ASTR 1210 (O'Connell) Study Guide

5. ANCIENT ASTRONOMY

Maya pyramid El Castillo at Chichen Itza
(Catherwood, ca. 1844)

A. Motions of the Planets on the Sky

• The speed of the motions depends on the planet, decreasing from rapid to slow in the order: Mercury, Venus, Mars, Jupiter, Saturn.

• The general (average) motion of the planets against the star background is eastward in the sky.

• Mercury and Venus never move very far from the Sun (48 degrees in the case of Venus) and appear to move back and forth in front of/behind it.

• At least once per year, each of the planets halts its eastward motion and loops backward for a brief period before starting to move eastward again. This backward loop is called retrograde motion.

• The planets are confined to a relatively narrow band on the sky that is roughly centered on the ecliptic (the annual track of the Sun). The planets therefore are always to be found in the 12 Zodiacal constellations.

• The extreme north/south positions of the Sun, Moon, and planets differ from one another.
  • We now know that these differences are determined by the inclinations of their orbital planes to the celestial equator.

  • The Sun moves along the ecliptic, so its maximal N/S positions are 23.5 degrees from the equator, as described in Guide 04.

  • The Moon's orbit is inclined 5 degrees to the ecliptic, so its maximal N/S positions are 28.5 degrees from the equator. 5 degrees may sound small, but it is 10 times the angular diameter of the Moon.

  • The orbit of each planet has a different inclination with respect to the ecliptic. A planet's N/S extremes are affected both by its orbital inclination and its distance from the Earth.

B. Astronomical Measurements Without Instruments

• Heliacal risings: Helios is the Greek word for the Sun. Stars are said to exhibit "heliacal risings" if they rise in the east just before the Sun. This is a (rough) method of tracking the Sun's changing position with respect to the stars (recall that the Sun moves about 1 degree east every day against the stars). Hence it is a date-keeping method. For example, in ancient Egypt a heliacal rising of the brightest star, Sirius, was used to forecast the Nile's annual flood. The method can only be used for stars bright enough to be visible in the twilight sky.

• Horizon intercepts: The alignment of a rising/setting object with distinct features on the distant horizon as seen from a special location is called a "horizon intercept." This allows one to track the date using the N/S position of the setting/rising Sun against the horizon (more accurate than using heliacal risings). It also allows tracking of the motions of the Moon and planets. The horizon is a convenient reference plane for tracking celestial objects; it is harder to provide alignment devices that track objects when they are high in the sky.
  Note: accurate Earth-sky angular measurements of this kind require establishment of a reference direction. For instance, two fixed points yielding a well-defined fixed line toward the horizon is a reference against which to measure anglular positions of intercepts. The two points could both be natural (e.g. a nearby rock and a tree on the distant horizon) or they could both be artificial, as in ...

• Internal building alignments. Special designs, intended to assist in making astronomical measurements or to reflect a recurring important astronomical event (e.g. an equinox or solstice), have been found in many ancient buildings. Discovery and analysis of such features is an important aspect of a new research field: "Archaeo-Astronomy" (see ASTR 3410).
  Many ancient building alignments were intended to mark the rise or set (i.e. the horizon intercepts) of important astronomical objects as follows; the listed examples will be shown in class:
  • The Sun at the equinoxes (east-west alignment): e.g. the Egyptian pyramids

  • The Sun at a solstice (its extreme N/S positions; these are not east-west, but rather 23.5 degrees from the celestial equator): e.g. Stonehenge

  • The Moon at its N/S extremes (28.5 degrees from the celestial equator): e.g. Stonehenge

  • Bright stars

  • Planets at their N/S extremes: e.g. El Caracol (Maya)

C. Astronomical Records

Although pre-literate societies were able to transmit some scientific information via oral histories and recitation, they rarely progressed far in understanding the world. They had a faulty record of their own histories, let alone nature. Even crude methods of recording data provide enormous advantages. Paradoxically, low-tech stone records survive better than paper records.
The earliest extant astronomical records (Chinese) are over 4500 years old. The best astronomical records prior to the European Renaissance were developed by the Babylonians, Greeks, Chinese, and Maya. At right is a Babylonian almanac written in "cuneiform" script on a clay tablet. The surviving Maya records (see below) reveal sophisticated observational capabilities.

D. Maya Astronomy

The Maya flourished 250-900 AD in the area now belonging to Mexico, Guatemala, and Honduras. They built many elaborate cities, including large pyramidal and other public & ceremonial buildings. Maya societies had a harsh, militaristic character, and city-states frequently waged war on one another. The civilization suddenly disintegrated ca. 900 AD (disease? drought? political instability? invasion?), some 600 years before the Spanish Conquest. Not only did Maya society collapse, but most of their fabulous cities were abandoned and almost completely forgotten---becoming crumbled mounds swamped by jungle vegetation known only to local people. They were only rediscovered in the 1840's by American explorer John Stephens and popularized by the artwork of Frederick Catherwood (see his engraving at the top of this page). For other examples of Catherwood's work, click here. The Maya kept detailed written records, mainly of dynastic histories but also including astronomical texts. Regretably, most written documents were destroyed by the Spanish after the Conquest (1520 AD), and only a few "codices" survive (example pages are shown above and to the right). Fortunately, large amounts of carved material were undisturbed and are now being slowly translated. The records show a fascination--even an obsession--with astronomical time cycles. Maya astronomers made persistent, careful observations of the Sun, Moon, Venus, and other planets. They built an elaborate and complex calendar system, in which civic and religious ceremonies were tied to celestial cycles. The two major ritualistic cycles had lengths of 260 days and 52 years. In contrast to most calendars, the concept of a lunar month did not play a major role in this system. Astronomer "daykeepers" were needed to maintain the alignment of the sacred calendars with the real sky and to divine the meaning of changes in the sky. They consequently had high status in Maya society. Despite their remarkable architectual accomplishments, the Maya had only limited metalworking skills (primarily jewelry) and therefore lacked metal observational instruments. They presumably made most of their astronomical observations using wooden sighting devices and building or horizon alignments. Interestingly, they never invented the wheel. The Maya apparently lived in deep fear of eclipses and the planet Venus (even though they had enough data to realize that the Moon and Venus moved in strictly predictable ways). A preoccupation with Venus would be natural for an observationally-skilled culture because it is, by far, the brightest starlike object in the sky and exhibits very complex motions by virtue of its proximity to Earth. Viewed from Earth, Venus has a 584 day (19 month) cycle of "configurations" with respect to Sun; the Sun and Venus have a 2922 day (8 year) cycle with respect to the bright stars. The cycle features complicated motions of Venus with respect to the Earth's horizon and other astronomical objects and large changes in the Venusian brightness. (We will show simulations in class.)

Chichen Itza Today     Astronomical Tables in the Dresden Codex

• Venus was believed to be a malevolent god, whose demands for blood sacrifice at critical times led to ritual murder by the Maya of both captives and their own citizens, including children. The Maya assiduously tracked Venus to forecast the god's intent toward themselves. But there is no evidence they understood the physical nature of Venus or the origin of the celestial motions, which they attributed entirely to supernatural volition.

The Long Count and the End of the World

The Maya believed in a recurring cosmic cycle of birth and destruction in which the gods struggled to nurture a fruitful human species. Three cycles, each ending in catastrophe for the world, were thought to have preceded the current, fourth, cycle. Time within a cycle was tracked by the Long Count, in which each day was assigned a unique number. Counts were expressed in a modified base-20 system, the longest unit of which was the baktun. A baktun is 20x18x20x20 = 144,000 days or 394 solar years long. Some Maya documents suggest that a cosmic creation cycle would end in worldwide disaster after exactly 13 baktuns, or 5125 years. By cross-correlating with unique astronomical events and historical dates after the Spanish conquest, archaeologists were able to convert Long Count dates to those in the Julian (Western) calendar. The starting date of the current cycle (and the end of the previous one) was determined to be 11 August 3114 BC. But that implies that the end of the fourth cycle occurred on 21 December 2012!
You can find much speculation on the Internet about the meaning of the cycle turnover in 2012, including irresponsible predictions of a Doomsday. Obviously, given the absence of a catastrophe at the predicted time, the predictions were nonsense; the doomsday hucksters have since retreated into silence to count their money.
Remember that for all their skill in tracking the planets, the Maya world view was riddled with superstition, and they showed no insight regarding the true physical nature of the universe or even the size and shape of the Earth. Their writings were vague and contradictory concerning the cosmic cycles, and some inscriptions anticipate eras as much as 20²⁰ years in an inconceivably distant future. Finally, as is obvious from the historical record, there was no worldwide cataclysm in 3114 BC, at the end of the last 13 baktun cycle. Same with 2012, and we have now started the first baktun of a new cycle.

• A montage of photographs of the lunar phases is shown above right. Click for an enlargement.

• Other than the apparent daily and annual motions of the Sun, the lunar phases are the most dramatic of the cycles visible in the sky. They were especially important before the invention of artificial lighting, because they determined people's ability to move around at night.

• The key clue is that the phase of the Moon correlates directly with its angular distance from the Sun. See this drawing, which shows the phases and location of the Moon at sunset during the first two weeks of a lunar cycle. The Sun is always at the western horizon at the times shown.

• The Greeks, having invented solid geometry, realized that this behavior implies that the Moon is a sphere, half of which is always illuminated by the Sun. It is not self luminous and shines only by reflected light.

• The fraction of the sunlit hemisphere which we can see from Earth determines the lunar phase. We see a "full", "crescent", or dark ("new") Moon depending on the angle between the Sun and Moon as viewed from Earth. See the illustration below. (The Moon moves counterclockwise in its orbit in the diagram.) The Moon repeats its phases after a period of 29.5 days.

• As in the case of the planets (see A above), the apparent motions on the sky of the Moon are a composite of its intrinsic motions in its orbit and the motion of our observing platform, the Earth.

• The Moon is the only known natural satellite of Earth, moving in a modestly elliptical orbit with an average radius of 238,000 miles (384,000 km). Its sidereal orbital period with respect to the "fixed" stars is 27.3 days. It moves eastward in its orbit as viewed from Earth, about 13 degrees per day (changing rise/set times by ~50 minutes/day). The lunar orbit is tilted slightly (5 degrees) out of the ecliptic plane.

• Because Earth moves in its own orbit around the Sun, the Moon does not return to the same position with respect to the Sun as seen from Earth (e.g. 180 degrees away from Sun) for 29.5 days, 2 days longer than its sidereal period. This is called its synodic period, and the phases repeat after one synodic period. The situation is shown here. The 29.5 day cycle of phases roughly defines our calendrical "month."

• This time lapse movie (472K) composed of still photographs of the Moon during a 29.5 day cycle vividly illustrates the relationship between shadowing and phases. The changes in the apparent size of the Moon and the slight "rocking" motion (known as libration) are caused by the fact that the lunar orbit is non-circular in shape.

• In a more subtle background cycle, the orientation of the Moon's orbit with respect to the ecliptic changes over an 18.6 year period, which affects the timing of eclipses (see below).

• There is good evidence that the people who built Stonehenge (ca. 2500 BC) had made measures of the Moon's position throughout the 18.6 yr orbital cycle. See the supplement page Eclipses and Stonehenge for details.

F. Polar Precession

• The gravity of the Moon & Sun act on the "bulge" at Earth's equator. This produces a cyclical change in the direction on the celestial sphere toward which the Earth's pole points. It is very slow: a 26,000 yr cycle corresponding to only a 0.5 degree shift in stellar positions per century. Though subtle, precession was first detected in 150 BC by the Greek astronomer Hipparchos through comparison of measured star positions over several centuries.
  

  
  

• Though Polaris is near the N. pole now, it will not be in a few 1000 years. Click here for an animation of the pole's position on the sky at different dates. [Note: the point marked "zenith" in this animation is not the zenith but the north celestial pole.]

G. Eclipses

• A lunar eclipse occurs when the shadow of the Earth strikes the Moon

• A solar eclipse occurs when the shadow of the Moon strikes the Earth. In the right circumstances, the Moon just covers the Sun's face as seen from Earth, leading to a (short-lived) total eclipse.

• The geometry of a lunar eclipse is illustrated in the following diagram:
  
  Lunar Eclipse Geometry

• A lunar eclipse can only occur near Full Moon, and

• A solar eclipse can only occur near New Moon

Bennett textbook: Ch. 2.3 (lunar phases, eclipses), 3.1 (ancient astronomy)
Study Guide 5
The Aztec Calendar Stone
Optional reading: Eclipses and Stonehenge
Optional reference on Maya astronomy: Skywatchers of Ancient Mexico by Anthony F. Aveni (Univ. of Texas Press, 1980/97).
FLIP ALERT! On Wednesday, 6 February, we will do a quasi-"flip" on the material in this Study Guide concerning lunar phases, precession, and eclipses. I.e. Sections E, F, and G of the Guide together with the related reading in the textbook, Section 2.3. I won't lecture on this material, but there will be SEVERAL PUZZLAHS on it, with discussion if necessary.

Bennett textbook: Ch. 3.2
Study Guide 6
Optional references: Bertrand Russell, A History of Western Philosophy; Arthur Koestler, The Sleepwalkers; Timothy Ferris, Coming of Age in the Milky Way; J. L. E. Dreyer, A History of Astronomy from Thales to Kepler.

Introduction to Archaeoastronomy (UMd)
Astronomy of the Egyptian Great Pyramid
Lunar Phase Now
Eclipses and Stonehenge (O'Connell)
Maya Civilization & Astronomy:
MesoWeb (good general site)
MesoAmerica Photos & Articles (Jacobs)
Photos of Maya Cities (McKenzie)
Teotihuacan: City of the Gods
Introduction to Maya Astronomy
The Maya Calendar (from "Tales of the Maya Skies," Chabot Science Center)
Brief notes on the Maya calendar and on ancient structures in the Americas
(Chevalier, UVA Astr 3410)
Astronomical Contents of the Dresden Codex (Boehm)
The Maya Calendar (Meyer)
El Caracol, A Maya Observatory
The Aztec Calendar Stone (O'Connell)
"The Great 2012 Doomsday Scare" (E. C. Krupp)
Debunking the "2012 Doomsday". A site injecting science and common sense into the
overheated Internet rhetoric about the end of the world on 12/21/2012.
Maya Culture on the big screen: Mel Gibson's Apocalypto
Trailer
Wikipedia entry (summary, sources, criticism)

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Last modified February 2013 by rwo

Text copyright © 1998-2013 Robert W. O'Connell. All rights reserved. Precession and lunar phase diagrams by Nick Strobel. Precession animation by Scott R. Anderson. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1210 at the University of Virginia.