There is this popular claim on Internet that the star Sirius does not precess like other stars.
The idea comes from mainly Greeks and Egyptians using Sirius to track seasons, as part of the Sothic cycle.
Wikipedia says that Sirius is used for the Sothic cycle because it's ~40 degrees away from the ecliptic, but there are other stars which are 40 degrees and even further away from ecliptic, why only Sirius? Why is this property only present in Sirius?.
This and this website, of questionable reputation conjectures that our Sun revolves around Sirius with the period of 24,000 years which is approximately equal to time taken for one cycle of precession of equinoxes, therefore Sirius always staying still in the sky.
Given that the distance between Sun and Sirius is around 8 light years, 24000 years seems to be too quick a time period, but then to calculate the time period of twin star systems is complicated as the distance changes dramatically. Also there is the Centauri system which is around 4 light years away from the Sun. Can the Sun, Sirius and Centauri systems together form a bigger system which has a time period of 24000 years?
Is this model even feasible? If not, why does Sirius not precess like other stars?