Keith M. Hunter
An Ideal Earth-Moon Configuration under the Ancient Egyptian CalendarIn the distant past the ancient Egyptian calendar established from the dynastic period and onwards, was based upon a 360 days per year cycle perfectly harmonised with a moon orbit of 30 days. Through the interplay of these two cycles there were thus precisely 12 months to one full year. Yet even so, the ancient Egyptian astronomers were of course fully aware of the fact that the true (observed) length of both cycles did not in fact match such a harmonious configuration. Indeed, and as noted previously, in the case of the tropical year for example, the ancient Egyptians well knew that its true length was some 365 and 1/4 days. And in consequence, they thus developed their mythical stories to account for the increase to the earth year.
Knowing then from observations that the length of the year was not exactly 360 days per year, it will come as no surprise to learn also that the ancient Egyptian astronomers were well aware of the fact that neither does the moon complete one full orbit about the earth exactly every 30 days. (For the purpose of clarity, one should note here that the type of moon orbit that is being referred to is what is known to astronomers as the synodic month, which is the periodic ‘plan view’ conjunction of the moon and the earth, together with the sun). Indeed, the moon in its orbit of the earth has a very complex elliptical motion. As a result of this, the length of each month fluctuates between about 29 and 30 days, the average observed period being 29.53059 days, by modern determination. In actually tracking the moon the astronomers of the past would traditionally follow its journey through the sky to determine the full time interval between successive ‘new moon’ phases i.e. where the moon is almost completely covered in shadow with just a slight crescent of light beginning to develop. Only when the next new moon was sighted, would the astronomers declare its length.
Further to the above, it is also of note that the ancient Egyptian astronomers had a very similar sort of view of the length of the moon month as with the earth year. For concerning the existence of the 5 extra days of the latter period, the Egyptians held them as almost an anomalous addition to the year. They were in fact considered to be not a part of the ‘true’ year at all. Indeed, they were blatantly thought of as ‘unlucky’. Much the same holds true respecting the length of the moon synodic month. Only months that possessed a length of 30 days (as determined by the astronomers) were held to be ‘complete’ and true months. Those that were only 29 days were held to be somehow incomplete and ‘deficient’.
It is very interesting to note then from the ancient Egyptian calendar that underlying the observed time cycles for both the earth year and the moon month, there exists this ‘ideal template’ of 360 days and 30 days respectively, for the real orbits of these two noted bodies, and that all of their observations were somehow involved with charting the measure of disagreement and lack of harmony between the observed cycles and the noted ideals.
With it already proven quite decisively that the earth did indeed once possess a perfect orbit of 360 days at some point in the past, and that at such a time the moon itself in its own orbit was slightly closer to the earth, one has to suspect that at the very same moment, the moon synodic period must itself have been 30 days in duration - for each and every successive month, with no variation. And indeed, that the actual mean length of the synodic month as currently observed, must itself have been transformed via a distinct and exacting physical law of proportion, of exactly the same type as that already shown to have governed the relative changes to the earth year and moon semi-major axis. Such would indeed confirm the physical truth of the ancient Egyptian calendar as a whole, revealing it not to have been established as some general approximation of the observed cycles of the earth and moon, as some might believe, but rather a true reminder of a once existent celestial configuration of a most harmonious nature. Does the evidence support such a view though? Most assuredly it does.
A very careful evaluation of the orbital periods of the earth tropical year and the moon synodic month does appear to reveal the existence of a further physical law of proportion that connects them in terms of relative change; one that would appear to be based upon a very low set of powers, whose values are in fact highly suggestive in their own right. A detailed study of the relevant periods helps to establish the law as follows:
As revealed by modern methods of observation, the lengths of each
of the noted orbital periods for the earth and moon are as follows**:
Earth Tropical Year = 365.2421897 days
Moon orbit (Synodic Month) = 29.53059 days
Set against the ideal values of the ancient Egyptian Calendar, the ratios of change are given as follows:
365.2421897 / 360 = 1.014561638
29.53089 / 30 = 0.984353
TY = Tropical Year (Present)
SM = Synodic Month (Present)
ty = Tropical Year (past)
sm = Synodic Month (past)
By using known values for the above specified components, with
the exception of the synodic month ideal, it is possible to calculate
the measure of this remaining value, and then compare it for accuracy
against an exact value of 30 solar days. Using the above formula, this
is achieved in the following stages:
1) 365.2421897 / 360 = 1.014561638
2) 1.014561638 to the 12th power = 1.189436453
3) 1.189436453 to the 11th root = 1.0158958917
4) 1.0158958917 x 29.53059 = 30.000005039 days
Set against the precise ideal of 30 solar days for the duration of the moon synodic month, as under the Egyptian calendar, the above result is quite simply astounding in its accuracy. And as such one can propose therefore a further general law of proportion linking specifically the earth tropical year and moon synodic month:
Where: TY & SM are ratios:
TY = Tropical Year (Present) / Tropical Year (Past)
SM = Synodic Month (Present) / Synodic Month (Past)
What one may note in particular from the form of this law, at
least in contrast to those given in other essays, is that it is
indicative of an inverse transformation. Essentially, an increase in the
length of the Earth year is accompanied by a decrease in the length of
the lunar month, as determined by the specified power relationship.
The Ancient Egyptian Calendar, In Conclusion
Acceptance of the above new law implies that the ancient Egyptian
calendar composed of 360 days combined with a 30 day moon synodic
month, was indicative of the true orbital periods of the earth and moon,
as were once manifest in some remote age. And indeed, with the newly
presented law above, one may thus summarise the full features of the
ideal earth-moon configuration, as proven to exist in line with the
other noted laws of proportion given elsewhere:
Ideal Earth-Moon System:
360 days (Earth Tropical Year)
30 days (Moon Synodic Month)
21600 Ideal Geographical Miles (Earth Equatorial Circumference)
1296000 Ideal Geographical Miles (Moon Orbital Celestial Equator)
As can be seen then, it is the ideal orbital periods that are thus modelled by the ancient Egyptian calendar.
References:*For more information on the Sothic cycle one may consult the following article that is more deeply concerned with this aspect of the ancient Ancient Egyptian Calendar