The main event of the life of ancient Egypt was always the flooding of the Nile, which coincided roughly with the heliacal rising of the brightest star in the sky, Sirius ( α of the constellation Canis Major). The heliacal rising of a star is its appearance on the eastern horizon in the early dawn. This implies that the star has a certain height above the horizon, and the Sun a certain height below the horizon (the arcus visionis). Different values are adopted according to the authors, in general, it takes the Sun to -7° and 2° or 3° for Sirius. But other factors are involved in this phenomenon, as the brightness of the star, the azimuth difference between the Sun and the star, and also the transparency of the atmosphere. There are several ways to calculate the heliacal rising of Sirius, including the iterative method in which is calculated for each day of July and August the rising of Sirius as compared with the position of the Sun until the arcus visionis selected reaches the limit of visibility value.
The method developed by Pierre Bretagnon (IMCCE - Observatoire de Paris) is more direct and elegant. In a given place and for a value of the visibility criterion (arcus visionis), it gives each year the date of the heliacal rising of Sirius. This so simple solution was obtained by inverting the series giving the local coordinates of celestial bodies over time and place.
In addition, we obtain with five additional rounds, the time of the heliacal rising of Sirius, the azimuth at rising of the star, the azimuth of the Sun at the rising of Sirius, time and azimuth of the sunrise. The formulae of Pierre Bretagnon are obviously very useful for science historians and Egyptologists. (It was published in the journal "Discovery" of the Palais de la Découverte (June 2003 No. 309).
The following algorithm developed by Pierre Bretagnon calculates the date and time of the heliacal rising of the star Sirius (Sothis) over the period from the year -4400 to year 2800 for all places the Earth between latitudes 22° and 32° North and longitudes 25° to 35° East. The arcus visionis is the difference in height between the star and the center of the Sun at the time of the rising of the star.
The results are given either solely in the Julian calendar, or in the Julian calendar for years prior to 1583 and in the Gregorian calendar for years posterior or equal to 1583.
This program provides in addition to the date of the heliacal rising, the azimuth of the star at its rising, the timing of sunrise and azimuth of the Sun at sunrise, and the date of the summer solstice.
Credit: P. Rocher, IMCCE/observatoire de Paris