycles that not only accurately described the planet's motion, but also related it to other cosmic and terrestrial concerns.

Determination of the Hubble constant

Establishing accurate extragalactic distances has provided an immense challenge to astronomers since the 1920s. The situation has improved dramatically as better detectors have become available, and as several new, promising techniques have been developed. For the first time in the history of this difficult field, relative distances to galaxies are being compared on a case-by-case basis, and their quantitative agreement is being established. New instrumentation, the development of new techniques for measuring distances, and recent measurements with the Hubble Space telescope all have resulted in new distances to galaxies with precision at the ±5–20% level. The current statistical uncertainty in some methods for measuring H0 is now only a few percent; with systematic errors, the total uncertainty is approaching ±10%. Hence, the historical factor-of-two uncertainty in the value of the H0 is now behind us.