History of Astronomy

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History of Astronomy — Middle East


The Crescent Moon.

From the days of ancient Mesopotamia, months in the Middle Eastern world began with the first sighting of a crescent Moon following the New Moon. The Sumerian god of the Moon, known as "Sin" or "Nanna," was believed to have been created after the Earth, and to have given birth to the Sun, planets, and stars. This carried over into the later Babylonian mythology. The Moon was thus highly important in the pantheon of Sumeria and later Babylon.

Bad weather sometimes prevents the sighting of the crescent Moon, and so ancient astronomers devised tables to determine the start of a new month. Such tables were not universally followed, in part because the older approximations were not always correct. To this day in Islamic countries, if an approximate technique does not agree with actual sightings, the sighting of the crescent Moon is taken as the true start of a month.

The Explanatory Supplement to the Astronomical Almanac, section 12.411, Visibility of the Crescent Moon, states that under "optimal conditions," the Crescent Moon can be observed 15.4 hours after a New Moon (when the Moon conjuncts the Sun), but is usually not visible until at least 24 hours after the New Moon.

On rare occasions in an arid desert atmosphere with excellent visibility, the Crescent Moon has been sighted as early as 12 hours after a New Moon.

This knowledge can help us affix Julian and Gregorian calendar dates to some historic Middle Eastern calendrical dates.

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Early Jewish Timekeeping and Cosmology. The earliest mention of the nature of timekeeping in the Bible is found in Genesis Chapter 1, and bears some resemblance to earlier Mesopotamian writings of the Moon, ruler of the night, marking the days (months):

14. And God said, Let there be lights in the firmament of the heaven to divide the day from the night ; and let them be for signs, and for seasons, and for days, and years... 15. And God made two great lights ; the greater light to rule the day, and the lesser light to rule the night : he made the stars also. 17. And God set them in the firmament of the heaven to give light upon the earth, 18. And to rule over the day and over the night, and to divide the light from the darkness : and God saw that it was good.
Genesis 1:5 also mentions a day as being an evening and the morning: "...And the evening and the morning were the first day."

2 Kings 19:15 mentions God between (or above) cherubim:

And Hezekiah prayed before the Lord, and said, O Lord God of Israel, which dwellest between the cherubims, thou art the God, even thou alone, of all the kingdoms of the earth; thou hast made heaven and earth.
Later, 2 Kings Chapter 20 describes how Hezekiah was dying, and was then told by Isaiah of the Lord's promise to extend his life. Asking for a sign from Isaiah, Isaiah then seems to describe the shadow moving on a sundial:
9. And Isaiah said, This sign shalt thou have of the Lord, that the Lord will do the thing that he hath spoken : shall the shadow go forward ten degrees, or go back ten degrees?
10. And Hezekiah answered, It is a light thing for the shadow to go down ten degrees : nay, but let the shadow return backward ten degrees.
11. And Isaiah the prophet cried unto the Lord : and he brought back the shadow ten degrees backward, by which it had gone down in the dial of Ahaz.

The patriarch Abram (later commanded by God to change his name to Abraham) was born in Chaldea. Genesis chapter 12 mentions how Tehrah took his son, Abram (the father of Isaac), and others and left their native "Ur of the Chaldees, to go into the land of Canaan; and they came unto Haran and dwelt there" (Genesis 12:31). Coming from Chaldea, they must have brought with them elements of Mesopotamian culture, including their methods of timekeeping. Joshua 24:2 says

...Thus saith the Lord God of Israel, Your fathers dwelt on the other side of the flood in old time, even Terah, the father of Abraham, and the father of Nachor: and they served other gods.

Before the Exodus out of Egypt, Jews followed local civil calendars. As with their Semitic ancestors, days began at sundown and months began with the first visible crescent Moon following a New Moon.

Exodus relates how the Lord gave the nation of Israel a new first month, for religious purposes. God told Moses, in Exodus Chapter 12 [King James Version],

2. This month shall be unto you the beginning of months : it shall be the first month of the year to you. 3. Speak ye unto all the congreagation of Israel, saying, In the tenth day of this month they shall take to them every man a lamb, according to the house of their fathers, a lamb for an house : ... 6. And ye shall keep it up until the fourteenth day of the same month : and the whole assembly of the congregation of Israel shall kill it in the evening.... 8. And they shall eat the flesh in that night, roast with fire, and unleavened bread ; and with bitter herbs they shall eat it.... 11. And this shall ye eat it ; with your loins girded, your shoes on your feet, and your staff in your hand ; and ye shall eat it in haste : it is the Lord's passover.... 14. And this day shall be unto you for a memorial ; and ye shall keep it a fast to the Lord throughout your generations ; ye shall keep it a feast by an ordinance for ever. 15. Seven days shall ye eat unleavened bread ; even the first day ye shall put away leaven out of your houses : for whosoever eateth leavened bread from the first day until the seventh day, that soul shall be cut off from Israel.

In 587 B.C.E., the Babylonian army under Nebuchadnezzar conquered Judah, plundering Jerusalem and dispersing the Jews of the area. The Biblical Book of Daniel describes how Daniel was brought to Babylon. Daniel Chapter 2 relates:

1. And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him. 2. Then the king commanded to call the magicians, and the astrologers, and the sorcerers, and the Chaldeans, for to shew the king his dreams.
It is interesting that the Book of Daniel identifies the Chaldeans as separate from the "magicians, astrologers, and sorcerers." This distinction is made elsewhere as well, for example to interpret the "writing on the wall" in Chapter 5 of Daniel.

The second chapter of Daniel continues with these "magicians, astrologers, sorcerers, and Chaldeans" unable to tell the king his dream or interpret it. Daniel, by then in Babylon, sees the king's dream and interpretation in a dream himself. Nebuchadnezzar rewards Daniel by making him ruler of the Babylon province.

In 539 B.C.E., the Persian King Cyrus conquered Chaldea. He then sought to have a temple rebuilt in Jerusalem. Ezra, Chapter 1 [KJV] says:

2. Thus saith Cyrus king of Persia, The Lord God of heaven hath given me all the kingdoms of the earth ; and he hath charged me to build him an house at Jerusalem, which is in Judah. 3. Who is there among you of all his people? his God be with him, and let him go up to Jerusalem, which is in Judah, and build the house of the Lord God of Israel, (he is the God,) which is in Jerusalem.
Ezra 3:1 continues, "And when the seventh month was come, and the children of Israel were in the cities, the people gathered themselves together as one man to Jerusalem."

Of Ezra himself, we know from Ezra 7:6: "Thus Ezra went up from Babylon ; and he was a ready scribe in the law of Moses, which the Lord God of Israel had given : and the king granted him all his request, according to the hand of the Lord his God upon him." Today people believe that Ezra introduced the Babylonian month names to Jerusalem. Ezra Chapter 6 mentions a Babylonian month name, Adar, and relates the keeping of the passover:

15. And this house was finished on the third day of the month of Adar, which was in the sixth year of the reign of Darius the king.... 19. And the children of the captivity kept the passover upon the fourteenth day of the first month.... 22. And kept the feast of unleavened bread seven days with joy : for the Lord had made them joyful, and turned the heart of the king of Assyria unto them, to strengthen their hands in the work of the house of God, the God of Israel.

The Book of Isaiah refers both to the "four corners of the earth" (Isaiah 11:12) and to the "the circle of the earth" (Isaiah 40:22):

It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth hem out as a tent to dwell in...

Psalm 19 begins with a description of the heavens, and contains a tribute to the Sun:

1. The heavens declare the glory of God; and the firmament sheweth his handywork.
2. Day unto day uttereth speech, and night unto night sheweth knowledge.
3. There is no speech nor language, where their voice is not heard.
4. Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun,
5. which is as a bridegroom coming out of his chamber; and rejoiceth as a strong man to run a race.
6. His going forth is from the end of the heaven, and his circuit nto the ends of it : and there is nothing hid from the heat thereof.

Like the Mesopotamians, the Bible mentions waters above Heaven. Psalm 148 begins:

1. Praise ye the Lord. Praise ye the Lord from the heavens : praise him in the heights.
2. Praise ye him, all his angels : praise ye him, all his hosts.
3. Praise ye him, sun and moon : praise him, all ye stars of light.
4. Praise him, ye heavens of heavens, and ye waters that be above the heavens.
5. Let them raise the name of the Lord : for he commanded, and they were created.
6. He hath also established them for ever and ever : he hath made a decree which shall not pass.

The Hebrew month names, beginning with the Passover month, that formed in Jerusalem during this time were (Babylonian/Chaldean month names follow in brackets):

  1. Nisan or Nissan [Nisanu]
  2. Iyyar [Ayaru]
  3. Sivan [Simanu]
  4. Tammuz [Du'uzu]
  5. Av [Abu]
  6. Elul [Ululu]
  7. Tishri [Tashritu]
  8. Marcheshvan, later shortened to Cheshvan [Arach-Samna]
  9. Kislev [Kislimu]
  10. Teveth [Shabatu]
  11. Shevat [Tebetu]
  12. Adar [Adaru]

There are also some mentions of Orion, the Pleiades (Seven Sisters), and Arcturus in the Bible (although these translations are from the King James Version, and there is no universal agreement on translation of astronomical objects from the Hebrew). Job, Chapter 9 says:

1. Then Job answered and said, 2. I know it is so of a truth; but how should man be just with God?... 9. Which maketh Arcturus, Orion, and Pleiades, and the chambers of the south.
"Chambers of the south" could refer to southern constellations. Job, Chapter 38 contains a response from God:
1. Then the Lord answered Job out of the whirlwind, and said,... 32. Canst thou bring forth Mazzaroth [constellation] in his season? or canst thou guide Arcturus with his sons?
Amos 5:8 says:
Seek him that maketh the seven stars [Pleiades] and Orion, and turneth the shadow of death into the morning, and maketh the day dark with night...
Worship of the heavens was considered evil. 2 Kings, Chapter 21, tells how Manasseh, son of Hezekiah, turned toward the worship of evil:
2. And he did that which was evil in the sight of the Lord, after the abominations of the heathen, whom the Lord cast out before the children of Israel.
3. For he built up again the high places which Hezekiah his fatehr had destroyed ; and he reared up altars for Ba'al, and made a grove, as did Ahab king of Israel ; and worshipped all the host of heaven, and served them....
5. And he built altars for all the host of heaven in the two courts of the house of the Lord.
6. And he made his son pass through the fire, and observed times, and used enchantments, and dealt with familiar spirits and wizards : he wrought much wickedness in the sight of the Lord, to provoke him to anger.
Chapter 5 in the Book of Amos also condemns worship of the stars:
25. Have ye offered unto me sacrifices and offerings in the wilderness forty years, O house of Israel?
26. But ye have borne the tabernacle of your Moloch and Chiun your images, the star of your god, which ye made to yourselves.
27. Therefore will I cause you to go into captivity beyond Damascus, saith the Lord, whose name is The God of hosts.
In Jeremiah 10:2, the Lord dismisses "the signs of heaven":
Thus saith the Lord, Learn not the way of the heathen, and be not dismayed at the signs of heaven ; for the heathen are dismayed at them.

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The Macabees and the Dead Sea Scrolls. When Alexander the Great conquered new lands, he allowed local people to carry on their religious practices. Upon his death, his kingdom was divided among his generals. Judea (Israel) came under control of the Syrian General, Antiochus III.

When his son, Antiochus IV, became King of the Syrian Empire, he sought to impose the Hellenistic religion throughout his kingdom. He converted the Jerusalem Temple to the worship of Greek deities, and tried to eradicate Judaism.

When a similar desecration was about to happen in the Jewish temple of Modi'in, the priest Matthias slew the perpetrator and encouraged the people of the town to rise up against the Syrian armies. As Matthias was dying, he charged his son, Judas who was called Macabee (Vulgate, Liber I Macchabeorum 2:4: "Iudas qui vocabatur Macchabeus), to carry on his work.

Against unbelievable odds, on the 25th day of the ninth month of Kislev in the year 165 B.C.E. in the Julian proleptic calendar, Judah the Macabee ultimately attacked Jerusalem and drove out the Syrian armies. From that time on, Jews celebrated a new eight-day "Festival of Lights" to commemorate the Jerusalem Temple's restoration and the victory of the forces of "light" over the forces of "darkness." Today this celebration is known as Chanukah.

These events are recorded in the Biblical Books Macabees I and Macabees II. The King James Version Bible does not include these books. The Latin Vulgate Bible does (Liber I & II Macchabeorum). The Gospel According to St. John 10:22 refers to Chanukah as the Feast of the Dedication (of the new temple): "And it was at Jerusalem the feast of the dedication, and it was winter."

As the priestly Macabees rose to power, a rivalry developed with the Pharisees that was to continue into the days of the Roman Empire. Some of Dead Sea Scrolls of Qumran contain criticisms of the Pharisees and their practices, pointing to their possible origin with the Macabees.

The Dead Sea Scrolls include texts of the Priestly Courses (mishmarot), the schedule of 24 families rotating to serve for a week at the Temple of Jerusalem. The order for worship first began under King David as described in I Chronicles 24:7-18.

I Chronicles 1:31 mentions sacrifices for a new Moon: "And to offer all burnt sacrifices unto the Lord in the sabbaths, in the new moons, and on the set feasts, by number, according to the order commanded unto them, continually before the Lord..."

The Qumran calendar consists of 364 days, exactly 52 seven-day weeks. This allowed feasts to occur on the same day of the week every year.

At the same time, the existing luni-solar calendar year consisted of 12 months that alternated between 29 and 30 days, for a total of 6 x (29 + 30) = 354 days (ten days shorter than the Qumran solar calendar). However, every three years an extra 30-day month was added to this calendar. So in the luni-solar calendar, three years consisted of (3 x 354) + 30 days = 1092 days. Three years in the Qumran solar calendar was 3 x 364 = 1092 days, the same length. Therefore the Qumran solar calendar and the alternative luni-solar calendar coincided once every three years.

The Qumran texts also mention the importance of observation of the Moon's phases to correct the numerical formula if necessary.

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The Modern Hebrew Calendar. Today the world Jewish community uses a luni-solar calendar devised by Hillel II in 358 or 359 AD. The days begin at sundown and so are solar-based. The months begin with a new crescent Moon, and so are lunar-based. The year is determined by the position of the Sun, and so is solar-based.

The modern Hebrew calendar has 12 lunar months in a common year, with a thirteenth (intercalary) month in a leap year. Hillel II standardized each month to have 29 or 30 days. A month began with the first visible crescent Moon following a New Moon.

This calendar adopted the 19-year Metonic cycle, where leap years occur in years 3, 6, 8, 11, 14, 17, and 19. The present cycle (as of 2005) began on 2 October 1997. That date was the beginning of the 19-year Metonic cycle, and marked year 5758 in the Hebrew calendar.

The Hebrew month names and lengths are:

  1. Nisan (30 days)
  2. Iyyar (29 days)
  3. Sivan (30 days)
  4. Tammuz (29 days)
  5. Av (30 days)
  6. Elul (29 days)
  7. Tishri (30 days)
  8. Cheshvan (29 or 30 days)
  9. Kislev (29 or 30 days)
  10. Teveth (29 days)
  11. Shevat (30 days)
  12. Adar (29 days) in common years, Adar I (30 days) in leap years
  13. Adar II (29 days, leap year only)

There are three possibilities for the length of Cheshvan and Kislev. In a Deficient Year, Cheshvan and Kislev both have 29 days; this makes the common year 353 days, and the leap year 383 days. In a Regular Year, Cheshvan has 29 days and Kislev has 30 days; this makes the common year 354 days, and the leap year 384 days. In a Complete Year, Cheshvan and Kislev both have 30 days; this makes the common year 355 days, and the leap year 385 days.

In the modern Hebrew calendar, Passover begins on 15 Nissan (which starts after sundown on 14 Nissan — the "evening" as commanded by God) and ends on 22 Nissan. Reform Jews celebrate Passover for seven days; others begin a day earlier, celebrating for eight days.

The First Passover took place in the Spring. Intercalary (leap) months are inserted as needed so that Passover always occurs in the Spring. This event ties together the lunar and solar cycles of the modern Hebrew calendar.

Exodus 13:4 says, "This day came ye out in the month Abib." The modern Hebrew calendar uses the month names that Ezra gave them, adopting the month names of his birthplace in captivity in Babylon.

As in the days of ancient Babylon, an intercalary month (Adar II) was inserted when necessary according to the seasons. The 19-year Metonic cycle was not strictly followed if doing so would start Passover before the springtime.

The Hebrew civil year begins on Rosh Hashanah, the first day of Tishri. Leviticus Chapter 23 explains:

23. And the Lord spake unto Moses, saying, 24. Speak unto the children of Israel, saying, In the seventh month, in the first day of the month, shall ye have a sabbath, a memorial of blowing of trumpets, an holy convocation.... 27. Also on the tenth day of this seventh month there shall be a day of atonement... 34. Speak unto the children of Israel, saying, The fifteenth day of this seventh month shall be the feast of tabernacles for seven days unto the Lord.... 42. Ye shall dwell in booths seven days ; all that are Israelites born shall dwell in booths : 43. That your generations may know that I made the children of Israel to dwell in booths, when I brought them out of the land of Egypt : I am the Lord your God.
The seventh month is called Tishri in the modern Hebrew calendar. The tenth day, the day of atonement, today is called Yom Kippur. The Harvest Festival, Succoth, begins on Tishri 15 and lasts for seven days. This is also known as the Feast of the Tabernacle or the Festival of Booths (sukkot, temporary shelters Israelites built during their exodus from Egypt to Canaan).

Because the first seven months all have fixed lengths, Passover and Succoth are always the same number of days apart, even in years with an intercalary month (leap years).

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The Islamic Calendar. The Islamic (Hijri) calendar is purely lunar. There are 12 lunar months in the calendar year. This is an average of 354.36 days in a year (about 11 days short of the solar year), so this puely lunar calendar revolves through the seasons about once every 33 years.

The epoch of the Islamic calendar dates from the Hijri (the journey of Mohamed from Mecca to Medina). According to the Explanatory Supplement to the Astronomical Almanac, astronomers consider this first Islamic New Year date, 1 A.H. (Anno Higerae, or the Year of Hijri) Muharram 1, to be 16 July 622 (Julian Calendar). According to the Explanatory Supplement, the astronomical New Moon occurred (assuming ΔT=1.0 hour) on 14 July 622 (Julian) at 04:44 Universal Time. The Crescent Moon was therefore probably observed on the evening of 16 July 622 (Julian).

The Quran, Sura IX, 36-37 is the basis of the Islamic calendar:

36. Surely the number of months with Allah is twelve months in Allah's ordinance since the day when He created the heavens and the Earth, of these four being sacred; that is the right reckoning; therefore be not unjust to yourselves regarding them, and fight the polytheists all together as they fight you all together, and know that Allah is with those who guard (against evil). 37. Postponing (of the sacred month) is only an addition in unbelief, wherewith those who disbelieve are led astray, violating it one year and keeping it sacred another, that they may agree in the number (of months) that Allah has made sacred, and thus violate what Allah has made sacred; the evil of their doings is made fairseeming to them; and Allah does not guide the unbelieving people.
The practice in the Middle East at that time was to insert intercalary (leap) months to keep the Lunar months synchronized with the Solar seasons (and in fact the month names, dating to the days of Babylon, denote seasons). By his statement above, Mohamed forbade these intercalary months.

In the year 17 A.H. (638 Julian), Caliph `Umar I defined the Hijra Era and laid out the Islamic calendar.

The months in the Islamic calendar are:

  1. Muharram
  2. Safar
  3. Rabi' al-awwal (Rabi' I)
  4. Rabi' al-thani (Rabi' II)
  5. Jumada al-awwal (Jumada I)
  6. Jumada al-thani (Jumada II)
  7. Rajab
  8. Sha'ban
  9. Ramadan
  10. Shawwal
  11. Dhu al-Qi'dah
  12. Dhu al-Hijjah
The days of the seven-day week are numbered. They are:
  1. Yawm al-'ahad (Sunday, the first day)
  2. Yawm al-'ithnayn (Monday)
  3. Yawm ath-thalaathaa' (Tuesday)
  4. Yawm al-'arba`a' (Wednesday)
  5. Yawm al-khamiis (Thursday)
  6. Yawm al-jum'a (Friday)
  7. Yawm as-sabt (Satturday, the Sabbath Day)

The early Islamic community became keenly interested in accurate methods to predict the Crescent Moon. Circa 760 C.E., Caliph al-Munsur had the Indian astronomical text Surya Siddhanta translated into Arabic. The famous ninth-Century astronomer-mathematician al-Khwarizimi of Baghdad calculated tables of astronomical phenomena including phases of the Moon and the Crescent Moon using methods from the Surya Siddhanta. According to the Surya Siddhanta, the Crescent Moon becomes visible when it is at least 78° behind the Sun at sunset.

Around 900 C.E., several translations were made of Ptolemy's Almagest into Arabic.

These translations of the Surya Siddhanta and Almagest became the foundation of astronomical science in the early Islamic world. However, Islamic astronomers were keen observational astronomers and realized that the techniques in these older texts were not perfect. They endeavored to improve astronomical theory.

The most famous of these Islamic astronomers was the eleventh-Century astronomer al-Biruni. He named his treatise Canon. He accurately solved the problem of Qibla — the direction to face the kaaba in Mecca for prayers, creating tables for longitudes and latitudes in the Islamic world.

In Saudi Arabia, the government adopted astronomical calculations in 1999 C.E. In Saudi Arabia, on the 29th day of each month, the times of the setting Sun and the setting Moon at Mecca are compared. If the Moon sets before the Sun, the month is given a 30th day. If the Sun sets before the Moon, the month ends on this 29th day. This method generated some controversy, as the times of Moonset and sunset do not guarantee the visibility of the crescent Moon.

Effective 16 March 2002, Saudi Arabia added the refinement that in addition to the Moon setting after the Sun in Mecca, the geocentric New Moon also had to occur before sunset at Mecca. This is an improvement over the previous method, but still does not gurantee the visibility of the crescent Moon, and so there is still some controversy about this in the Muslim community.

Mecca is located in Saudi Arabia, at 39°45' East Longitude and 21°29' North Latitude.

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The Persian Calendar. The Persians developed astronomical science to a very high degree during Europe's Middle Ages.

One Persian astronomer, Omar Khayyam (1048-1131 C.E.), became known in the West initially though Edward Fitzgerald's translation of his book of poetry, the Rubaiyat. He was invited to Esfahan by the local Shah, and built an observatory there.

Omar Khayyam measured the year to be 365.24219858156 days long. This was probably accurate to five decimal places at the time, about a one-second accuracy — an unprecedented accomplishment in his day.

Knowing the length of the year to great precision, he joined a team of seven other astronomers to reform the calendar in 1079. The result of their efforts was the Jilaalii Calendar.

This was a solar calendar, with 12 months each of 30 days, followed by five days (just like the ancient Egyptian calendar), or by six days in a leap year. Like calendars of nearby India and parts of the Semitic areas, the year began at the Vernal Equinox.

The modern Persian calendar gives 31 days to the first six months, 30 days to the next five, and 29 days (30 in a leap year) to the last month. The month names are:

  1. Farvardiin (31 days)
  2. Ordiibehesht (31 days)
  3. Khordaad (31 days)
  4. Tiir (31 days)
  5. Mordaad (31 days)
  6. Shahriivar (31 days)
  7. Mehr (30 days)
  8. Abaan (30 days)
  9. Aazar (30 days)
  10. Dey (30 days)
  11. Bahman (30 days)
  12. Esfand (29 days, 30 in leap year)
In the modern calendar, a new year begins the day the Sun will traverse the equator from South to North after midday in Tehran, Iran 35°45' North latitude, 51°30' East longitude).

The leap year structure makes this calendar the most accurate in the world among those in common use. The calendar follows a cycle of 2820 years, composed of 21 cycles of 128 years followed by one cycle of 132 years (21 x 128 + 132 = 2820 years). A 128 year cycle consists of one 29 year subcycle followed by three 33 year subcycles (29 + 3 x 33 = 128 years). The 132 year cycle is divided into one 29 year subcycle, two 33 year subcycles, and one 37 year subcycle (29 + 2 x 33 + 37 = 132 years).

A leap year occurs when the year number in a subcycle is greater than 1 (the first year), and when divided by 4 gives a remainder of 1. So for example in a 29 year subcycle, the leap years are year numbers 5, 9, 13, 17, 21, 25, and 29. Thus a 29 year subcycle has 7 leap years; a 33 year subcycle has 8 leap years; and a 37 year subcycle has 9 leap years.

The total number of days in 2820 years is therefore

2820 x 365 + 21 x (7 + 3 x 8) + (7 + 2 x 8 + 9) = 1,029,983 days.
This gives an average year length of 1,029,983 / 2820 days per year, or 365.2419858 days per year. The length of the tropical year (equinox to equinox) at the epoch J2004.0 was 365.242190 days per year, a difference of about 0.00000858 days per year, an error of about 0.74 seconds per year. If the length of the year stayed constant, this calendar would be accurate to about one day in 116,529 years.

In comparison, the Gregorian calendar averages to 365.2425 days per year over a 400 year cycle (400 x 365.25 - 3 days per 400 years), and so is accurate to about one day every 3,226 years.

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