Pistol: "The summer solstice in the year 2570 BC did not occur +/- 2 days around June 26, it occurred exactly on July 15 and the Heliacal rise of Sothis is first seen on July 7th, any earlier and the suns light overpowers the star."
Yours are Julian dates, mine Gregorian!!
Schaeffer's dates for the heliacal rising of Sirius:
"The most frequently asked question is the heliacal rising date of Sirius in old Egypt. Half-a-year ago I investigated this in the most rigorous possible manner. I used exact precession formulae, Sirius' proper motion, extracted extinction coefficients from the literature for several sites in Egypt, took the solar ephemeris from Bretagnon & Simon, and used the best modern theory. My results are in reasonable agreement with the common wisdom among Egyptologists." (Schaeffer 1996):
3500 BC July 16 Julian
3000 BC July 17 Julian
2500 BC July 17 Julian
2000 BC July 17 Julian
Someone once calculated that July 17 (Julian) is June 24 (Gregorian), but my Astronomy software has the Gregorian date June 26th.
CT