Black Genesis: The Prehistoric Origins of Ancient Egypt

APPENDIX 2
SOTHIC CYCLES AND IMHOTEP’S CALENDAR WALL
The Sothic cycle is the duration of synchrony between a 365-day Egyptian civil calendar and the heliacal rising of Sirius.
A difficulty with calculating this cycle lies in defining heliacal rising. The basic concept of heliacal rising is the day of
the year on which Sirius first seems to reappear on the eastern horizon just before the sun rises. Obviously, it would be
problematic if we were to apply this purely visual definition. If the weather happened to be cloudy or the sky was filled
with dust, an otherwise viewable reappearance would be missed, perhaps for many days. A more sensible definition could
be the day on which Sirius would be visible, if the viewing conditions were optimal, and optimal is defined as a specific
angular relationship of sun, Sirius, and horizon.
In order to understand the Sothic cycle, we must first look at two related cycles. Today the length of the tropical year
is 365.2422 days, so that a 365-day civil calendar would return the day of summer solstice to the same calendar date
every 1,507.1 years. (We can call this the solstice-to-civil cycle.) Today the length of the sidereal year (with respect to the
distant stars) is 365.2564 days, so that a 365-day calendar would return a star sign or zodiac constellation date to the
same calendar date every 1,423.8 years. (We can call this the sidereal-to-civil cycle.) This difference between the siderealto-civil
cycle of 1,423.8 years and the solstice-to-civil cycle of 1,507.1 years is due to the precession of Earth’s pole, the
precession of the equinox. If Earth did not precess, then the sidereal-to-civil cycle would be the same as the solstice-tocivil
cycle. Further, those sidereal and solstice rates are as measured today, while the actual precession rate varies slightly
over time, which means these cycle durations also vary. Because the heliacal rising is a combination of sidereal and solar
measurements—essentially, a complex addition of the two—we would expect the Sothic cycle, to first approximation, to
be the average of the sidereal and solstice cycles, which, given today’s rates, would be 1,465.4 years. This is remarkably
close to the purely calendar-based cycle of 1,460 years—the cycle between two types of civil calendar systems (one that
adds a day every four years, like our leap year, and a fixed, 365-day calendar such as the Egyptian civil calendar).
Yet we would expect an actual Sothic cycle to vary from our rough estimate, due to several factors. First, the
precession rate varies with time; the rate has been steadily increasing since roughly 8000 BCE. Today, the precession rate
is about 50.29 arc seconds per year, while around 4000 BCE the rate was roughly 1 arc second per year slower. Due to
this effect alone, almost half of one year would be added to the Sothic cycle over the span of about two Sothic cycles. A
second factor is that the tropical year itself also changes over time—but this effect is orders of magnitude smaller. A
third factor, more difficult to estimate but which has a greater effect, is due to the change in declination of the star and its
drift in right ascension relative to the vernal point—the day relative to solstice moves steadily through the year so that the
angular relationship of star to sun to horizon is altered.
Still, we can fairly easily use SkyMapPro to measure the Sothic cycles. First, we set the latitude to that of Djoser’s
step pyramid (29.871 degrees north) and we set the year to 2781 BCE and we set the day to summer solstice. The result
is that on that day, when Sirius is at altitude 1 degree, the sun is at altitude -8.96 degrees 45 minutes before the center of
the sun disk passes the horizon. This is clearly a good reference for heliacal rising, because Sirius is certainly bright
enough to be seen briefly under such conditions. We call this summer solstice day, the first day of Thoth (1 Thoth) on the
Egyptian civil calendar, and we note that SkyMapPro calls this day July 16, 2781 BCE. We make this the definition of
Sirius heliacal rising—the day of the year when Sirius is at altitude 1 degree and the sun is simultaneously at altitude -
8.96 degrees or lower. Next, we search for the previous year when Sirius rose heliacally on a first day of Thoth (1 Thoth)
according to the Egyptian civil calendar. We know that SkyMapPro uses Julian years (365.25 days per year), so we note
that what SkyMapPro calls July 16, 4241 BCE, is a first day of Thoth on the Egyptian civil calendar. When we look at
that date, we see that when Sirius was at 1 degree altitude, the sun was at -9.41 degrees altitude just below the horizon,
and the day before 1 Thoth, the sun was only -8.70 degrees below the horizon—less than our criterion of 8.96 degrees—
so in that year the first day of Thoth was indeed the day of reappearance of Sirius.
We must remember, however, that a given date for heliacal rising of Sirius should persist for about four years in a
row on the Egyptian civil calendar, so in order to nail down the exact Sothic cycle, we must check the following years.
We see, then, that two years later, 4239 BCE, on the first day of Thoth with Sirius at altitude 1 degree, the sun was -9.05
degrees altitude, which still satisfies heliacal rising (and this time, eleven days before summer solstice). In later years, all
the way up until 2781 BCE, the first day of Thoth was not the heliacal rising date. So this Sothic cycle extended from
4239 BCE to 2781 BCE (in Julian years), which is 1,459 Egyptian civil calendar years.
By a similar method, we find that the next first day of Thoth-Sirius heliacal rising was 1325 BCE (twelve days after