ANCIENT EGYPTIAN GEODESY

The diagonal line from Memphis to Abu Roash extends to Alexandria on the northwestern edge of the Nile delta. Just as this line from Alexandria to Giza is 51.85° south of due east, the line from Port Said to Giza is 51.85° south of due west. The Port Said-Alexandria-Giza triangle has the same angular dimensions as the Great Pyramid.

The base lengths of the Great Pyramid are 440 cubits. The height is 280 cubits and the apothem (the slant height of the faces) is 356 cubits. Converted to miles, the base length is .143 miles and the slant height is .116 miles. The distance from Giza to the Port of Alexandria is just under 116 miles and the distance from Giza to Port Said is also just under 116 miles. The distance from Port Said to Alexandria is just under 143 miles. The triangle inscribing the Delta in the illustration below has the same angular dimensions and is precisely 1,000 times larger than the Great Pyramid.

The apex of the triangle is located at Giza and the two corners are a couple of miles beyond Port Said and Alexandria. As shown by the bathymetric image, the Mediterranean Sea is very shallow just beyond the delta. Prior to the final meltdown from the last Ice Age approximately 7,500 years ago, the corners of this triangle were above sea level.

Underwater ruins have recently been discovered in the immediate vicinity of the northwest corner, just outside the Port of Alexandria. All of the points along the arc in the diagram are 116 miles from Giza, 1,000 times the length of the apothem of the Great Pyramid. Textual evidence from ancient Egyptian sources refers to a predynastic capital city known as Behdet, located near the shoreline in the middle of the delta. This city has not been found in modern times and may also be located just beyond the shoreline, 116 miles from Giza.

The length of the apothem of the Great Pyramid and the length of the sides of the triangle that inscribe the delta are also precise measures of the circumference of the earth, in relation to the precession of the equinoxes. One full cycle of precession takes 25,776 years. The average length of each of the 12 astronomical ages is 2,148 years:

25,776 years ÷ 12 = 2,148 years

356 cubits converts to 611.73 feet and this converts to .11586 miles:

356 cubits x 20.62 ÷ 12 = 611.73 feet

611.73 feet ÷ 5,280 = .11586 miles

.11586 miles x 2,14800 = 24,887 miles

356,000 cubits converts to 115.86 miles.

115.86 miles x 214.8 = 24,887 miles

24,887 miles is a precise expression of the circumference of the earth.

Alexandria is located at 30° 00' east longitude and Port Said is located at 32° 19' east longitude. Halfway between the two, the Great pyramid is located at 31° 09' east longitude. The longitude of the Great pyramid was regarded as the prime meridian in the remote past. More recently, the rose line that runs through Paris, France was regarded as the prime meridian and presently the longitude of Greenwich, England is regarded as the prime meridian. Paris is located at 2° 19' east longitude. Just as 2° 19' of longitude separates Alexandria from Port Said, 2° 19' of longitude also separates Greenwich from Paris.

Luxor (Thebes) became the capitol of ancient Egypt after Memphis and remained an important monumental city throughout dynastic Egypt. Located at 25° 42' N, the distance from Luxor to the equator is one-fourteenth of the circumference of the earth:

360° ÷ 14 = 25° 42'

The traditional southern border of dynastic Egypt was marked by the first cataract of the Nile and the monumental city of Philae, at 24° 00' N. The distance from Philae to the equator is one-fifteenth of the circumference of the earth:

360° ÷ 15 = 24° 00'

At Nabta Playa, astronomically aligned megalithic stone circles have been dated to 4,000 B.C. Located at 22° 30' N, the distance from the equator to Nabta is ¼ of the distance from the equator to the north pole. The distance from the equator to Nabta is is also one-sixteenth of the circumference of the earth:

90° ÷ 4 = 22° 30'

360° ÷ 16 = 22° 30'

Giza is six degrees north of Philae. Six degrees is 1/15th of the distance from the equator to the north pole. Six degrees is also 1/60th of the circumference of the earth:

90° ÷ 15 = 6°

360° ÷ 60 = 6°

Eratosthenes was born in Cyrene (now Shahhat, Libya) around 276 B.C. and after studying in Alexandria and Athens he became the third director of the Library of Alexandria. He is presently referred to as the father of geodesic science and the first man to measure the earth, but in his own day his nickname was Beta, which means second. Eratosthenes' works have been lost although the titles of his major works have come down to us from secondary sources, such as his treatise On the Measurement of the Earth.

Eratosthenes heard (or read) that at noon on the summer solstice the sun shined directly into a deep well near the southern border of ancient Egypt in the city of Syene, marking the latitude of Syene as the Tropic of Cancer. Eratosthenes reported that Syene and the Tropic of Cancer were located at 23° 51' north latitude. He also reported that in Alexandria at noon on the summer solstice the sun cast a shadow with an angle of 7° 12'. This led Eratosthenes to believe that Alexandria was 7° 12' north of Syene, at 31° 03' north latitude. Eratosthenes understood that 7° 12' is 1/50th of 360°, thus 1/50th of the circumference of the earth, so he concluded that the distance from Syene to Alexandria was 1/50th of the circumference of the earth.

Eratosthenes reported that Syene was due south of Alexandria on the same meridian, and he reported that the distance from Syene to Alexandria was 5,000 stadia. The stadia that Eratosthenes referred to is in dispute. The most widespread view is that he was referring to a Greco/Roman stadia of 600 Roman feet. This stadia times 5,000 times 50 is about 15% longer than the actual circumference of the earth, which most commentators regard as a good estimate for Eratosthenes' day.

Syene is actually located at 24° 06' north latitude. The Tropic of Cancer was located at 23° 51' north latitude during the dynastic period of ancient Egypt, but by the time of Eratosthenes the tropic had moved down to 23° 45' north latitude. The sun shines directly down on an area of the earth covering one-half of one degree of latitude. When the Tropic of Cancer was at 23° 51' N, the northern edge of the sun at noon on the summer solstice would have shined directly down into the well at Syene, one-quarter of one degree north of the Tropic of Cancer. In Eratosthenes' day, the tropic had moved too far south for the sun to shine directly down into the well at Syene.

Alexandria is actually located at 31° 12' north latitude. Since the tropic was at 23° 45' north latitude in Eratosthenes' day and since the northern edge of direct downward sunlight is an additional one-quarter of one degree north, the northern edge of direct downward sunlight on the summer solstice in Eratosthenes' day would have been at 24° 00' north latitude and the angle of the shadow cast by the northern edge of the sun at noon on the summer solstice in Alexandria would have been 7° 12', just as Eratosthenes reported.

Syene is actually almost three full degrees of longitude east of Alexandria The distance from Syene to Alexandria is not 5,000 stadia regardless of what stadia is employed, because Syene is so far east of Alexandria. The reason Eratosthenes got the latitude for Alexandria wrong was because he was basing the difference on an incorrect assumption about the latitude of Syene, an incorrect assumption about the latitude of the tropic and because he was unaware that the sun shines directly down on an area one-quarte of one degree north of the tropic.

 Although the distance from Alexandria to Syene is not equal to 1/50th of the circumference of the earth, the distance from the latitude of Alexandria to the latitude of Philae, six minutes south of Syene at the southern border of ancient Egypt, is equal to 1/50th of the circumference of the earth (7° 12'). According to Livio Stecchini, the ancient Egyptians employed a stadia of 300 cubits, although this measure was not in use during Eratosthenes' day. The ancient Egyptian cubit of 20.62 inches, times 300, times 5,000 equals 488 miles. The distance due north-south from the latitude of Alexandria to the latitude of Syene is 488 miles.

Modern scholars say it is a happy coincidence that all of Eratosthenes' errors tended to cancel out, resulting in a fairly accurate measure of the circumference of the earth, even though most of his data and calculations were wrong. All of this suggests that Eratosthenes did not stray too far from accurate conclusions because he already knew from fragmentary records in the Library of Alexandria that the boundaries of ancient Egypt had originally been set at 1/50th of the circumference of the earth and that the distance from the latitude of Alexandria to the latitude of Syene was 1,500,000 cubits or 5,000 ancient Egyptian stadia. If Eratosthenes acknowledged this, it could explain the loss of all of his works even though other Greek works from before, during and after his time have survived.

Although the city of Akhenaten at Amarna was already in ruins by the time of Eratosthenes, modern excavations indicate that the southern boundary of Amarna was close to 27° 36' north latitude, precisely half-way between the latitude of Alexandria and the latitude of the southern border of ancient Egypt at Philae. The southern boundary of Amarna is 3.6° south of Alexandria, precisely 1/100th (one percent) of the 360° circumference of the earth. The southern boundary of Amarna is 3.6° north of Philae, also precisely 1/100th (one percent) of the 360° circumference of the earth.

Written around 440 B.C., chapter two of The Histories of Herodotus contains the following statement:

"From Heliopolis to Thebes is nine days' sail up the river; the distance is eighty-one schoenes, or 4860 furlongs. If we now put together the several measurements of the country we shall find that the distance along shore is, as I stated above, 3600 furlongs, and the distance from the sea inland to Thebes 6120 furlongs. Further, it is a distance of eighteen hundred furlongs from Thebes to the place called Elephantine."

Located in the middle of the Nile, Elephantine Island was a part of the ancient city of Syene. The deep well at Syene that Eratosthenes mentions is on Elephantine Island. 6120 furlongs from the sea to Thebes, plus 1800 furlongs from Thebes to Elephantine, equals 7920 furlongs from the southern border of Egypt to the sea. This is the same number as the measure of the diameter of the earth in English miles.

The length of the ancient Egyptian schoene was 12,000 cubits. Herodotus says that 81 schoenes is equal to 4860 furlongs. This is a ratio of 60:1. 1/60th of 12,000 cubits is 200 cubits, or 300 ancient Egyptian feet, for the furlong used by Herodotus. At 20.62 inches or 1.7183333 English feet per cubit, 200 cubits is 343.6666 English feet. 7920 of these furlongs is 2,721,840 English feet, or 515.5 miles. The distance, due north-south, from the northern coast of the delta at 31° 33' N, to the latitude of Syene/Elephantine ( 24° 6' N), is also 515.5 miles. However, the distance along the Nile from the northern shore of Egypt to Elephantine is much longer because of the twists and turns of the Nile. Even as the crow flies, the distance from the northern edge of the delta to Elephantine is considerably longer because Elephantine is about two degrees further east than the northernmost point of the delta.

In the modern era, the ability to accurately measure long distances along the same longitude only became possible with the advent of accurate chronometers in the 18th century A.D. It would have been impossible for Herodotus to accurately measure the length of Egypt from north to south, along the same longitude, by sailing up the Nile as he suggests. Like Eratosthenes, the accuracy of Herodotus' report suggests that his information came from older and more advanced sources.

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(2009-12-11)     The [First] Theorem of Thales
The  fundamental  theorem of (classical) geometry.

Quand l'ombre de l'homme sera égale à l'homme,
l'ombre de la Pyramide sera égale à la Pyramide.
 Bernard Lefèbvre,  lecturing on  Thales  (1973)

Thales of Miletus  was born in the seventh century BC.  An engineer by trade, he is the first of the  Seven Sages of Greece.  Thales is credited with the first rational speculations about Nature  (natural philosophy).

The advent of natural philosophy was a fundamental step on the way to a real understanding of Nature, compared to the primitive approach of "explaining" everything by divine intervention  (a viewpoint which is arguably still with us, unfortunately).  This became  modern physics  only with the revolutionary introduction of the  scientific method  of comparing speculations and observations!

Thales is also touted as the founder of  classical geometry,  although some of it predates him  (including the construction with straightedge and compass of the circle circumscribed to a triangle, by the Phrygian mathematician Euphorbus).

Legend has it that Thales was asked to tell the height of the  Pyramid  (possibly, the Pyramid of Cheops).  His answer came down to me  (via my high-school philosophy teacher)  in the eloquent form quoted at the beginning of this section.  Consider the  shadow  of the Pyramid and the shadow of a man  (or, rather, the shadow of a vertical pole whose height is easy to measure).  Here's the key:

[First]  Theorem of Thales :  If the corresponding sides of two triangles are parallel, the trianles are  similar  and the lengths of their sides are  proportional.

[ Pause ]

How does this help?  The two shadows may be proportional to the two heights and we can quickly measure the shadow and the height of the vertical pole  but  we know  neither  the height of the Pyramid nor the length of its shadow!  Think about it:  You are by yourself in this flat desert with your graduated yardstick next to a pole of known height.  How can you find the height of the Great Pyramid?

[ Answer ]

For over two millenia, the geometry of Thales, which would be formalized by Euclid three centuries later, was thought to apply to our  physical  Universe.  The universe of classical geometry is postulated to be homogeneous  (Euclid's  fourth postulate  states that all right angles are equal)  and unaffected by scaling  (a statement equivalent to Euclid's  fifth postulate).

The scale invariance of the microscopic Universe was questioned by the ancient Greeks  (Democritus did speculate the existence of indivisible "atoms" with a definite size)  but it was thought to be an idiosyncracy of the  content  of the Universe...  Noneuclidean geometries were not even considered before the 19-th century.  However, we know now that the large-scale structure of our physical Universe is indeed noneuclidean  (this is a consequence of  General Relativity).  Yet, this conclusion could not have been reached without the likes of Thales and Euclid who set an ideal to compare against.

 

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(2006-10-19)     Obliquity of the Ecliptic
Latitude of the Tropic of Cancer.  Tilt of the Earth's axis of rotation.

Local  high noon  is the middle of the solar day.  It's when the Sun casts the shortest shadows.  On the summer solstice (June) and on the winter solstice (December)  the Sun's rays make two different angles with the local vertical.  The difference between these angles is always  twice  the  obliquity of the ecliptic.

Claudius Ptolemy (AD 87-165) reports that  Eratosthenes of Cyrene  (276 BC-194 BC)  had estimated the obliquity of the Ecliptic to be:

11/83 of a half circle (180°)   =   23.8554°   =   23°51'20". 

Eratosthenes, was merely 8' off the mark, which is typical of the uncertainty in good angular measurements from antiquity (0.2°). It turns out that the  obliquity of the ecliptic  changes slowly over time, but its value in the times of Eratosthenes (i.e., when he was in his late thirties) can be accurately estimated to be  23°43'30", by putting T = -22.4 in this modern formula:

23°26'21.45" - 46.815" T - 0.0006" T² + 0.00181" T³  

The above is a standard approximation for the mean obliquity of the ecliptic, as a function of the time T counted from "January 1.5" of the year 2000 and expressed in "Julian centuries" of exactly 36525 days.

This means that, in the time of Eratosthenes, the Tropic of Cancer was about 17 nautical miles (30 km)  north of its current (2006) latitude of 23°26'18". 

The above formula also says that the Tropic of Cancer was at the latitude quoted by Eratosthenes  (11p/83)  around 1347 BC.  Some have argued, backwards, that Eratosthenes did not measure the obliquity himself  (with a respectable accuracy for that period)  but used extremely accurate data from those earlier times...  This is either far-fetched or completely ludicrous.

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(2006-11-06)     The Ancient Wells of Syene
A vertical well in Syene is completely sunlit only once a year...

This ancient observation may have been part of the Egyptian folklore in the times of Eratosthenes.  Exactly  how ancient  an observation could that be?

The latitude of Syene (modern Aswan) is  about 24°06'N.  From the surface of the Earth, the radius of the Sun is seen at an angle of about 15'.

We're essentially told that the edge of the Sun was lighting up the entire bottom of a vertical well at Syene, just for a brief moment at noon on the summer solstice.  So, the center of the Sun must have been directly overhead at a point exactly 15 angular minutes (15 nautical miles) to the south.

Therefore, the latitude of the Tropic of Cancer must have been 23°51' at the time of the reports, if we assume they are perfectly accurate.  The above formula says that this happened about 33 centuries ago:  Around 1300 BC.

However, as the verticality of a well is certainly of limited precision,  that date doesn't mean much.  The legendary observations could be made even today with a well that's tilted by less than half a degree in the proper direction...  Any casual (or not-so-casual) observer will swear such a well to be "vertical".

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(2006-10-14)     252 000 stadia around   (700 stadia per degree)
The size of the Earth, according to Eratosthenes (276-194 BC).

Eratosthenes of Cyrene  became librarian of the  Great Library of Alexandria  around 240 BC, when his teacher Callimachus died.

Eratosthenes knew the above story about the wells of Syene.  He took that to mean that the Sun was directly overhead at noon on the summer solstice in Syene (modern Aswan).  This is almost true, because Syene is  almost  on the  Tropic of Cancer.  Eratosthenes did not know about the slow evolution with time of the latitude of the Tropic of Cancer and he took the above at face value.  Let's do the same (slight) mistake by using the modern map at right, as if Eratosthenes were alive today...  From his own location in Alexandria, Eratosthenes saw that, at noon on the summer solstice, the Sun's rays were tilted 1/50 of a full circle from the zenith  (i.e., 7.2° from the local vertical).  If we assume that Syene is due south from Alexandria, this says that the distance from Alexandria to Syene is 1/50 of the Earth circumference  (a posteriori, that's only 6% off).

The error from the difference in longitude between the two cities roughly compensates the error which places Syene on the Tropic of Cancer.  That's because, as the above map shows, the meridian of Alexandria  (about 30°E)  crosses the Tropic of Cancer at a point which is about the same distance from Alexandria as Syene (Aswan).

As the distance between Alexandria and Syene, was reputed to be 5000 stadia, Eratosthenes estimated the circumference of the Earth to be  250 000 stadia.  This estimate was then rounded up to  700 stadia  per degree, which corresponds actually to  252 000 stadia  for the whole circumference  (360°).

http://www.numericana.com/answer/ancient.htm

'Terra Australis Incognita'

Eratóstenes mide el radio de la Tierra

        Eratóstenes nació en Cirene en el año 276 a. C y se cree que era de origen caldeo. Fue matemático, astrónomo y geógrafo. Alrededor del año 255 a. C fue nombrado director de la Biblioteca de Alejandría por el rey Ptolomeo Evegetes. Trabajó con problemas de matemáticas, como la duplicación del cubo y los números primos. Hemos podido conocer algo de sus trabajos, merced a comentarios y citas de otros autores.

        Una de sus principales contribuciones a la ciencia y a la astronomía fue su trabajo sobre la medición de la Tierra. Estando en la Biblioteca de Alejandría, encontró un informe de observaciones sobre Siena, ciudad situada a unos 800 Km. al sur de Alejandría, en el que se decía que el día del solsticio de verano (21 de junio) a mediodía, los objetos (como por ejemplo, los obeliscos) no producían sombra y en el fondo de los pozos podía verse la luz del sol. Esto se debe a que está ciudad está sobre la línea del trópico (en realidad, 33' al norte del Trópico de Cáncer)

        Eratóstenes realizó observó que, en Alejandría, el mismo día y a la misma hora no se producía este mismo hecho. Asumió de manera correcta que el Sol se encontraba a gran distancia y que sus rayos, al alcanzar la tierra, lo hacían en forma (prácticamente) paralela. Esto ratificaba su idea de que la superficie de la Tierra era curva pues, de haber sido plana, no se hubiese producido esta diferencia entre las dos ciudades. El siguiente paso fue medir en Alejandría el ángulo que formaban los rayos del sol con la vertical que por construcción es igual al ángulo cuyo vértice está en el centro de la Tierra (ver gráfico superior). Este ángulo resulto ser de 7º 12' ( = 7'2º) que unido al hecho conocido de que la distancia entre las dos ciudades era de 5.000 estadios, dieron como conclusión que la circunferencia de la Tierra medía 360·5000/7'2; es decir, 250.000 estadios. Aunque no se tienen datos exactos, se sabe que el estadio equivale a unos 160m (actualmente se suele tomar 158m). Por tanto, 250.000 estadios son aproximadamente 250.000*160/1000 = 40.000 Km. Esto equivale a un radio de 6.366 Km. o 6.286 si tomamos los 158m, contra los 6.371 Km. que son los admitidos hoy en día.

        Las únicas herramientas de Eratóstenes fueron palos, ojos, pies y cerebro, y además el gusto por la experimentación. Con estos elementos dedujo la circunferencia de la Tierra con un error bastante pequeño, lo que constituye un logro notable para el año en que tuvo lugar.

        Otros logros suyos son: la creación de uno de los calendarios más avanzados de su época y una historia cronológica del mundo desde la guerra de Troya. Realizó investigaciones en geografía dibujando mapas del mundo conocido, grandes extensiones del río Nilo y describió la región de Eudaimon, actual Yemen, en Arabia.

        Suidas afirma que, desesperado tras perder la vista, se dejó morir de hambre a la edad de ochenta años (año 194 a.C., en Alejandría)

http://mimosa.pntic.mec.es/jgomez53/matema/practica/eratostenes.htm

Eratóstenes y la circunferencia terrestre

Hoy vamos a ver el primer experimento de una serie de tres que comentaré en sucesivos días y que fueron bastante decisivos en la historia de la ciencia. Los tres tienen un elemento en común: la Tierra. En estos experimentos la Tierra participa como un elemento más, y precisamente el objetivo de estos tres experimentos es medir alguna característica de la tierra: su circunferencia, su rotación y su densidad.

El radio de la Tierra

Es increíble que, mientras en Europa en el sigo XV aún se discutía si la Tierra era redonda o plana, muchos siglos antes, en el siglo III a.C. los griegos no sólo sabían que la Tierra era redonda, sino que habían sido capaces de medir su tamaño.

Los griegos sabían que la tierra era redonda por diversas evidencias: la sombra que proyectaba la Tierra sobre la Luna en los eclipses lunares era siempre circular; o cuando un barco se alejaba en el horizonte, lo último en desaparecer siempre eran las velas.

Uno de estos griegos, el matemático y astrónomo Eratóstenes fue el que llevo a cabo el experimento para medir el la circunferencia de la tierra, utilizando unos medios, como veremos de lo más sencillos.

Durante el tiempo en el que Eratóstenes realizó el experimento, vivía en la ciudad de Alejandría, que se encontraba a unos 5.000 estadios al norte de la ciudad de Siena (1 estadio = 167,7 metros). La ciudad de Siena era conocida porque el día del solsticio de verano, el 21 de Junio, a las 12 del mediodía, los rayos del Sol caían completamente perpendiculares. En ese momento los habitantes de Siena podían ver el Sol exactamente sobre sus cabezas, y los edificios, columnas, postes, etc. no producían sombra alguna. En realidad esto ocurre porque Siena se encuentra situada en el trópico de Cancer.

Eratóstenes, sabiendo esto, utilizó esta peculiaridad para calcular la circunferencia de la Tierra. Situado en Alejandría, a las 12 del mediodía del solsticio de verano, colocó un palo vertical (se cree que un reloj de sol) y midió la longitud sombra que producía. Usando algo de trigonometría básica pudo hallar el ángulo que formaba la sobra con el palo, que resultó ser de 1/50 de circunferencia (unos 7º12'). De esta forma, y como veremos a continuación con ayuda de la figura 1, supo que la distancia entre Alejandría y Siena era 1/50 de la circunferencia total de la Tierra, por lo que la Tierra tendría que tener de cincunferencia 50 veces la distancia de 5.000 estadios que separaba ambas ciudades, esto es, 250.000 estadios. Eratótenes decidió añadir la cantidad de 2.000 estadios para hacerla divisible entre 60 y facilitar cálculos posteriores.


En la figura 1 se muestra esquemáticamente una parte de la Tierra. La letra S representa la ciudad de Siena, en el trópico de cáncer. La letra A, al norte, representa la ciudad de Alejandría, donde se encontraba Eratóstenes. La letra C es el centro de la Tierra. Como se puede observar, los rayos solares, representados mediante flechas, caen perpendicularmente sobre la ciudad de Siena, pero con un cierto ángulo sobre Alejandría. Este ángulo produce que el poste situado en A proyecte una sobra sobre el punto P. El ángulo que se forma entre los rayos y el poste colocado en A es exactamente el mismo que el formado por A, C y S.

El valor calculado por Eratóstenes era de 41.950 km, un valor bastante aproximado a los 40.120 km medidos en la actualidad. Pero lo grandioso del experimento es la sencillez de su ejecución, compuesta por un simple palo, su sombra, y por supuesto la Tierra y el Sol.

    Esta constelación es la más débil de todo el Zodiaco y tiene una procedencia mesopotámica, aunque hay varias dudas que rodean su origen. Sin embargo, su importancia durante el segundo y primer milenios a.C. sería enorme, pues el solsticio de verano tenía lugar con el sol en esta constelación (en realidad, durante la época clásica,  en la frontera entre Géminis y Cáncer, mientras que actualmente, debido a la precesión, ocurre en la frontera entre Tauro y Géminis), de ahí el nombre de Trópico de Cáncer.

Cáncer (Cartes du Ciel)

 Arato no menciona ningún mito asociado a esta constelación y sería Eratóstenes quien lo haría:

Parece que fue la diosa Hera quien lo colocó en el firmamento. Cuenta Paniasis¹ en su obra Heraclia que un cangrejo salió de la laguna en la que Heracles luchaba con la hidra y le mordió el pie él solo, sin concurso de otros. Heracles, irritado, lo aplastó con el pie, y desde entonces el cangrejo alcanzó una gran fama y se le cuenta como uno de los doce signos del Zodiaco. Algunas estrellas de esta constelación reciben el nombre de Asnos, y fue el dios Dioniso el que los elevó al cielo. Anexo a ellos se encuentra el llamado pesebre. He aquí su historia: cuando los dioses partieron a la guerra contra los Gigantes², se dice que el dios Dioniso, Hefesto y unos sátiros subieron a lomos de unos asnos; cuando aún los Gigantes no los habían divisado, los asnos se pusieron a rebuznar hallándose a corta distancia, y los Gigantes se echaron a correr al oír los rebuznos. En recompensa por dicha acción los asnos pasaron a formar parte de la constelación de Cáncer, a la zona de poniente. Cáncer tiene dos estrellas muy brillantes sobre su caparazón, que son los Asnos, y una nebulosa que se encuentra entre éstos compone el llamado Pesebre; da la impresión de estar flanqueado por los Asnos. Cáncer tiene una estrella de escaso brillo sobre cada pata del lado derecho y en la pata anterior del lado izquierdo dos poco brillantes, otras dos sobre la pata segunda, una en la tercera; igualmente presenta una en el extremo  de la cuarta pata, otra sobre la boca y tres iguales y no muy granes sobre la pinza de la derecha; otras dos iguales, de no gran tamaño, sobre la pinza de la izquierda. Suman un total de dieciocho.

                                    Catasterismos

Notas:

1)      Autor de poesía épica del siglo V a.C..

2)      Seres monstruosos que nacieron de Gea (la Tierra) al ser fecundada por la sangre de Urano (el Cielo), castrado por su hijo Cronos (el Tiempo). Posteriormente se rebelarían contra el dominio de Zeus y los dioses Olímpicos, retirándose al interior de la Tierra tras perder la guerra, desde donde se manifiestan como responsables de las fuerzas telúricas.

    Como vemos, Eratóstenes relaciona a esta constelación con uno de los trabajos de Hércules, el de la Hidra (ver esta constelación), como otras constelaciones zodiacales de origen no griego. Eratóstenes hace referencia a los Asnos (γ y δ Cnc) y al Pesebre o Praesepe (denominado en la actualidad también como la Colmena, cuyo nombre de catálogo es M44 o NGC 2632), un cúmulo abierto de estrellas débiles que parece una nebulosa a simple vista, situado entre los Asnos. El Pesebre fue denominado por Bayer como Nubilum. La historia de estos dos asterismos muy posiblemente tenga un origen griego anterior a la asociación de esta constelación con un cangrejo por influencia mesopotámica, lo que explica el hecho de que Arato apenas hable de Cancer pero sí le dedique unas palabras al Pesebre:

Observa también el Pesebre. Semejante a una pequeña nebulosa, marcha englobado en el Cangrejo en dirección Norte; en torno suyo giran dos estrellas que brillan poco, ni muy alejadas ni muy cerca de él, sino que, a simple vista, se diría que están a un codo de distancia poco más o menos; una está al Norte, la otra está orientada al Sur. Se les llama los Asnos y en medio está el Pesebre.

                                    Fenómenos, 892-896

    Aparte del mito asociado a los Asnos narrado por Eratóstenes, otro cuenta que eran los Asnos que permitieron a Dioniso, enloquecido por Hera, atravesar una laguna yendo hacia el oráculo de Dodona. El dios otorgó la capacidad de habla a uno de los animales, el cual compitió posteriormente con Príapo por la longitud del miembro viril. Como el concurso lo ganó el Asno, Príapo le dio muerte. Después, Dioniso catasterizaría a los animales.

Cáncer en Mesopotamia

    En las tablas Mul-Apin aparece con el nombre de Al-lul, en sumerio “cangrejo”. En época neobabilónica se denominaba a esta constelación Du’uzu o Du-Zu, que significa precisamente “cangrejo”. Pese a todo, muchos estudiosos (Belmonte) sugieren un posible origen egipcio para esta constelación (junto con Aries), pues es posible que dividieran la parte correspondiente a los cuartos delanteros de la constelación del Gran León, donde siglos atrás había tenido lugar el solsticio de verano, para otorgársela a otra en la que tenía lugar este fenómeno, debido a la precesión de los equinoccios. Esta nueva constelación estaría asociada al escarabajo pelotero, el dios egipcio Jeper o Jepri, símbolo de la eterna renovación, el devenir,  la transformación y evolución por excelencia (eso es lo que significa precisamente la palabra hpr en egipcio). Precisamente, Jeper es una de las manifestaciones del dios Sol: Jepri es Ra cuando amanece (al atardecer era el dios Atum), tras haber sufrido la “muerte” de la noche y haber recorrido el inframundo (periodo durante el cual se asimilaba Ra a Osiris, dios de los muertos por excelencia), siendo regenerado por la diosa celeste Nut. Precisamente, la relación de Jepri-Cancer con Leo existía de forma explícita en la mitología egipcia, pues Jepri-Ra aparecía al amanecer a lomos del doble león Aker.

    De todas formas, el origen egipcio de esta constelación es bastante discutible, siendo el mesopotámico más aceptado.

     Como anécdota comentar que la forma de esta constelación suele ser la de un cangrejo de mar, pero en muchos atlas celestes ha aparecido como cangrejo de río.

Nombre de las estrellas:

α Cnc (4.3m): Acubens, de Az-Zubana,  “pinza”. Sertan, Sartan.

β Cnc (3.8m): Al Tarf, de At-Tarf, “la mirada”

γ Cnc (4.7m): Asellus Australis, el "burro del sur".

δ Cnc (4.2m): Asellus Borealis, "burro del norte".

ζ Cnc (5.1m): Tegmen, Tegmeni, Tegmine.

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