Lunar Calendar (Ancient Egypt)

Lunar calendar in hieroglyphics
	Animation of the moon phases

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There were two lunar calendars in ancient Egypt :

While the civil lunar calendar was based on the original Egyptian calendar ,
the astronomical Sothis lunar calendar was tied to very complex calculations and observations.

Both lunar calendars are mixed forms, as they cannot be classified as pure lunisolar and lunar calendars . The oldest documented mentions of lunar calendar dates can be found from around 2350 BC. In the pyramid texts . However, the use of astronomical records was already possible under King Wadji around 2880 BC. Documented.

Geminos of Rhodes described around 70 BC. The ancient Egyptian lunar calendar as a "peculiar principle, which the Egyptians, in contrast to other cultures, do not use to display their year. The holy feasts are important to you. This is what their calendars are based on ”. The Geminos Declaration aptly shows the mythological role of the ancient Egyptian lunar calendar, whose central function was limited to the dating of the heavenly festivals , while the Egyptian administrative calendar functioned as the annual calendar.

In the priesthood, the task was incumbent to put the firmament, the responsible astronomers that the to be celebrated days on the "head" ( "Greatest seer") by observations and calculations proclaim left. After the announcement, the actual date was noted in the administrative calendar and recorded in the respective temple diary .

Historical bases

So-called old light: The crescent moon 63 hours before the new moon. The dark part of the moon is clearly visible; the narrow crescent moon is overexposed.

The Egyptian term for months was "pesdjenet". Each month received an ordinal number , for example “pesdjenet 1”. In addition to the twelve main months, a thirteenth leap month was inserted if the first month began before the New Year of the civil calendar or the heliacal rise of Sirius.

In contrast to the other ancient oriental countries , the lunar month did not begin a short time after the new moon with the new light , but with the first day of not seeing the moon at dawn . The length of the period between old and new light depends , among other things, on the geographical location of the observation site. In southern latitudes of the northern hemisphere, the duration of the invisibility of the moon is shorter than in northern latitudes, which leads to longer observation phases of the moon in southern areas compared to northern regions.

The times of observation were also dependent on various other factors: the flatter the ecliptic , the earlier the moon reaches the minimum height and becomes invisible; the higher the ecliptic, the later the time of invisibility. Another factor is the lunar orbit inclined towards the ecliptic . Today's lunar orbit deviates from the ecliptic by 5.2 °. The points of intersection of the lunar and sun orbits move in the opposite direction to the moon's own motion. This observation was also made in what was then Egypt. In the Nile Delta region, the ecliptic reaches its greatest inclination with 83.7 ° at the autumn equinox , the lowest value with 36.3 ° in the spring equinox . The mean values of around 60 ° fall between January and July . Associated with this, between the end of September and the end of October, the duration of the invisibility of the moon is shortest; Converting to the shortest invisibility period between the last visible old light and the new moon results in around 16 hours in the Nile Delta region and around 10 minutes less in Elephantine . The longest period is between mid- March and mid- April , around 33 hours in the Nile Delta region.

If the new moon falls at 10 p.m. in September and October, the old light can still be seen at dawn on the morning of the same day, with new moons before 10 p.m. the last old light could mostly only be seen on the morning of Be observed the day before. If, on the other hand, the actual new moon occurs around 10 p.m. at the time of the winter and summer solstice , no crescent moon can be seen on the same day. The first day of the month in the ancient Egyptian lunar calendar could also be on the day after the new moon. Thirty-one day lunar months are therefore documented in several papyri .

January	February	March	April	May	June	July	August	September	October	November	December
Period of invisibility of the moon between the old light and the new moon in the Memphis region
23 hours	26 hours	30 hours	33 hours	29 hours	26 hours	22 hours	20 hours	17 hours	16 hours	17 hours	20 hours

First and second lunar month day

Djehuti was the first month in the lunar calendar from the 19th dynasty

The ancient Egyptian lunar month always began with sunrise , analogous to the ancient Egyptian day , whereby the first non-sighting of the crescent moon after the last altar light fell in the twelfth hour of the previous day. Just as the sun god Re " renewed " himself on the night of his invisibility , in ancient Egyptian mythology the first lunar day also symbolized the "day of the renewal of Horus " with the subsequent "birth", which began on the first night of the first lunar day was completed with sunrise on the second lunar day of the month. The last sighting of the old light usually represented the last day of the lunar month.

In the coffin texts , the second lunar day of the month is considered "the day on which the moon is small". A Ptolemaic text from the Khonsu Temple in Karnak describes the first two lunar month days ". The moon is received on the day of invisibility and born on the second Mondmonatstag" From the Pyramid Texts of the Old Kingdom , it appears that the second Mondmonatstag with the " sky rise of deceased king "was connected as" coronation and apparition day ":" Your appearance belongs to the second lunar day of the month ".

Error in observing the moon

Moon data that is based on observation can lead to a short-term error rate of one day in poor visibility or weather-related invisibility. If an ancient Egyptian observer was faced with this problem due to bad weather, he only had the option of estimating or looking at written records in the form of moon tables. The synodic period is also subject to fluctuations in time; compared to the mean in ancient Egypt up to about 6.5 hours. This fact leads to smaller deviations within the lunar cycles .

A wrong assessment corrected itself in the following months and was corrected with the next Altlicht recordings. The update of the error was not possible from a statistical point of view and therefore had no influence on the long-term entries. Comparisons of ancient Egyptian data with the astronomical values resulted in an agreement of 85% and corresponds to the reliability rate of the new light sightings in Mesopotamia .

Falsification tendencies in lunar data

In ancient Egypt, deliberate falsifications of calendar moon observations are not known, since no uncomfortable cultic laws were attached to certain phases of the moon . There are no indications of the inclusion of individual additional days for calendar correction and were unknown in the Egyptian calendars until the Canopus Decree . There is also a lack of evidence of incorrect information in the calendars to subsequently link special religious events with important phases of the moon. Assumptions that the date of the Megiddo battle under Thutmose III. was subsequently postponed to the new moon day, could not be proven so far and cannot be reconciled with the existing moon tables.

Holidays

The following days were considered special days in the lunar calendar, which the Egyptians celebrated as lunar festivals every month:

1st day: New moon, "death and day of renewal" of Horus
Day 2: Birth of Horus
Day 6: Day before half moon (" Senut ")
Day 7: half moon
Day 15: Full moon (" Unification Festival ")
Day 22: half moon

The civil lunar calendar

In the civil lunar calendar is one of the change year -bonded synodisches lunar year, which by the natural seasons wandered. The earliest beginning was the 1st Achet or the following day.

Presumably the civil lunar calendar was developed together with the astronomical calendar at the beginning of the 3rd millennium BC. Introduced. The first clear indications of use can be found in the Middle Kingdom , since the Egyptian festivals " Chenep-scha " and " Menchet ", which are mentioned in the Al Lahun papyri , are probably linked to the civil lunar calendar. This form of the year can only be proven with certainty in the New Kingdom .

From the Greco-Roman period at the latest, a schematic data cycle was introduced that was no longer related to direct observation of the moon.

Lunar cycles

The Egyptian calendar length of 365 days was very suitable for calculating and planning religious festivals, as the associated lunar cycles ( lunations ) made a clear calculation possible.

25-year cycle

Period	Cycle duration	Egyptian days	Lunar months	Lunar days	deviation	1-day shift
25-year cycle in the ancient Egyptian civil lunar calendar (period 3000 to 1 BC)
3000-1500 BC Chr.	25 years	9,125	309	9,124,9563	0.0437 days (1 h 3 min)	after 572.44 Egyptian years
1500-1 BC Chr.	25 years	9,125	309	9.124.9545	0.0455 days (1 h 5 min)	after 549.45 Egyptian years
3000-1 BC Chr.	25 years	9,125	309	9,124.9554	0.0446 days (1 h 4 min)	after 560.54 Egyptian years

As a result, the lunar month days in the Egyptian calendar fell on the same day after 25 years. The deviation was so small that a one-day change did not occur until the 23rd cycle. The astronomers only had to record the observations once for the first 25 years in order to have a calculation scheme for at least the next 21 cycles.

Leap cycle and leap years

In the 25-year period, nine leap months were necessary to ensure that the first day of the lunar year fell on the first day or the following days of Achet in the Egyptian administrative calendar. Because of the additional month, the respective leap years were named " Big Year ", which is already used more often in the Middle Kingdom . Accordingly, the year without leap months was considered a " Little Year ".

A schematic 25-year switching cycle was only introduced very late. The Papyrus Carlsberg 9 contains a circuit diagram for a period of 25 years, which shows the beginning of the lunar months in the Egyptian administrative calendar. The papyrus was not written before 144 AD. The original artwork could date back to the fourth century BC. And refers, among other things, to the switching cycles from 19 AD, the sixth year of reign under Tiberius , to the seventh year of reign in 144 AD under Antoninus Pius . The leap months were set to years 1, 3, 6, 9, 12, 14, 17, 20 and 23 in the switching scheme.

The switching calendar only listed the dates for every other month in order to compensate for any changes in rhythm. The 25-year cycle probably began with the 1st Thoth . The Ptolemies adopted the cycle in the third century BC. And added a day to the date noted in it. In this context, Otto Neugebauer established a connection between the cycle dates and the beginning of the Egyptian lunar months in the fourth century BC. BC, although the difference in the time difference by one day also means that it was dated to the fifth century BC. Chr. Allows. It is a matter of controversy whether the switching scheme was adopted during the rule of the Achaemenid Empire .

Other cycles

Cycle duration	Egyptian days	Lunar months	Lunar days	deviation	Cycle period
Other monthly cycles in the civil lunar calendar (period 3000 to 1500 BC)
14 years	5,110 days	173 lunations	5,108.794 days	minus 1.206 days	about 4,237 years
11 years	4,015 days	136 lunations	4,016,162 days	plus 1.162 days	about 3,455 years

The Sothis lunar calendar

Sirius as a signal generator for the new lunar year in the Sothis lunar calendar

The provisions of the Sothis lunar calendar were similar to those of the civil lunar calendar. The synodic lunar year was tied to the heliacal rising of Sirius. The coupling to Sirius brought about a relative constancy of the seasons, since the heliacal rise of Sirius from the end of the 5th to the beginning of the 3rd millennium BC. Chr. Slowly migrated from June 3rd to June 15th.

The Sothis lunar calendar is already documented in the Middle Kingdom. The knowledge of the constant feast days of the Old Kingdom , which continued unchanged in later times and were linked to the Sothis lunar calendar, make an existence before the early dynastic period seem possible, although archaeological evidence for this is lacking.

Around the year 2755 BC. At the time of the Sechemib , the rare event occurred that both the arrival of the Nile flood in the delta, the heliacal rising of Sirius in Memphis and the New Year's day of the Sothis lunar calendar fell on Achet I (June 19) .

Switching rule

Richard Anthony Parker suspects that the first lunar month began at least eleven days after Sothis rise; If the new moon fell before the eleventh day or at the time of the rising of Sothis, an additional lunar month was switched. Parker further assumes that the goal was to always have the Sothis rise fall in the twelfth lunar month . Parker explains the eleven-day difference after Sothisrise with the same difference between the solar and lunar years . According to Parker's hypothesis, the switching rule he adopted includes lunar year lengths of 354 or 385 days, which in the arithmetic mean lead to a 365-day lunar year.

The theory Parker raises technical questions that in the Egyptology in part, led to rejections of this switching control, especially as the crucial question could not be answered satisfactorily so far: Parker's approach is based on the assumption that a year was known of 365 days. However, it is questionable how such a rule should work without a 365 day year beforehand. In addition, in the otherwise known lunar calendars, a thirteenth month was switched to a 365-day year without any mathematical reference. On the other hand, the ancient Egyptian calendar was initially the only calendar that knew a year of 365 days, which is why there are no comparisons.

In addition, Egyptologists refer to the lack of evidence that clearly confirms Parker's switching rule, since the ancient Egyptian records he used also allow other procedures. The practice used in the Old Kingdom of assigning the five intervening days of the Egyptian administrative calendar and the day of the rising of Sothis to the new year “as days before the 1st Achet I ” speaks against Parker's “target”, at least in the Old Kingdom, of always rising Sothis in the twelfth Wanting to move a month.

19-year cycle

The Sothis cycle duration depends on the geographical observation point . For the ancient Egyptian places in question, the Sothis periods show differences, but these only have a long-term effect in the lunar cycles. In contrast to the civil lunar calendar, the lunar month days in the Sothis lunar calendar fell on the same day every 19 years.

Observation site	1 Sothis year	19 Sothis years	235 lunar months	deviation	1-day shift
Sothis lunar cycle (period 2770 to 1500 BC)
Nile Delta	365.2500098 days	6939.7502 days	6939.6917 days	0.0585 days	after about 325 years
Memphis	365.2500103 days	6939.7502 days	6939.6917 days	0.0585 days	after about 325 years
Elephantine	365.2500217 days	6939.7504 days	6939.6917 days	0.0587 days	after about 324 years

The 19-year cycle with the lunar months shifted by one day at the earliest after 324 years. The comparison to the civil lunar calendar shows a higher dynamic in the Sothis lunar calendar. A simple forecast was nevertheless possible for several pharaohs' reigns. For example, the calculation scheme for the lunar month days at the end of the 12th dynasty (1793 BC) when the 18th dynasty was founded (1550 BC) was still valid in the existing 19-year cycle period. Planning the religious festivals turned out to be easier in the Sothis lunar calendar, as there were only 18 instead of 24 shifts within the Sothis lunar cycle. Compared to the later nineteen-year Meton cycle , the Sothis lunar cycle in ancient Egypt was somewhat more precise.

Ancient Egyptian records and lunar data analysis

Al-Lahun papyri lunar dates

In Al-Lahun , locals found fragmentary papyri that they offered for sale at the art market in 1899 to Ludwig Borchardt , who a short time later acquired the records on behalf of the Egyptian Museum in Berlin . On the papyri, among other things, dates of the lunar calendar are written down, some of which Borchardt published for a short time as Papyrus Berlin . Due to the naming of kings and officials, the papyri could be dated to the late 12th Dynasty in the Middle Kingdom .

In addition to the indication of the heliacal rise of Sirius in the seventh year of the reign of Sesostris III. Entries of fixed dates in connection with lunar month entries from temple diaries have been preserved. The Sirius date made it possible to assign the lunar dates to the kings Sesostris III. and Amenemhet III. which is why the Al-Lahun papyri are of great importance in their role as a reliable chronological support of ancient Egyptian history.

Other mentions of lunar dates

In the New Kingdom , various lunar dates are known in the ancient Egyptian administrative calendar; more rarely, however, the days of the new moon. Thutmose III. calls for example during his preparations for the battle of Megiddo the "day of the new moon festival". In addition, isolated lunar dates from coronation and celestial festivals are documented. In connection with the records of the year of the reign of the respective kings, the logged lunar data are helpful, but without being able to reliably confirm a specific year in the previously available chronology of the New Kingdom if other parallel names of events are missing.

In the late and Greco-Roman times , on the other hand, precise temporal assignments can be made, since the corresponding ancient Egyptian lunar dates are confirmed by calendar new moon entries of other cultures; for example for the year 432 BC A parapegma mention in connection with the Attic calendar .

Astronomical lunar dates

Lengths of the tropical year (solar year).

Precession motion of the earth

The precession and the slowing down of the earth's rotation cause the duration of a synodic month and a solar year to change , which is why the current values cannot be included in historical calculations. Mathematicians and astronomers such as Jean Meeus , Fred Espenak and most recently LV Morrison and FR Stephenson were able to carry out more precise calculations based on historical evaluations. Compared to earlier dating models , there were deviations that are known as the " astronomical delta T ". The changed values are meanwhile also used in NASA's calculation programs.

The ancient Egyptian chronology is based to a not inconsiderable degree on calendar assignments of the Sothis and moon dates. As a reference point used by most Egyptologists Memphis next to the Censorinus -Date in Sothic cycle chosen as the basis for calculation. At the same time, the lunar dates were transferred to the ancient Egyptian calendar system, whose classification was also only made on the basis of the reference location Memphis and the Censorinus records. Another possible "source of error" is the assignment of the first lunar day to the day. In Egyptology , the old calculation models or calculation values from the records of various Egyptologists , whose first publications can date back to 1937, are currently still being used.

Winfried Barta published several new moon values in 1980; for example the astronomical new moon for November 22nd (Julian date) in the year 1353 BC. Chr. For 6:48 o'clock, however without taking into account the changed moon rise times. Barta took the results of his calculations as an opportunity to postulate the day of the astronomical new moon as the “first day of the lunar month” . According to new research by Rita Gautschy, Barta's calculations regarding the astronomical new moon are correct. However, there was only a very short period of visibility of a few minutes for the previous day. A safe old light sighting can therefore not be confirmed for this day. It is possible that November 21st acted as the first lunar day of the month. The last unequivocal old light sighting can only be confirmed for November 20th. The calculation differences of other Egyptologists are for the period of the 14th century BC. Around nine hours and in some cases lead to incorrect assignments of the new moon days, which in turn can lead to a wrong setting of a regency period. In addition, in older specialist literature, the beginning of the day is often equated with the dawn before sunrise, although in Egyptian mythology the twelfth hour of the night is assigned to the heliacal rising. In addition, the beginning of the first hour of the day is defined in the groove book , among other things :

“This is how [the command] arises that he (Re) departs to heaven, in the 'hour that satisfies' (1st hour of the day). So his figure becomes strong and tall. At night the ( dean's stars as) bas emerge in the sky while driving. The dean stars follow Re as he rises in the "hour that satisfies". During the day they are not visible to people. "

- Nutbuch, Sethos I - script:

Due to unclear statements in the Almagest , numerous Egyptologists interpreted the information there in the older specialist literature as evidence that the first lunar day of the month was to be connected with dawn. More recent investigations are also based on other ancient Egyptian texts which, as Alexandra von Lieven found, place the beginning of the first lunar day at the time of sunrise. The different calculation methods in the specialist literature sometimes lead to different dates of the first lunar day of the month. In this context, Siegfried Schott and Rolf Krauss refer to possible changes to the calendar system and emphasize that the previous, older chronological lunar data assignments can lose their validity, which leads to partial changes in the reign of the ancient Egyptian kings.

literature

Leo Depuydt : The demotic mathematical Papyrus Carlsberg 9 reinterpreted . In: Willy Clarysse, Antoon Schoors, Harc Willems: Egyptian religion: The last thousand years; Studies dedicated to the memory of Jan Quaegebeur (Festschrift) . Peeters, Leuven 1998, ISBN 90-429-0669-3 .
Rolf Krauss : Sothis and moon dates: studies on the astronomical and technical chronology of ancient Egypt. Gerstenberg, Hildesheim 1985, ISBN 3-8067-8086-X .
Jean Meeus , Denis Savoie: The history of the tropical year. In: The journal of the British Astronomical Association. Vol. 102, No. 1, 1992 ( bibcode : 1992JBAA..102 ... 40M ).
Jean Meeus: Astronomical Algorithms - Applications for Ephemeris Tool 4.5 , Barth Leipzig 2000, ISBN 3-335-00400-0 , calculation program Ephemeris Tool 4.5 .
Jean Meeus: More Mathematical Astronomy Morsels. 1st English edition, Willmann-Bell, Richmond VA 2002, ISBN 0-943396-74-3 .
Otto Neugebauer : A history of ancient mathematical astronomy . Springer, Berlin 2006 (reprint 1975), ISBN 3-540-06995-X , pp. 563-565.
Richard Anthony Parker : Egyptian Astronomy, Astrology and calendrical reckoning. In: Charles-Coulson Gillispie: Dictionary of scientific Biography (= American Council of Learned Societies. Vol. 15, Supplement 1). (Roger Adams, Ludwik Zejszner: Topical essays. ) Scribner, New York 1978, ISBN 0-684-14779-3 , pp. 709-710.
Richard Anthony Parker: The calendars of ancient Egypt. Chicago Press, Chicago 1950.
Siegfried Schott: Ancient Egyptian festival dates. Publishing house of the Academy of Sciences and Literature, Mainz / Wiesbaden 1950
Alexandra von Lieven : Floor plan of the course of the stars - the so-called groove book . The Carsten Niebuhr Institute of Ancient Eastern Studies, Copenhagen 2007, ISBN 978-87-635-0406-5 .

Web links

Joachim Friedrich Quack: Between sun and moon - time calculation in ancient Egypt , original publication in: H. Falk (ed.), From the ruler to the dynasty. On the nature of continuous calculation of time in antiquity and the present , Bremen 2002, pp. 27–67, pdf.

Remarks

↑ Values deviating from today's value of 29.530589 days, because the earth's precession is taken into account .
↑ The period from 3000 to 1500 BC Chr. Based average lunar month length of 29.530603 days.
↑ The period from 1500 to 1 BC Chr. Based average lunar month length of 29.530597 days.
↑ The period from 3000 to 1500 BC Chr. Based average lunar month length of 29.5306 days.
↑ The date of June 19, 2755 BC. In the Gregorian calendar corresponds to July 18 in the proleptic calendar.

Individual evidence

↑ ^a ^b PT 794B; 1260A; 1711B; see. Winfried Barta In: Studies on Ancient Egyptian Culture (SAK) 8 . Buske, Hamburg 1980, p. 47.
↑ Geminus, Isagoges , S. 107th
^ Siegfried Schott: Ancient Egyptian festival dates . P. 47.
↑ ^a ^b Rolf Krauss: Sothis and moon data: studies on the astronomical and technical chronology of ancient Egypt . Pp. 22-23.
↑ Winfried Barta In: Studies on ancient Egyptian culture (SAK) 8 . Buske, Hamburg 1980, p. 39.
^ Rainer Hanig: Large Concise Dictionary Egyptian-German: (2800–950 BC) . von Zabern, Mainz 2006, ISBN 3-8053-1771-9 , p. 774.
^ Richard-Anthony Parker: The calendars of ancient Egypt . § 281.
↑ ^a ^b ^c ^d ^e Jean Meeus: Astronomical algorithms . Willmann-Bell, Richmond 2002, ISBN 0-943396-61-1 , p. 194.
↑ Rolf Krauss: Sothis and moon data: Studies on the astronomical and technical chronology of ancient Egypt . P. 27.
↑ Rolf Krauss: Sothis and moon data: Studies on the astronomical and technical chronology of ancient Egypt . P. 16.
^ Jean Meeus: Astronomical Algorithms - Applications for Ephemeris Tool 4.5 , Barth, Leipzig 2000 for: Ephemeris Tool 4.5 according to Jean Meeus, conversion program, 2001 .
^ LV Morrison, FR Stephenson: Historical Values of the Earth's Clock Error Delta T and the Calculation of Eclipses . Pp. 327-336.
↑ NASA: Calculation values Delta T by Jean Meeus, Fred Espenak, L. Morrison and FR Stephenson .
↑ Winfried Barta In: Studies on ancient Egyptian culture (SAK) 8 . Buske, Hamburg 1980, p. 42.
^ Rita Gautschy: Project moon data and eclipses: application of astronomical chronology in the ancient sciences ( moon data from the archive of Illahun: Chronology of the Middle Kingdom) . Journal of Egyptian Language and Antiquity 178, Vol. 1. 2011.
↑ NASA values ( memento from March 23, 2008 in the Internet Archive ).
↑ Alexandra von Lieven: Plan of the course of the stars. Pp. 55-57.

This version was added to the list of articles worth reading on July 2, 2009 .

[8] Values deviating from today's value of 29.530589 days, because the earth's precession is taken into account .

[9] The period from 3000 to 1500 BC Chr. Based average lunar month length of 29.530603 days.

[11] The period from 1500 to 1 BC Chr. Based average lunar month length of 29.530597 days.

[12] The period from 3000 to 1500 BC Chr. Based average lunar month length of 29.5306 days.

[15] The date of June 19, 2755 BC. In the Gregorian calendar corresponds to July 18 in the proleptic calendar.

[B47-1] PT 794B; 1260A; 1711B; see. Winfried Barta In: Studies on Ancient Egyptian Culture (SAK) 8 . Buske, Hamburg 1980, p. 47.

[2] Geminus, Isagoges , S. 107th

[3] Siegfried Schott: Ancient Egyptian festival dates . P. 47.

[K22-4] Rolf Krauss: Sothis and moon data: studies on the astronomical and technical chronology of ancient Egypt . Pp. 22-23.

[5] Winfried Barta In: Studies on ancient Egyptian culture (SAK) 8 . Buske, Hamburg 1980, p. 39.

[6] Rainer Hanig: Large Concise Dictionary Egyptian-German: (2800–950 BC) . von Zabern, Mainz 2006, ISBN 3-8053-1771-9 , p. 774.

[7] Richard-Anthony Parker: The calendars of ancient Egypt . § 281.

[M194-10] Jean Meeus: Astronomical algorithms . Willmann-Bell, Richmond 2002, ISBN 0-943396-61-1 , p. 194.

[13] Rolf Krauss: Sothis and moon data: Studies on the astronomical and technical chronology of ancient Egypt . P. 27.

[14] Rolf Krauss: Sothis and moon data: Studies on the astronomical and technical chronology of ancient Egypt . P. 16.

[16] Jean Meeus: Astronomical Algorithms - Applications for Ephemeris Tool 4.5 , Barth, Leipzig 2000 for: Ephemeris Tool 4.5 according to Jean Meeus, conversion program, 2001 .

[17] LV Morrison, FR Stephenson: Historical Values of the Earth's Clock Error Delta T and the Calculation of Eclipses . Pp. 327-336.

[18] NASA: Calculation values Delta T by Jean Meeus, Fred Espenak, L. Morrison and FR Stephenson .

[19] Winfried Barta In: Studies on ancient Egyptian culture (SAK) 8 . Buske, Hamburg 1980, p. 42.

[20] Rita Gautschy: Project moon data and eclipses: application of astronomical chronology in the ancient sciences ( moon data from the archive of Illahun: Chronology of the Middle Kingdom) . Journal of Egyptian Language and Antiquity 178, Vol. 1. 2011.

[21] NASA values ( memento from March 23, 2008 in the Internet Archive ).

[22] Alexandra von Lieven: Plan of the course of the stars. Pp. 55-57.