Thirty Meter Telescope

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Thirty Meter Telescope

Artist's rendering of proposed telescope
Alternative names	California Extremely Large Telescope
Location(s)	(proposed) Mauna Kea Observatory in Hawaii, United States
Coordinates	19.8327°N 155.4816°WCoordinates: 19.8327°N 155.4816°W
Organization	TMT International Observatory
Altitude	4,050 m or 13,290 ft
Wavelength	Near UV, visible, and Mid-IR (0.31–28 μm)
Built	mid-2020
First light	est. 2027
Telescope style	Segmented Ritchey–Chrétien telescope
Diameter	30 m or 98 ft
Secondary diameter	3.1 m or 10 ft
Tertiary diameter	2.5 m × 3.5 m or 8.2 ft × 11.5 ft
Collecting area	655 m2 or 7,050 sq ft
Focal length	f/15 (450 m)
Mounting	Altazimuth mount
Enclosure	Spherical calotte
Website	TMT.org
Location of Thirty Meter Telescope

The Thirty Meter Telescope (TMT) is a proposed astronomical observatory with an extremely large telescope (ELT) that has become the source of controversy over its planned location on Mauna Kea on the island of Hawaii in the US state of Hawaii. Construction of the TMT on land which is sacred to Native Hawaiian culture and religion attracted press coverage after October 2014, when construction was temporarily halted due to protests. While construction of the telescope was set to resume on April 2 and later on June 24, 2015, it was blocked by further protests each time. The Board of Land and Natural Resources approved the TMT project, but the Supreme Court of Hawaii invalidated the building permits in December 2015, ruling that the board had not followed due process. On October 30, 2018, the Court approved the resumption of construction. The TMT would become the last area on Mauna Kea on which any telescope will ever be built.

Scientists have been considering ELTs since the mid 1980s. In 2000, astronomers considered the possibility of a telescope with a light-gathering mirror larger than 20 meters in diameter. The technology to build a mirror larger than 8.4 meters does not exist; instead scientists considered using either small segments that create one large mirror, or a grouping of larger 8-meter mirrors working as one unit. The US National Academy of Sciences recommended a 30-meter telescope be the focus of U.S. interests, seeking to see it built within the decade. Scientists at the University of California and Caltech began development of a design that would eventually become the TMT, consisting of 492 segmented mirrors with nine times the power of the Keck telescope. Due to its immense light-gathering power and the optimal observing conditions which exist atop Mauna Kea, the TMT would enable astronomers to conduct research which is infeasible with current instruments. The TMT is designed for near-ultraviolet to mid-infrared (0.31 to 28 μm wavelengths) observations, featuring adaptive optics to assist in correcting image blur. The TMT will be at the highest altitude of all the proposed ELTs. The telescope has government-level support from several nations.

Background

In 2000, astronomers began considering the potential of telescopes larger than 20 meters in diameter. Two technologies were considered; segmented mirrors like that of the Keck Observatory and the use of a group of 8-meter mirrors mounted to form a single unit. The US National Academy of Sciences made a suggestion that a 30-meter telescope should be the focus of US astronomy interests and recommended it to be built within the decade. The University of California, along with Caltech began development of a 30-meter telescope that same year. The California Extremely Large Telescope (CELT) began development along with the Giant Magellan Telescope, the Giant Segmented Mirror Telescope (GSMT) and the Very Large Optical Telescope (VLOT). These studies would eventually become the Thirty Meter Telescope. The TMT would have nine times the collecting area of the older Keck telescope using slightly smaller mirror segments in a vastly larger group. Another telescope of a large diameter in the works is the European Extremely Large Telescope (E-ELT) being built in northern Chile.

The telescope is designed for observations from near-ultraviolet to mid-infrared (0.31 to 28 μm wavelengths). In addition, its adaptive optics system will help correct for image blur caused by the atmosphere of the Earth, helping it to reach the potential of such a large mirror. Among existing and planned ELTs, the TMT will have the highest altitude and will be the second-largest telescope once the E-ELT is built. Both use segments of small 1.44 m hexagonal mirrors—a design vastly different from the large mirrors of the Large Binocular Telescope (LBT) or the Giant Magellan Telescope (GMT). The TMT has government-level support from the following countries: Canada, China, Japan and India. The United States is also contributing some funding, but less than the formal partnership.

Proposed locations

In cooperation with AURA, the TMT project completed a multi-year evaluation of five sites:

• Roque de los Muchachos Observatory, La Palma, Canary Islands, Spain
• Cerro Armazones, Antofagasta Region, Republic of Chile
• Cerro Tolanchar, Antofagasta Region, Republic of Chile
• Cerro Tolar, Antofagasta Region, Republic of Chile
• Mauna Kea, Hawaii, United States (This site was chosen and approval granted in April 2013)
• San Pedro Mártir, Baja California, Mexico
• Hanle, Jammu and Kashmir, India

The TMT Observatory Corporation board of directors narrowed the list to two sites, one in each hemisphere, for further consideration: Cerro Armazones in Chile's Atacama Desert, and Mauna Kea on Hawaii Island. On July 21, 2009 the TMT board announced Mauna Kea as the preferred site. The final TMT site selection decision was based on a combination of scientific, financial, and political criteria. Chile is also where the European Southern Observatory is building the E-ELT. If both next-generation telescopes were in the same hemisphere, there would be many astronomical objects that neither could observe. The telescope was given approval by the state Board of Land and Natural Resources in April 2013. There has been opposition to the building of the telescope, based on potential disruption to the fragile alpine environment of Mauna Kea due to construction, traffic and noise, which is a concern for the habitat of several species, and that Mauna Kea is a sacred site for the Native Hawaiian culture. The Hawaii Board of Land and Natural Resources conditionally approved the Mauna Kea site for the TMT in February 2011. The approval has been challenged; however, the Board officially approved the site following a hearing on February 12, 2013.

Partnerships and funding

The Gordon and Betty Moore Foundation has committed US$200 million for construction. Caltech and the University of California have committed an additional US$50 million each. Japan, which has its own large telescope at Mauna Kea, the 8.3-metre Subaru, is also a partner.

In 2008, the National Astronomical Observatory of Japan (NAOJ) joined TMT as a Collaborating Institution. The following year, the telescope cost was estimated to be $970 million to $1.4 billion. That same year, the National Astronomical Observatories of the Chinese Academy of Sciences (NAOC) joined TMT as an Observer.

In 2010, a consortium of Indian Astronomy Research Institutes (IIA, IUCAA and ARIES) joined TMT project as an observer. The observer status is the first step in becoming a full partner in the construction of the TMT and participating in the engineering development and scientific use of the observatory (Subject to approval of funding from Indian Government). Two years later, India and China became partners with representatives on the TMT board. Both countries agreed to share the telescope construction costs, expected to top $1 billion.

The continued financial commitment from the Canadian government had been in doubt due to economic pressures. Nevertheless, on April 6, 2015, Prime Minister Stephen Harper announced that Canada would commit $243.5 million over a period of 10 years. The structure will be built by Dynamic Structures Ltd. in British Columbia, and then shipped to Mauna Kea.

Approval process

In 2008, the TMT corporation selected two semi-finalists for further study, Mauna Kea and Cerro Amazones. In July 2009, Mauna Kea was selected. Once TMT selected Mauna Kea, the project began a regulatory and community process for approval. Mauna Kea is ranked as one of the best sites on Earth for telescope viewing and is home to 13 other telescopes built at the summit of the mountain, within the Mauna Kea Observatories grounds. Telescopes generate money for the big island, with millions of dollars in jobs and subsidies gained by the state. The TMT would be one of the most expensive telescopes ever created.

• In 2010 the Governor of Hawaii signed off on an environmental study after 14 community meetings.
• The BLNR held hearings on December 2 and December 3, 2010 on the application for a permit.
• On February 25, 2011 the board granted the permits after multiple public hearings. This approval had conditions, in particular that a hearing about contesting the approval be heard.
• A contested case hearing was held in August 2011, which led to a judgment by the hearing officer for approval in November 2012. The telescope was given approval by the state Board of Land and Natural Resources in April 2013. This process was challenged in court with a lower court ruling in May 2014. The Intermediate Court of Appeals of the State of Hawaii declined to hear an appeal regarding the permit until the Hawaii Department of Land and Natural Resources first issued a decision from the contested case hearing that could then be appealed to the court.
• The dedication and ground-breaking ceremony was held, but interrupted by protesters on October 7, 2014. The project became the focal point of escalating political conflict, police arrests and continued litigation over the proper use of conservation lands. Native Hawaiian cultural practice and religious rights became central to the opposition, with concerns over the lack of meaningful dialogue during the permitting process.
• On December 2, 2015, the Hawaii State Supreme Court ruled the 2011 permit from the Hawaii Board of Land and Natural Resources was invalid. The high court stated: "BLNR put the cart before the horse when it approved the permit before the contested case hearing". and "Once the permit was granted, Appellants were denied the most basic element of procedural due process – an opportunity to be heard at a meaningful time and in a meaningful manner. Our Constitution demands more". In March 2017, the Board’s hearing officer, retired judge Riki May Amano, finished six months of hearings in Hilo, Hawaii, taking 44 days of testimony from 71 witnesses. On July 26, 2017, Amano filed her recommendation that the Land Board grant the construction permit.
• On September 28, 2017, the State of Hawaii Board of Land and Natural Resources (BLNR), acting on Amano's report, approved, by a vote of 5-2, a Conservation District Use Permit (CDUP) for the TMT. Numerous conditions, including the removal of three existing telescopes and an assertion that the TMT is to be the last telescope on the mountain, were attached to the permit.
• On October 30, 2018, the Supreme Court of Hawaii ruled the CDUP was valid, allowing construction to proceed.

Observatory design

The TMT would be a general-purpose observatory capable of investigating a broad range of astrophysical problems. Total diameter of the dome will be 217 feet with the total dome height at 180 feet (comparable in height to an eighteen-story building). Total area of the structure is projected to be 1.44 acres within a 5-acre complex.

Telescope

Thirty Meter Telescope design (late 2007).

The centerpiece of the TMT Observatory is to be a Ritchey-Chrétien telescope with a 30-metre (98 ft) diameter primary mirror. This mirror is to be segmented and consist of 492 smaller (1.4 m), individual hexagonal mirrors. The shape of each segment, as well as its position relative to neighboring segments, will be controlled actively.

A 3.6-metre (12 ft) secondary mirror is to produce an unobstructed field-of-view of 20 arcminutes in diameter with a focal ratio of 15. A flat tertiary mirror is to direct the light path to science instruments mounted on large Nasmyth platforms. The telescope is to have an alt-azimuth mount. Target acquisition and system configuration capabilities need to be achieved within 5 minutes, or ten minutes if relocating to a newer device. To achieve these time limitations the TMT will use a software architecture linked by a service based communications system. The moving mass of the telescope, optics, and instruments will be 1430 tons. The design of the facility descends from the W. M. Keck Observatory.

Adaptive optics

Integral to the observatory is a Multi-Conjugate Adaptive Optics (MCAO) system. This MCAO system will measure atmospheric turbulence by observing a combination of natural (real) stars and artificial laser guide stars. Based on these measurements, a pair of deformable mirrors will be adjusted many times per second to correct optical wave-front distortions caused by the intervening turbulence.

This system will produce diffraction-limited images over a 30-arc-second diameter field-of-view, which means that the core of the point spread function will have a size of 0.015 arc-second at a wavelength of 2.2 micrometers, almost ten times better than the Hubble Space Telescope.

Scientific instrumentation

Mirror sizes of existing and proposed telescopes. The two other new ELT the E-ELT and GMT are being built in the southern hemisphere

Early-light capabilities

Three instruments are planned to be available for scientific observations:

• Wide Field Optical Spectrometer (WFOS)' providing near-ultraviolet and optical (0.3–1.0 μm wavelength) imaging and spectroscopy over a more than 40-square arc-minute field-of-view. Using precision cut focal plane masks, WFOS would enable long-slit observations of single objects as well as short-slit observations of hundreds of objects simultaneously. WFOS would use natural (uncorrected) seeing images.
• Infrared Imaging Spectrometer (IRIS) mounted on the observatory MCAO system, capable of diffraction-limited imaging and integral-field spectroscopy at near-infrared wavelengths (0.8–2.5 μm). Principal investigators are James Larkin of UCLA and Anna Moore of Caltech. Project scientist is Shelley Wright of UC San Diego.
• Infrared Multi-object Spectrometer (IRMS) allowing close to diffraction-limited imaging and slit spectroscopy over a 2 arc-minute diameter field-of-view at near-infrared wavelengths (0.8–2.5 μm).

Protests

Cultural practitioner Joshua Lanakila Mangauil, along with Kahoʻokahi Kanuha and Hawaiian sovereignty supporters block the access road to Mauna Kea in October 2014, demonstrating against the building of the Thirty Meter Telescope.

The proposed construction of the TMT on Mauna Kea sparked protests and demonstrations across the state of Hawaii. Mauna Kea is the most sacred mountain in Hawaiian culture. The mountain is also conservation land held in trust by the state of Hawaii.

On October 7, 2014, the groundbreaking for the TMT was interrupted by demonstrators causing a postponement of construction In late March 2015, demonstrators again halted the construction crews. On April 2, 2015, about 300 protesters gathered on Mauna Kea, some of them trying to block the access road to the summit; 23 arrests were made. Once the access road to the summit was cleared by the police, about 40 to 50 protesters began following the heavily laden and slow-moving construction trucks to the summit construction site.

On April 7, 2015, the construction was halted for one week at the request of Hawaii state governor David Ige, after the protest on Mauna Kea continued. Project manager Gary Sanders stated that TMT agreed to the one-week stop for continued dialogue; Kealoha Pisciotta, president of Mauna Kea Anaina Hou, one of the organizations that have challenged the TMT in court, viewed the development as positive but said opposition to the project would continue. On April 8, 2015, Governor Ige announced that the project was being temporarily postponed until at least April 20, 2015. Construction was set to begin again on June 24, though hundreds of protesters gathered on that day, blocking access to the construction site for the TMT. Some protesters camped on the access road to the site, while others rolled large rocks onto the road. The actions resulted in 11 arrests.

On December 2, 2015, the Supreme Court of Hawaii invalidated the TMT's building permits, ruling that due process was not followed when the Board of Land and Natural Resources approved the permit before the contested case hearing. The TMT company chairman stated: "T.M.T. will follow the process set forth by the state." A revised permit was approved on September 28, 2017 by the Hawaii Board of Land and Natural Resources. On October 30, 2018, the Supreme Court of Hawaii ruled, 4-1, that the revised permit was acceptable and construction may proceed.

Babylonian astronomy

From Wikipedia, the free encyclopedia

A Babylonian tablet recording Halley's comet in 164 BC.

Babylonian astronomy was the study or recording of celestial objects during early history Mesopotamia. These records can be found on Sumerian clay tablets, inscribed in cuneiform, dated approximately to 3500–3200 BC.

In conjunction with their mythology, the Sumerians developed a form of astronomy/astrology that had an influence on Babylonian culture. Therein Planetary gods played an important role.

Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations may have been collected from various earlier sources. The earliest catalogue, Three Stars Each, mentions stars of the Akkadian Empire, of Amurru, of Elam and others.

A numbering system based on sixty was used, a sexagesimal system. This system simplified the calculating and recording of unusually great and small numbers. The modern practices of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians.

During the 8th and 7th centuries BC, Babylonian astronomers developed a new empirical approach to astronomy. They began studying and recording their belief system and philosophies dealing with an ideal nature of the universe and began employing an internal logic within their predictive planetary systems. This was an important contribution to astronomy and the philosophy of science, and some modern scholars have thus referred to this novel approach as the first scientific revolution. This approach to astronomy was adopted and further developed in Greek and Hellenistic astrology. Classical Greek and Latin sources frequently use the term Chaldeans for the astronomers of Mesopotamia, who were considered as priest-scribes specializing in astrology and other forms of divination.

Only fragments of Babylonian astronomy have survived, consisting largely of contemporary clay tablets containing astronomical diaries, ephemerides and procedure texts, hence current knowledge of Babylonian planetary theory is in a fragmentary state. Nevertheless, the surviving fragments show that Babylonian astronomy was the first "successful attempt at giving a refined mathematical description of astronomical phenomena" and that "all subsequent varieties of scientific astronomy, in the Hellenistic world, in India, in Islam, and in the West … depend upon Babylonian astronomy in decisive and fundamental ways."

The origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descendants in direct line from the work of the late Babylonian astronomers. Modern knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BC. The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age.

Old Babylonian astronomy

"Old" Babylonian astronomy was practiced during and after the First Babylonian Dynasty (ca. 1830 BC) and before the Neo-Babylonian Empire (ca. 626 BC).
The Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. Tablets dating back to the Old Babylonian period document the application of mathematics to the variation in the length of daylight over a solar year. Centuries of Babylonian observations of celestial phenomena were recorded in the series of cuneiform tablets known as the Enûma Anu Enlil—the oldest significant astronomical text that we possess is Tablet 63 of the Enûma Anu Enlil, the Venus tablet of Ammisaduqa, which lists the first and last visible risings of Venus over a period of about 21 years. It is the earliest evidence that planetary phenomena were recognized as periodic.

An object labelled the ivory prism was recovered from the ruins of Nineveh. First presumed to be describing rules to a game, its use was later deciphered to be a unit converter for calculating the movement of celestial bodies and constellations.

Babylonian astronomers developed zodiacal signs. they are made up of the division of the sky into three sets of thirty degrees and the constellations that inhabit each sector.

The MUL.APIN contains catalogues of stars and constellations as well as schemes for predicting heliacal risings and settings of the planets, and lengths of daylight as measured by a water clock, gnomon, shadows, and intercalations. The Babylonian GU text arranges stars in 'strings' that lie along declination circles and thus measure right-ascensions or time intervals, and also employs the stars of the zenith, which are also separated by given right-ascensional differences. There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, mainly from Babylonia.

Planetary theory

The Babylonians were the first civilization known to possess a functional theory of the planets. The oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet Venus that probably dates as early as the second millennium BC. The Babylonian astrologers also laid the foundations of what would eventually become Western astrology. The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC, comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.

Cosmology

In contrast to the world view presented in Mesopotamian and Assyro-Babylonian literature, particularly in Mesopotamian and Babylonian mythology, very little is known about the cosmology and world view of the ancient Babylonian astrologers and astronomers. This is largely due to the current fragmentary state of Babylonian planetary theory, and also due to Babylonian astronomy being independent from cosmology at the time. Nevertheless, traces of cosmology can be found in Babylonian literature and mythology.

In Babylonian cosmology, the Earth and the heavens were depicted as a "spatial whole, even one of round shape" with references to "the circumference of heaven and earth" and "the totality of heaven and earth". Their worldview was not exactly geocentric either. The idea of geocentrism, where the center of the Earth is the exact center of the universe, did not yet exist in Babylonian cosmology, but was established later by the Greek philosopher Aristotle's On the Heavens. In contrast, Babylonian cosmology suggested that the cosmos revolved around circularly with the heavens and the earth being equal and joined as a whole. The Babylonians and their predecessors, the Sumerians, also believed in a plurality of heavens and earths. This idea dates back to Sumerian incantations of the 2nd millennium BC, which refers to there being seven heavens and seven earths, linked possibly chronologically to the creation by seven generations of gods.

Omens

It was a common Mesopotamian belief that gods could and did indicate future events to mankind. This indication of future events were considered to be omens. The Mesopotamian belief in omens pertains to astronomy and its predecessor astrology because it was a common practice at the time to look to the sky for omens. The other way to receive omens at the time was to look at animal entrails. This method of recovering omens is classified as a producible omen, meaning it can be produced by humans, but sky omens are produced without human action and therefore seen as much more powerful. Both producible and unproducable omens however, were seen as messages from the gods. Just because gods sent the signs didn’t mean that Mesopotamians believed their fate was sealed either, the belief during this time was that omens were avoidable. In mathematical terms, the Mesopotamians viewed omens as “if x, then y”, where “X” is the protasis and “Y” is the apodosis. The relationship Mesopotamians had with omens can be seen in the Omen Compendia, a Babylonian text composed starting from the beginning of the second millennium on-wards. It is the primary source text that tells us that ancient Mesopotamians saw omens as preventable. The text also contains information on Sumerian rites to avert evil, or “nam-bur-bi”. A term later adopted by the Akkadians as “namburbu”, roughly, “[the evil] loosening”. The god Ea was the one believed to send the omens. Concerning the severity of omens, eclipses were seen as the most dangerous.

The Enuma Anu Enlil is a series of cuneiform tablets that gives insight on different sky omens Babylonian astronomers observed. Celestial bodies such as the sun and moon were given significant power as omens. Reports from Nineveh and Babylon, circa 2500-670 B.C.E., show lunar omens observed by the Mesopotamians. "When the moon disappears, evil will befall the land. When the moon disappears out of its reckoning, an eclipse will take place".

The Astrolabes

The astrolabes are one of the earliest documented cuneiform tablets that discuss astronomy and date back to the Old Babylonian Kingdom (not to be mistaken for the later astronomical measurement device of the same name). They are a list of thirty-six stars connected with the months in a year. Generally considered to be written between 1800-1100 B.C.E.. No complete texts have been found, but there is a modern compilation by Pinches, assembled from texts housed in the British Museum that is considered excellent by other historians who specialize in Babylonian astronomy. Two other texts concerning the astrolabes that should be mentioned are the Brussels and Berlin compilations. They offer similar information to the Pinches anthology, but do contain some differing information from each other.

The thirty-six stars that make up the astrolabes are believed to be derived from the astronomical traditions from three Mesopotamian city-states, Elam, Akkad, and Amurru. The stars followed and possibly charted by these city-states are identical stars to the ones in the astrolabes. Each region had a set of twelve stars it followed, which combined equals the thirty-six stars in the astrolabes. The twelve stars of each region also correspond to the months of the year. The two cuneiform texts that provide the information for this claim are the large star list “K 250” and “K 8067”. Both of these tablets were translated and transcribed by Weidner. During the reign of Hammurabi these three separate traditions were combined. This combining also ushered in a more scientific approach to astronomy as connections to the original three traditions weakened. The increased use of science in astronomy is evidenced by the traditions from these three regions being arranged in accordance to the paths of the stars of Ea, Anu, and Enlil, an astronomical system contained and discussed in the Mul.apin.

MUL.APIN

Mul.apin cuneiform tablet

MUL.APIN is a collection of two cuneiform tablets (Tablet 1 and Tablet 2) that document aspects of Babylonian astronomy such as the movement of celestial bodies and records of solstices and eclipses. Each tablet is also split into smaller sections called Lists. It was comprised in the general time frame of the astrolabes and Enuma Anu Enlil, evidenced by similar themes, mathematical principles, and occurrences.

Tablet 1 houses information that closely parallels information contained in astrolabe B. The similarities between Tablet 1 and astrolabe B show that the authors were inspired by the same source for at least some of the information. There are six lists of stars on this tablet that relate to sixty constellations in charted paths of the three groups of Babylonian star paths, Ea, Anu, and Enlil. there are also additions to the paths of both Anu and Enlil that are not found in astrolabe B.

The Connection Between a Calendar, Mathematics, and Astronomy

The exploration of the sun, moon, and other celestial bodies affected the development of Mesopotamian culture. The study of the sky led to the development of a calendar and advanced mathematics in these societies. The Babylonians were not the first complex society to develop a calendar globally and in nearby North Africa, The Egyptians developed a calendar of their own. The Egyptian calendar was solar based, while the Babylonian calendar was lunar based. A potential blend between the two that has been noted by some historians is the adoption of a crude leap year by the Babylonians after the Egyptians developed one. The Babylonian leap year shares no similarities with the leap year practiced today. it involved the addition of a thirteenth month as a means to re-calibrate the calendar to better match the growing season.

Babylonian priests were the ones responsible for developing new forms of mathematics and did so to better calculate the movements of celestial bodies. One such priest, Nabu-rimanni, is the first documented Babylonian astronomer. He was a priest for the moon god and is credited with writing lunar and eclipse computation tables as well as other elaborate mathematical calculations. The computation tables are organized in seventeen or eighteen tables that document the orbiting speeds of planets and the moon. His work was later recounted by astronomers during the Seleucid dynasty.

Neo-Babylonian astronomy

Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Achaemenid, Seleucid, and Parthian periods of Mesopotamian history. A significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar (747–734 BC). The systematic records of ominous phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses, for example. The Greco-Egyptian astronomer Ptolemy later used Nabonassar's reign to fix the beginning of an era, since he felt that the earliest usable observations began at this time.

The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323–60 BC). In the 3rd century BC, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous phenomena for each planet. About the same time, or shortly afterwards, astronomers created mathematical models that allowed them to predict these phenomena directly, without consulting past records.

Arithmetical and geometrical methods

Though there is a lack of surviving material on Babylonian planetary theory, it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. It had been thought that most of the predictive Babylonian planetary models that have survived were usually strictly empirical and arithmetical, and usually did not involve geometry, cosmology, or speculative philosophy like that of the later Hellenistic models, though the Babylonian astronomers were concerned with the philosophy dealing with the ideal nature of the early universe. Babylonian procedure texts describe, and ephemerides employ, arithmetical procedures to compute the time and place of significant astronomical events. More recent analysis of previously unpublished cuneiform tablets in the British Museum, dated between 350 and 50 BC, demonstrates that Babylonian astronomers sometimes used geometrical methods, prefiguring the methods of the Oxford Calculators, to describe the motion of Jupiter over time in an abstract mathematical space.

In contrast to Greek astronomy which was dependent upon cosmology, Babylonian astronomy was independent from cosmology. Whereas Greek astronomers expressed "prejudice in favor of circles or spheres rotating with uniform motion", such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits. There is no evidence that the celestial bodies moved in uniform circular motion, or along celestial spheres, in Babylonian astronomy.

Contributions made by the Chaldean astronomers during this period include the discovery of eclipse cycles and saros cycles, and many accurate astronomical observations. For example, they observed that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving swifter when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.

Chaldean astronomers known to have followed this model include Naburimannu (fl. 6th–3rd century BC), Kidinnu (d. 330 BC), Berossus (3rd century BCE), and Sudines (fl. 240 BCE). They are known to have had a significant influence on the Greek astronomer Hipparchus and the Egyptian astronomer Ptolemy, as well as other Hellenistic astronomers.

Heliocentric astronomy

The only surviving planetary model from among the Chaldean astronomers is that of the Hellenistic Seleucus of Seleucia (b. 190 BC), who supported the Greek Aristarchus of Samos' heliocentric model. Seleucus is known from the writings of Plutarch, Aetius, Strabo, and Muhammad ibn Zakariya al-Razi. The Greek geographer Strabo lists Seleucus as one of the four most influential astronomers, who came from Hellenistic Seleuceia on the Tigris, alongside Kidenas (Kidinnu), Naburianos (Naburimannu), and Sudines. Their works were originally written in the Akkadian language and later translated into Greek. Seleucus, however, was unique among them in that he was the only one known to have supported the heliocentric theory of planetary motion proposed by Aristarchus, where the Earth rotated around its own axis which in turn revolved around the Sun. According to Plutarch, Seleucus even proved the heliocentric system through reasoning, though it is not known what arguments he used.

According to Lucio Russo, his arguments were probably related to the phenomenon of tides. Seleucus correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the Earth's atmosphere. He noted that the tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.

According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.

None of his original writings or Greek translations have survived, though a fragment of his work has survived only in Arabic translation, which was later referred to by the Persian philosopher Muhammad ibn Zakariya al-Razi (865-925).

Babylonian influence on Hellenistic astronomy

Many of the works of ancient Greek and Hellenistic writers (including mathematicians, astronomers, and geographers) have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by earlier ancient Near Eastern civilizations, notably those in Babylonia, were forgotten for a long time. Since the discovery of key archaeological sites in the 19th century, many cuneiform writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by Abraham Sachs and later published by Otto Neugebauer in the Astronomical Cuneiform Texts (ACT). Herodotus writes that the Greeks learned such aspects of astronomy as the gnomon and the idea of the day being split into two halves of twelve from the Babylonians. Other sources point to Greek pardegms, a stone with 365-366 holes carved into it to represent the days in a year, from the Babylonians as well.

Since the rediscovery of the Babylonian civilization, it has been theorized that there was significant information exchange between classical and Hellenistic astronomy and Chaldean. The best documented borrowings are those of Hipparchus (2nd century BCE) and Claudius Ptolemy (2nd century CE).

Early influence

Some scholars support that the Metonic cycle may have been learned by the Greeks from Babylonian scribes. Meton of Athens, a Greek astronomer of the 5th century BCE, developed a lunisolar calendar based on the fact that 19 solar years is about equal to 235 lunar months, a period relation that perhaps was also known to the Babylonians.

In the 4th century BCE, Eudoxus of Cnidus wrote a book on the fixed stars. His descriptions of many constellations, especially the twelve signs of the zodiac show similarities to Babylonian. The following century Aristarchus of Samos used an eclipse cycle called the Saros cycle to determine the year length. However, the position that there was an early information exchange between Greeks and Chaldeans are weak inferences; possibly, there had been a stronger information exchange between the two after Alexander the Great established his empire over Persia in the latter part of the 4th century BCE.

Influence on Hipparchus and Ptolemy

In 1900, Franz Xaver Kugler demonstrated that Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. Later Greek knowledge of this specific Babylonian theory is confirmed by 2nd-century papyrus, which contains 32 lines of a single column of calculations for the Moon using this same "System B", but written in Greek on papyrus rather than in cuneiform on clay tablets.

It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar; i.e., 26 February 747 BC.

This raw material by itself must have been tough to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):

• 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
• 251 (synodic) months = 269 returns in anomaly
• 5458 (synodic) months = 5923 returns in latitude
• 1 synodic month = 29;31:50:08:20 days (sexagesimal; 29.53059413 ... days in decimals = 29 days 12 hours 44 min 3⅓ s)

The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year.
Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets.

Other traces of Babylonian practice in Hipparchus' work are

• first Greek known to divide the circle in 360 degrees of 60 arc minutes.
• first consistent use of the sexagesimal number system.
• the use of the unit pechus ("cubit") of about 2° or 2½°.
• use of a short period of 248 days = 9 anomalistic months.

Means of transmission

All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC.

Historians have also found evidence that Athens during the late 5th century may have been aware of Babylonian astronomy. astronomers, or astronomical concepts and practices through the documentation by Xenophon of Socrates telling his students to study astronomy to the extent of being able to tell the time of night from the stars. This skill is referenced in the poem of Aratos, which discusses telling the time of night from the zodiacal signs.

In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events.

What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar. He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2). Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophesied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely. Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own.

Maya astronomy

From Wikipedia, the free encyclopedia

Maya astronomy is the study of the Moon, planets, Milky Way, Sun, and other astronomical occurrences by the Precolumbian Maya Civilization of Mesoamerica. The Classic Maya in particular developed some of the most accurate pre-telescope astronomy in the world, aided by their fully developed writing system and their positional numeral system, both of which are fully indigenous to Mesoamerica. The Classic Maya understood many astronomical phenomena: for example, their estimate of the length of the synodic month was more accurate than Ptolemy's, and their calculation of the length of the tropical solar year was more accurate than that of the Spanish when the latter first arrived.

European and Maya calendars

European calendar

In 46 BC Julius Caesar decreed that the year would be made up of twelve months of approximately 30 days each to make a year of 365 days and a leap year of 366 days. The civil year had 365.25 days. This is the Julian calendar. The solar year has 365.2422 days and by 1582 there was an appreciable discrepancy between the winter solstice and Christmas and the Vernal equinox and Easter. Pope Gregory XIII, with the help of Italian astronomer Aloysius Lilius (Luigi Lilio), reformed this system by abolishing the days October 5 through October 14, 1582. This brought the civil and tropical years back into line. He also missed three days every four centuries by decreeing that centuries are only leap years if they are evenly divisible by 400. So for example 1700, 1800, and 1900 are not leap years but 1600 and 2000 are. This is the Gregorian calendar. Astronomers use the Julian/Gregorian calendar. Dates before 46 BC are converted to the Julian calendar. This is the proleptic Julian calendar. Astronomical calculations return a year zero and years before that are negative numbers. This is astronomical dating. There is no year zero in historical dating. In historical dating the year 1 BC is followed by the year 1 so for example, the year -3113 (astronomical dating) is the same as 3114 BC (historical dating).

Many mayanists convert Maya calendar dates into the proleptic Gregorian calendar. In this calendar, Julian calendar dates are revised as if the Gregorian calendar had been in use before October 15, 1582. These dates must be converted to astronomical dates before they can be used to study Maya astronomy because astronomers use the Julian/Gregorian calendar. Proleptic Gregorian dates vary substantially from astronomical dates. For example, the mythical creation date in the Maya calendar is August 11, 3114 BC in the proleptic Gregorian calendar and September 6, -3113 astronomical.

Julian days

Astronomers describe time as a number of days and a fraction of a day since noon January 1, -4712 Greenwich Mean Time. The Julian day starts at noon because they are interested in things that are visible at night. The number of days and fraction of a day elapsed since this time is a Julian day. The whole number of days elapsed since this time is a Julian day number.

Maya calendars

There are three main Maya calendars:

The Long Count is a count of days. There are examples of Long Counts with many places but most of them give five places since the mythical creation date - 13.0.0.0.0.

The Tzolk'in is a 260-day calendar made up of a day from one to 13 and 20 day names.

The Haab' is a 365-day year made up of a day of zero to 19 and 18 months with five unlucky days at the end of the year.

When the Tzolk'in and Haab' are both given, the date is called a calendar round. The same calendar round repeats every 18,980 days - approximately 52 years. The calendar round on the mythical starting date of this creation was 4 Ahau 8 Kumk'u. When this date occurs again it is called a calendar round completion.

A Year Bearer is a Tzolk'in day name that occurs on the first day of the Haab'. A number of different year bearer systems were in use in Mesoamerica.

Correlating the Maya and European calendar

The Maya and European calendars are correlated by using the Julian day number of the starting date of the current creation — 13.0.0.0.0, 4 Ajaw, 8 Kumk'u. The Julian day number of noon on this day was 584,283. This is the GMT correlation.

Sources of Astronomical Inscriptions

Maya Codices

At the time of the Spanish conquest the Maya had many books. These were painted on folding bark cloth. The Spanish conquistadors and catholic priests destroyed them whenever they found them. The most infamous example of this was the burning of a large number of these in Maní, Yucatán by Bishop Diego de Landa in July, 1562. Only four of these codices exist today. These are the Dresden, Madrid, Paris and Grolier codices. The Dresden Codex is an astronomical Almanac. The Madrid Codex mainly consists of almanacs and horoscopes that were used to help Maya priests in the performance of their ceremonies and divinatory rituals. It also contains astronomical tables, although less than are found in the other three surviving Maya codices. The Paris Codex contains prophecies for tuns and katuns (see Mesoamerican Long Count calendar), and a Maya zodiac. The Grolier Codex is a Venus almanac.

Ernst Förstemann, a librarian at the Royal Public Library of Dresden, recognized that the Dresden Codex is an astronomical almanac and was able to decipher much of it in the early 20th century.

Maya Monuments

Mayan stelae

Stela E at Quiriguá, possibly the largest freestanding stone monument in the New World

The Maya erected a large number of stelae. These had a Long Count date. They also included a supplementary series. The supplementary series included lunar data - the number of days elapsed in the current lunation, the length of the lunation and the number of the lunation in a series of six. Some of them included an 819-day count which may be a count of the days in a cycle associated with Jupiter. See Jupiter and Saturn below. Some other astronomical events were recorded, for example the eclipse warning on Quirigua Stela E - 9.17.0.0.0. A partial solar eclipse was visible in Mesoamerica two days later on 9.17.0.0.2 - Friday January 18, 771.

Calendric inscriptions

Many Mayan temples were inscribed with hieroglyphic texts. These contain both calendric and astronomical content.

Methods of astronomical observation

Figure from the Madrid Codex, interpreted as an astronomer

The Caracol at Chichen Itza is an observatory

Maya astronomy was naked-eye astronomy based on the observations of the azimuths of the rising and setting of heavenly bodies. City planning and alignment was often arranged in line with astronomical paths and events.

Many wells located in Mayan ruins were also observatories of the zenithal passage of the sun.

One of the most studied sites for the topic of Mayan astronomy is the Caracol at Chichen Itza. The Caracol is an observatory aligned to follow the path of Venus through the year. The grand staircase leading to the once cylindrical structure deviates 27.5 degrees from the alignment of the surrounding buildings to align with the northern extreme of Venus; the northeast-southwest diagonal of the site aligns with the sunrise of the summer solstice and the sunset of the winter solstice.

Astronomical Observations

Solar

The Maya were aware of the solstices and equinoxes. This is demonstrated in building alignments. More important to them were zenithal passage days. In the Tropics the Sun passes directly overhead twice each year. Many known structures in Mayan temples were built to observe this. Munro S. Edmonson studied 60 mesoamerican calendars and found remarkable consistency in the calendars, except for a number of different year bearer systems. He thought that these different year bearers were based on the solar years in which they were initiated.

The Maya were aware of the fact that the 365 day Haab' differs from the Tropical year by about .25 days per year. A number of different intervals are given on Maya Monuments that can be used to approximate the tropical year. The most accurate of these is that the tropical year exceeds the length of the 365 day Haab' by one day every 1,508 days. The occurrence of a particular solstice on a given date in the Haab' will repeat after the passage of 1,508 365-day Haab' years. The Haab' will lose one day every 1,508 days and it will take 1,508 Haab' years to lose one Haab' year. So 365 x 1,508 = 365.2422 x 1,507 or 1,508 Haab' years = 1,507 Tropical years of 365.2422 days.

The Tropical Year in the Maya codices

The solstices and equinoxes are described in many almanacs and tables in the Maya codices. There are three seasonal tables and four related almanacs in the Dresden Codex. There are five solar almanacs in the Madrid Codex and possibly an almanac in the Paris codex. Many of these can be dated to the second half of the ninth and first half of the tenth centuries.

The Dresden Codex

The upper and lower seasonal tables (pages 61–69) unify the Haab', the solstices and equinoxes, the eclipse cycle and the year bearer (0 Pop). The table refers to the middle of the tenth century but includes more than a dozen other base dates from the fourth to the eleventh centuries.

The rainmaking almanac (pages 29b to 30b) refers to the Haab' and the tropical year. During the year in question the summer solstice preceded the Half Year by a few days. This confirms that the year was either 857 of 899. It also describes a four-part rain-making ceremony similar to Yucatecan ceremonies known from modern ethnography.

The Spliced Table (pages 31.a to 39.a) is the combination of two separate tables. It includes rituals including those of the Uayab', the Half Year, agricultural and meteorological matters. It contains a reference to the Half Year, skybands, two of which contain Venus glyphs. The table has four base dates; two in the fourth century, one in the ninth and one in the tenth century. Three of these are also base dates in the seasonal table.

The Burner Almanac (pages 33c to 39c) contains the stations of the Burner cycle, a system for dividing the Tzolk'in that is known from the colonial history of Yucatán. The almanac also refers to eclipse seasons and stations of the tropical year. This almanac refers to a few years before and just after 1520, when the codex may have already been in the hands of the Spanish.

The Conjugal Almanac (pages 22c to 23c) is one of a series of almanacs dealing with conjugal relationships between pairs of deities. It may contain a reference to the vernal equinox.

In addition to the astronomical tables preserved in the Dresden codex, there are illustrations of different deities and their relation to the positions of the planets.

The Madrid Codex

Pages 10b,c - 11b, c of the Madrid Codex contain two almanacs similar to the seasonal tables of the Dresden Codex. In the lower almanac the Half Year of the Haab' occurred on the same day as the summer solstice, dating this event to the year 925.

The long almanac (pages 12b to 18b) includes iconography of the Haab, abundant rain and astronomy. The almanac contains several eclipse glyphs, spaced at correct eclipse intervals. The eclipse and calendar dates allow one to date the almanac to the year 924. The combination of this almanac and the seasonal almanacs in this codex are the functional equivalent of the two seasonal almanacs in the Dresden Codex.

Pages 58.c to 62.c are a tropical-year almanac. It is an 1820-day almanac made up of 20 rows of 91 days each. One of the captions associates an equinox with a glyph for Venus. This dates the almanac to a date between 890 and 962.

The Bird Almanac (pages 26c to 27c) has an unusual structure (5 x 156 = 780 days). One of its pictures is probably a reference to the vernal equinox. This almanac can't be dated.

The Paris Codex
 
The God C almanacs (pages 15a, b to 18a, b) are very incomplete and partially effaced. It is impossible to ascertain their lengths or dates. Two known Haab' rituals can be recognized. It's possible that the God C almanacs are equivalent to the seasonal tables in the Dresden Codex and the God C almanacs in the Paris Codex

The Books of Chilam Balam

The Book of Chilam Balam specifically refers to the Half Year, the solstices and equinoxes.

Building alignments

Anthony Aveni and Horst Hartung published an extensive study of building alignments in the Maya area. They found that most orientations occur in a zone 8°-18° east of north with many at 14° and 25° east of north. He believes that the 25° south of east orientations are oriented to the position on the horizon of sunrise on the winter solstice and that the 25° north of west orientations are aligned with sunset on the summer solstice.

Two diagonal alignments across the platform of the base Caracol at Chichén Itzá, are aligned with the azimuth of the sunrise on the summer solstice and an alignment perpendicular to the base of the lower platform corresponds to the azimuth of the sunset on the summer solstice. One of the windows in the round tower provides a narrow slit for viewing the sunset on the equinoxes. The Caracol was also used to observe the zenithal passage of the Sun. An alignment perpendicular to the base of the upper platform and one from the center of a doorway above the symbolate monument are aligned with the azimuth of the sunset on zenith passage days.

Other solar observatories are at Uaxactun, Oxkintok and Yaxchilan.

Lunar

Many inscriptions include data on the number of days elapsed in the current lunation, the number of days in the current lunation and the position of the lunation in a cycle of six lunations.

Modern astronomers consider conjunction of Sun and Moon (when the Sun and Moon have the same ecliptic longitude) to be the New Moon. The Maya counted the zero day of the lunar cycle as either the first day when one could no longer see the waning crescent Moon or the first day when one could see the thin crescent waxing Moon (the Palenque system). Using this system, the zero date of the lunar count is about two days after astronomical new Moon. Aveni and Fuls analysed a large number of these inscription and found strong evidence for the Palenque system. However Fuls found "…at least two different methods and formulas were used to calculate the moon's age and position in the six-month cycle…"

Mercury

Pages 30c-33c of the Dresden codex are a Venus-Mercury almanac. The 2340-day length of the Venus-Mercury almanac is a close approximation of the synodic periods of Venus (4 x 585) and Mercury (20 x 117). The Almanac also refers to the summer solstice and the Haab' uayeb ceremonies for the tenth century AD.

Venus

Venus was extremely important to the people of Mesoamerica. Its cycles were carefully tracked by the Maya.

Because Venus is closer to the Sun than the Earth, it passes the Earth during its orbit. When it passes behind the Sun at superior conjunction and between the Earth and the Sun at inferior conjunction it is invisible. Particularly dramatic is the disappearance as evening star and its reappearance as the morning star approximately eight days later, after inferior conjunction. The cycle of Venus is 583.92 days long but it varies between 576.6 and 588.1 days. Astronomers calculate heliacal phenomena (first and last visibility of rising or setting bodies) using the arcus visionis - the difference in altitude between the body and the center of the Sun at the time of geometric rising or setting of the body, not including the 34 arc minutes of refraction that allows one to see a body before its geometric rise or the 0.266,563,88... degree semidiameter of the sun. Atmospheric phenomena like extinction are not considered. The required arcus visionis varies with the brightness of the body. Because Venus varies in size and has phases, a different arcus visionus is used for the four different rising and settings.

Dresden Codex

The Dresden codex pages 24 and 46 to 50 are a Venus almanac. Bricker and Bricker write:

"The Venus table tracks the synodic cycle of Venus by listing the formal or canonical dates of planet's first and last appearances as 'morning star' and 'evening star'. The emphasis, both iconographic and textual, is on first appearance as morning star (heliacal rise), the dates of which are given quite accurately, This first appearance was regarded as a time of danger and the major purpose of the Venus table was to provide warnings of such dangerous days. The table lists the tzolkin days for the four appearance/disappearance events during each of the 65 consecutive Venus cycles, a period of approximately 104 years. The table was used at least four times with different starting dates, from the tenth through the fourteenth centuries AD."

Because the Maya canonical period was 584 days and the synodic period is 583.92 days, an error accumulated in the table over time. Possible correction schemes from the codex are discussed by Aveni and Bricker and Bricker.

The Dresden Codex pages 8–59 is a planetary table that commensurates the synodic cycles of Mars and Venus. There are four possible base dates, two in the seventh and two in the eighth centuries.

Pages 30c-33c of the Dresden codex are a Venus-Mercury almanac. The 2340-day length of the Venus-Mercury almanac is a close approximation of the synodic periods of Venus (4 x 585) and Mercury (20 x 117). The Almanac also refers to the summer solstice and the Haab' uayeb ceremonies for the tenth century AD.

The Grolier Codex

The Grolier Codex lists Tzolk'in dates for the appearance/disappearances of Venus for half of the Venus cycles in the Dresden codex. These are the same dates listed in Dresden.

Building Alignments

The Caracol at Chichen Itza contains the remains of windows through which the extreme elongations of the planet can be seen. Four of the main orientations of the lower platform mark the points of the maximum horizontal displacement of the planet during the year. Two alignments of the surviving windows in the upper tower align with the extreme positions of the planet at its greatest north and south declinations.

Building 22 at Copan is called the Venus temple because so many Venus symbols are inscribed on it. It has a narrow window that can be used to observe the greatest elongations of Venus.

The Governors Palace at Uxmal differs 30° from the northeast alignment of the other buildings. The door faces southeast. About six kilometers from the door is a pyramidal hill. From the door one could observe the appearance of Venus just before reaching an extreme elongation. The cornices of the building have hundreds of masks of Chaac with Venus symbols under the eyelids.

Inscriptions

De Meis has a table of 14 Long Count inscriptions that record heliacal phenomena of Venus.

De Meis has a table of 11 Long Counts that record the greatest elongation of Venus.

The Bonampak murals depict the victory of king Chaan Muan with his enemies lying down, pleading for their lives on a date which was the heliacal rising of Venus and a zenith passage of the Sun.

Mars

The Dresden Codex

The Dresden Codex contains three Mars tables and there is a partial Mars almanac in the Madrid codex.

Pages 43b to 45b of the Dresden codex are a table of the 780-day synodic cycle of Mars. The retrograde period of its path, when it is brightest and visible for the longest time, is emphasized. The table is dated to the retrograde period of 818 AD. The text refers to an eclipse season (when the moon is near its ascending or descending node) that coincided with the retrograde motion of mars.

The upper and lower water tables on pages 69–74 share the same pages in the Dresden Codex but are different from each other.

The upper table has 13 groups of 54 days - 702 days. This is the time needed for Mars to return to the same celestial longitude, if the celestial period included a retrograde period. The table was revised for reuse; it has seven base dates from the seventh to the eleventh centuries.

The lower water table has 28 groups of 65 days - 1820 days. This table has only one picture - a scene of torrential rain on page 74. This has been erroneously interpreted as a depiction of the end of the world. The purpose of the table is to track several cultural and natural cycles. These are planting and harvesting, drought, rain and hurricane season, the eclipse season and the relationship of the Milky Way to the horizon. The table was periodically revised by giving it five base dates from the fourth to the twelfth centuries.

The Dresden Codex pages 8–59 is a planetary table that commensurates the synodic cycles of Mars and Venus. There are four possible base dates, two in the seventh and two in the eighth centuries.

The Madrid Codex

Page 2a of the Madrid codex is an almanac of the synodic cycle of Mars. This heavily damaged page is probably a fragment of a longer table. The 78-day periods and iconography are similar to the table in the Dresden Codex.

Jupiter and Saturn

Saturn and particularly Jupiter, are two of the brightest celestial objects. As the Earth passes superior planets in its orbit closer to the Sun they appear to stop moving in the direction of travel of their orbits and back up for a period before resuming their path through the sky. This is apparent retrograde motion. When they start or end retrograde motion their daily motion is stationary before going in another direction.

Inscriptions

Lounsbury found that the dates of several inscriptions commemorating dynastic rituals at Palenque by K'inich Kan Bahlam II coincide with the departure of Jupiter from its secondary stationary point. He also showed that close conjunctions of Jupiter, Saturn and/or Mars were probably celebrated, particularly the "2 Cib 14 Mol" event on about July 21, 690 (Proleptic Gregorian calendar date) - July 18 astronomical.

The Dumbarton Oaks Relief Panel 1 came from El Cayo, Chiapas - a site 12 kilometers up the Usumacinta river from Piedras Negras. Fox and Juteson (1978) found that two of these dates are separated by 378 days - close to the mean synodic period of Saturn - 378.1 days. Each date also falls a few days before Saturn reached its second stationary point, before ending its retrograde motion. The Brickers identified two additional dates that are part of the same series.

Susan Milbrath has extended Lounsbury's work concerning Jupiter to other classic and post-classic sites. Central to her work is her identification of God K (K'awil) as Jupiter. Another component of her work is the tying together of the synodic cycles of Jupiter and Saturn with the katun cycles of the Long Count. She finds a clear link between God K images and dates coinciding with its stationary points in retrograde. She believes that K'awil is the god of the retrograde cycles of Jupiter and Saturn. The Brickers question this interpretation.

Maya Codices

No clear Jupiter or Saturn almanac can be found in the codices.

Eclipses

The Dresden Codex

The Dresden codex pages 51 and 58 are an eclipse table. The table contains a warning of all solar and most lunar eclipses. It does not specify which ones will be visible in the Maya area. The length of the table is 405 lunations (about 33 years). It was meant to be recycled and has a periodic correction scheme. The starting date is in the eighth century and has corrections allowing it to be used up to the eighteenth century. The table also relates eclipses and lunar phenomena to the cycles of Venus, possibly Mercury and other celestial and seasonal phenomena.

An eclipse can occur when the Moon's orbit crosses the ecliptic. This happens twice a year and is referred to as the ascending or descending node. An eclipse can occur during a period 18 days before or after an ascending or descending node. This is an Eclipse season. Three entry dates in the Dresden Codex eclipse table give the eclipse season for November - December 755.

The Madrid Codex

Pages 10a - 13a of the Madrid Codex are an eclipse almanac similar to the one in the Dresden Codex. The table is concerned with rain, drought, the agricultural cycle and how these correspond with eclipses. These eclipses probably correspond to the eclipses in the Dresden Codex (the eighth or ninth century).

The Paris Codex

The Katun Pages (pages 2-11) in the Paris Codex are concerned with the rituals to be performed at Katun completions. They also contain references to historical astronomical events during the fifth to the eighth centuries. These include eclipses, references to Venus and the relationship of Venus to named constellations.

Inscriptions

Lord Kan II of Caracol had altar 21 installed in the center of a ball court. It has inscriptions that mark important dates of the accomplishments of his ancestor Lord Water and himself. Lord Kan II used the dates of important astronomical phenomena for these. For example:

• 9.5.19.1.2 9 Ik 5 Uo - April 14, 553, total lunar eclipse - Accession of Lord Water, grandfather of Kan II
• 9.6.8.4.2 7 Ik 0 Zip - April 27, 562, annular solar eclipse 8 days ago and penumbral lunar eclipse in 7 days - Star war to Tikal
• 9.7.19.10.0 1 Ahau 3 Pop - March 13, 593, partial solar eclipse five days ago - Ball game

The stars

The Maya identified 13 constellations along the ecliptic. These are the content of an almanac in the Paris Codex. Each of these was associated with an animal. These animal representations are pictured in two almanacs in the Madrid Codex where they are related to other astronomical phenomena - eclipses and Venus - and Haab rituals.

Paris Codex

Pages 21-24 of the Paris Codex are a zodiacal almanac. It is made up of five rows of 364 days each. Each row is divided into 13 subdivisions of 28 days each. Its iconography consists of animals, including a scorpion suspended from a skyband and eclipse glyphs. It dates from the eighth century.

Madrid Codex

The longest almanac in the Madrid codex (pages 65-72,73b) is a compendium of information about agriculture, ceremonies, rituals and other matters. Astronomical information includes references to eclipses, the synodic cycles of Venus and zodiacal constellations. The almanac dates to the middle of the fifteenth century.

The Milky Way

The Milky Way appears as a hazy band of faint stars. It is the disc of our own galaxy, viewed edge-on from within it. It appears as a 10°-wide band of diffuse light passing all the way around the sky. It crosses the ecliptic at a high angle. Its most prominent feature is a large dust cloud that forms a dark rift in its southern and western part.

There is no almanac in the codices that refers specifically to the Milky Way but there are references to it in almanacs concerned with other phenomena.

Precession of the equinoxes

The equinoxes move westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic, returning to the same position approximately every 26,000 years.

The "Serpent Numbers" in the Dresden codex pp. 61–69 is a table of dates written in the coils of undulating serpents. Beyer was the first to notice that the Serpent Series is based on an unusually long distance number of 1.18.1.8.0.16 (5,482,096 days - more than 30,000 years). Grofe believes that this interval is quite close to a whole multiple of the sidereal year, returning the sun to precisely the same position against the background of stars. He proposes that this is an observation of the precession of the equinoxes and that the serpent series shows how the Maya calculated this by observing the sidereal position of total lunar eclipses at fixed points within the tropical year. Bricker and Bricker think that he based this on misinterpretation of the epigraphy and give their reasons in Astronomy in the Maya Codices.