Thanks for that on stars, and that's my understanding of the situation.

From memory Alpha Draconis or Thuban was just a few arc minutes from the pole c.2790 BC and Sirius would have risen heliacally on New Year's Day 2770 BC assuming the integrity of the Egyptian calendar.

This could be a coincidence or it could mean that AE decided to start or re-start the calendar in 2770 BC because Thuban had been observed drawing closer and closer to the pole of the night sky over the preceding decades and centuries. The first annual appearance of Sirius at dawn could have been chosen as New Year's Day because it is the brightest star in the sky.

The first annual appearance of Sirius foreshadowed the annual flooding of the Nile in the Pyramid Age, shifting only very slowly away from the true solar year.

Sirius is bright because it is relatively close to the sun and does not have exactly the same motion as most other fixed stars. The annual cycle of Sirius was between 365.249 days and 365.251 between 1 BC and 3000 BC or thereabouts.

The annual cycle of the sun is 365.242 days and that of Sirius is close to 365.250 days so the rising of Sirius is delayed by 0.008 days per year so I suppose the sun would complete an extra cycle in about 365.242 days/0.008 = 45655 years if the year of Sirius remained the same.

The constellations have a slightly longer annual cycle to returned to exactly the same position. The circle traced by the pole of the night sky is a retrograde motion resulting in a cycle of less than 26,000 years, but we don't know this cycle was observed in Egypt. I noted down a figure of 365.25636 days for the stars to return to same position so the cycle of the stars is about 25,800 years.

Sirius rose on the next day in the calendar year every 4 years in theory, but there might easily be an error of a year on the change of day due to observation conditions. If the cycle of Sirius had been exactly 365.250 days then presumably Sirius would have risen on New Year's Day every 1461 calendar years:
1461 calendar years x 365 days = 1460 cycles of Sirius x 365.250 days per cycle.

The first annual appearance of Sirius is known to have taken place in Egypt on New Year's Day in AD 139 so should have taken place in approximately 1322 BC and 2782 BC or more precisely 1314 BC and 2770 BC according to Dr Edwards in 1970.

I am not sure what the dating convention is for calculating years BC, but if it is the solar year then period between this special event is about 1,456 solar years from Edwards.

1456 solar years is approximately 1457 calendar years of 365 days which is approximately 1456 cycles of Sirius.
1457 calendar years x 365 days per year = 1456 cycles of Sirius x 365.2507 days per cycle

The heliacal rising of Sirius on New Year's Day must have been a notable event but we don't know that AE tracked this cycle. Sirius may have been regarded as merely a marker of the solar cycle. If we find evidence of a cycle of 1460 years in an Egyptian design it may have nothing to do with this modern astronomical knowledge.

Let us suppose the Egyptian cycle of 309 lunar months in 25 calendar years of 365 days was observed in the Pyramid Age, or at least a fixed calendar year of 365 days. The Egyptians would then have been able to predict a delay of 1 day for the spring equinox every 4 calendar years with a delay of an Egyptian week of 10 days expected every 40 solar years. This equates to a delay of 365 days after 1460 solar years, so the ancient Egyptians may have assumed 1461 calendar years of 365 days in exactly 1460 solar years of 365 1/4 days.

There are 1509 calendar years of 365 days in 1508 solar years of 365.242 days (by my calculation), so any representation of 1460 could be an estimation of this cycle rather than knowledge of the cycle of Sirius.

At present nobody has proved that AE had a perception of a cycle of 1460 years but it often appears in the literature. The observation of Edwards is, however, valid.

It seemed likely to me that the Great Pyramid had been built c.2770 BC at the start of a perceived cycle of 1,460 years when Alpha Draconis was close to the pole of the night sky.

Haas Lehner et al had radiocarbon dated samples suggesting that the Great Pyramid was 388 years older than the historical date in 1992, and I was informed of this study by the Egyptian Exploration Society in 2002. A date of 2770 BC appeared to be tenable.

Unfortunately desk researchers like myself face the seemingly never ending problem of changes with every new study from the orientation of the Great Pyramid to the age of the pyramid from radiocarbon samples.

I had a look at the Dash / Lehner 2015 survey of the base of the Great Pyramid on academia and this seems to rule out my new theory of a virtual triangle in the base square of the pyramid (if it is the best survey ever undertaken).

The Dash / Lehner survey is in accord with Smyth's determination of the azimuth for the east side of the corner sockets but from an assessment of both the base square and pavement because the north-east corner socket is too badly damaged just as Smyth predicted would be the case.

I think the pyramid was based on a stellar alignment on the east side of the pyramid, and that the east side was built first with the edge of pavement, side of pyramid and line of corner sockets all intended to be parallel with the orientation determined at the foundation level of the corner sockets prior to building the pyramid and pavement. The determination of the orientation is close to 5 arc minutes west of true north probably accurate to well within an arc minute.

It seems very likely that the aim was to align the pyramid to the bearing of the pole of the night sky. The pole is precisely 30 degrees above the horizon at Giza. The sun passes over the equator at the equinox so the sun is precisely 30 degrees from the vertical at mid-day on the equinox as viewed from the Great Pyramid. I drew a picture of these angles on page 128 of my monograph on the Grand Gallery.

Smyth determined the latitude of the Great Pyramid as 30.0 degrees on rounding to the first decimal place, or more precisely 29.98 degrees (29 degrees 58 minutes 51 seconds). I expect the true latitude is even more precise on Google Earth, but presumably still very close to 30 degrees which is 1/12 of a circumference of a circle.

Is this why days were divided into 12 hours?

Mark

PS
I looked at data on Sirius by Bradley E. Schaefer





Edited 6 time(s). Last edit at 10/24/2018 04:30PM by Mark Heaton.