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This observation was almost certainly made at Itj-Tawy, the Twelfth Dynasty capital, which would date the Twelfth Dynasty from 1963 to 1786 The Sothic cycle is a specific example of two cycles of differing length interacting to cycle together, here called a tertiary cycle.
This is mathematically defined by the formula 1/a 1/b = 1/t or half the harmonic mean.
In the case of the Sothic cycle the two cycles are the Egyptian civil year and the Sothic year.
The Sothic year is the length of time for the star Sirius to visually return to the same position in relation to the sun.
A heliacal rise of Sirius was recorded by Censorinus as having happened on the Egyptian New Year's Day between 140-142.
Thus he was able to compare the day on which Sirius rose in the Egyptian calendar to the day on which Sirius ought to have risen in the Julian calendar, count the number of intercalary days needed, and determine how many years were between the beginning of a cycle and the observation.
Stars that reside close to the ecliptic or the ecliptic meridian will on average exhibit observational years close to the sidereal year of 365.2564 days.
The ecliptic and the meridian cut the sky into four quadrants.
The ancient Egyptian civil year, its holidays, and religious records reflect its apparent establishment at a point when the return of the bright star Sirius to the night sky was considered to herald the annual flooding of the Nile.We have seen that this small step helps to keep most fake profilers at bay.All approved members start with full membership benefits for a week.The axis of the earth wobbles around slowly moving the observer and changing the observation of the event.If the axis swings the observer closer to the event its observational year will be shortened.