Keith M. Hunter
In part 1, it was shown that a physical law of proportion, of the
same type as that discovered by Kepler, appears to govern the relative
transformation of both the earth tropical year and the physical
equatorial circumference of the planet. In accordance with the noted
law, both of these variables were found to be transformed in direct
proportion to one another. Moreover, it was also shown that under an
earth year of 360 days with the stated law being operative, the actual
(accompanying) equatorial circumference of the earth would have been
almost exactly 21600 Ideal Geographical Miles (1 IGM = 6000 feet).
Such intriguing connections would seem to provide significant support for the view that the earth itself may indeed, as the ancients believed, have once possessed an earth year of exactly 360 days in some remote era. However, is there any still further evidence that could aid confirmation? Most assuredly there is.
Of angular measure, it was stated previously that the basic primary units were in accordance with a base-60 progression i.e. 360 (degrees) x60 > 21600 (minutes of arc) x60 > 1296000 (seconds of arc). However, with the law discovered in the previous section, it would seem quite clear, at the very least concerning the former two sets of figures, that there is indeed a real physical basis to the values as stated.
Indeed, it has already been shown that the second value of note
(21600) has a very real association with the earth, in that it was
directly representative of its equatorial circumference in IGM, when the
planet possessed 360 days to one complete yearly orbit. With this in
mind, were one then to focus upon the number 21600, as an actual
circular measure in terms of a real distance unit i.e. the ideal
geographical mile, instead of the abstract minute of arc unit, then
multiplying this value by 60, would generate a circle, extended into
space from the surface of the earth, 60 times greater than the earth’s
own physical circumference:
21600 x 60 = 1296000 ideal geographical miles
Does such a circle though possess any real significance? Indeed it does, for remarkably, it so transpires that the current orbit of the moon is almost exactly 60 times the circumference of the physical earth form. Exactly, but not quite. And this point indeed is critical.
Recalling the Egyptian myth concerning the increase to the tropical year from 360 days it was stated that one of the consequences of the earth gaining its 5 extra days or so, was that the moon became weaker and smaller in the sky. One could very well interpret this to mean that the moon extended its orbit from the earth in order to compensate for an increased earth orbital period from 360 days to 365. Such a point is well worth exploring further.
With the above taken into consideration, it would seem not unreasonable to suspect that a value of 1296000 IGM, would have been representative of none other than the actual circular celestial equator of the moon orbit, at the very time when the earth possessed a precisely 360 days per year. (NB: Recall that the circular celestial equator of the moon is at 90 degrees to its actual orbital path about the earth).
Also, bearing in mind that an actual physical law of proportion has been found to govern the relative transformation of the physical earth and earth tropical year, it is highly likely that another law similar in character, may also exist, that would govern the transformation of the physical earth equator, also relative to the moon’s (mathematically equivalent geometrical component) circular celestial equator. Evaluating the relevant measures of such a proposed ideal earth-moon system, with respect to those as currently manifest, may well reveal the identity of such a law.
With it proposed then that the ideal moon celestial equator was 1296000 IGM - existent at a time when the earth itself possessed 360 days per year - how does this figure compare with that of the current moon celestial equator? And moreover, just how exactly should one evaluate the two measures (the proposed ideal and current) together when seeking a proportional law of transformation? The answer is not as straightforward as one would expect.
In proceeding, most people would doubtless at this stage simply
take what is the presently known (observed) value for the moon
semi-major axis, and multiply it by 2 times PI in order to obtain a
value for the current moon celestial equator:
Moon Semi-major Axis = 384404 kilometres 
Therefore: 384404 x 0.6213711922 x 0.88 = 210194.66315 IGM
And: 210194.66315 x 2 x PI = 1320692.01917 IGM
However, this would be a mistake, though not an obvious one. The explanation is somewhat complicated to be sure.
In evaluating the ideal moon celestial equator, it would be wholly improper to do so with respect to the above derived value of 1320692.01917 IGM (for the current equator), quite simply because it is falsely generated, relying as it does upon PI as the conversion factor linking the full major axis of the moon orbit to that of its circular celestial circumference. A rather odd statement to hear no doubt. And yet, as difficult as it may be to understand, the truth of the matter is, that respecting the correct ratio between the circumference of a circle and its diameter, though MATHEMATICALLY, PI is right. PHYSICALLY, it can be wrong. And in this instance, it most definitely is wrong.
Indeed, the correct conversion factor that would appear
physically valid respecting the dynamics of the earth and moon, is in
fact, 22/7; a fractional value well known to the ancients and oftentimes
cited as being employed by them as a simple approximation of PI.
Comparing both values together, one can note their subtle differences:
PI = 3.1415926535897932384626433832795
22/7 = 3.1428571428571428571428571428571
Of course, from a numerical perspective, one can clearly see that they are very close. That being said however, qualitatively they are very different. Indeed, as is evident, the numeric sequence of PI is non-recurring. It is what is referred to as an ‘irrational’ number. 22/7 by contrast is an ordered sequence that repeats itself.
The critical point to note here though in contrasting the two values, is that respecting proportional laws as operative within the universe, PI has no PHYSICAL VALIDITY as such. Rather, it is the rational fraction of 22/7 that correctly links up the various the physical-celestial components of orbital bodies via efficient laws of proportion, which actually govern their real transformation; this fact being confirmed via series of very intriguing mathematical associations.
If one is taken to employ 22/7 instead of PI to generate a value for
the current moon celestial equator, it then becomes possible to reveal a
most decisive association between the transformation of the moon orbit
and that of the earth form, such as does indicate the presence of a
valid operative law of proportion; which indeed, one would FAIL to
notice if PI were employed. Consider the following:
Using 22/7 to generate the circumference of the Moon celestial equator:
210194.66315 x 2 x (22/7) = 1321223.59697 IGM
With this value now in hand, the numerical ratio between it and the suggested ideal can now be determined:
1321223.59697 / 1296000 = 1.01946265198
The question now therefore, is whether or not there exists some
sort of connection between this value, indicative of the extension of
the moon orbit, and the ratio already noted for the change in the earth
tropical year (including also the earth’s physical equator) i.e.
It would appear so.
For indeed, the noted moon ratio, transformed by a combination of
powers very similar, though slightly different, to those found in
Kepler’s 3rd Law, can be reduced most exactingly to the earth
year/equator ratio. The level of correspondence is quite exceptional:
1.01946265198 = Moon celestial equator ratio of increase
1.01456163805 = Earth tropical year/physical equator ratio of increase
1.01946265198 Cubed = 1.05953171276
1.05953171276 Reduced to the 4th Root = 1.01456176184…
Answer compared directly with known tropical year ratio of increase:
As one can see, the values are an extremely close match; exact to 6 places after the decimal point, and close to seven. From this, one may thus put forward for acceptance a further law of proportion as an additional physical law, to be linked up with that as given in part 1:
Where PE (e) & CE (m) are ratios:
PE (e) = Physical Equator, Earth (present) /
Physical Equator, Earth (past)
CE (m) = Celestial Equator, moon (present) /
Celestial Equator, moon (past)
With an acceptance of the fact that the celestial equator of an
orbit is indeed 2 x 22/7 the measure of its Semi-major axis - 22/7 being
the correct PHYSICAL constant in this case, as opposed to the
MATHEMATICAL constant of PI - one can easily grasp the close
correspondence of this new law to that discovered by Kepler.
For whereas Kepler’s law demonstrated a link between a change to the earth’s tropical year and a change to its own orbital semi-major axis, via the powers 2 and 3, the above is indicative of a law linking an earth tropical year change (also) with a simultaneous change to the semi-major axis of the moon orbit, in this instance by a law based upon a power combination of 4 and 3.
Based then upon the realisation that the geometry of celestial orbits
is identical to that of celestial forms, and also that further laws of
proportion of the same type as Kepler’s 3rd law apply to other celestial
bodies, being based upon a variety of unique combinations of powers
that actively govern their physical-orbital transformation; it is quite
clear then, that with the discovery of the two noted laws linked
specifically to the earth-moon system, that powerful support exists for
the ancient belief in a once existent earth year of 360 days.
For indeed, the newly discovered laws identify precisely the mechanics of the proposed celestial changes, as laid out in the Egyptian myth, related at the beginning of this discussion.
1) The pregnancy of Nut is akin to a human pregnancy almost. For, as
is obvious in the case of pregnant women; as their babies grow, they
‘swell up’ and become bigger. In the myth, when Nut the sky goddess
becomes pregnant however, it is the earth that swells up; a physical
expansion to accompany the increased number of days per year from a 360
2) The actual ‘children’ of Nut are the 5 (and 1/4) extra days
added to the initial 360 days, with the first stated law of proportion
(as given in part 1) indicating that the increase to the number of days
per year i.e. the ‘birth’ of Nut’s ‘children’, is in direct proportion
to the ‘swelling up’ of the earth i.e. an increase to its equatorial
3) At the same time that the earth underwent its physical
transformation in direct proportion to the increase to its tropical
year, the moon was itself forced to extend its orbit from the earth.
This is explained in the Egyptian myth as the moon becoming weaker and
smaller in the sky, due to Khonsu having ‘lost its light’ in the game of
Senet with Thoth. In this instance however, the extension of the moon
orbit (celestial equator) is not directly in proportion that of the
increase in the earth year (from the ideal of 360 days), as the law by
which it is governed involves a power combination of 3 and 4.
Consequently, due to the character of this law, the proportional
increase to the moon celestial equator is slightly greater than that of
the earth tropical year (or earth physical equator); being about
1.01946265198, as opposed to 1.01456163805.
The ancient Egyptian myth, combined then with the physical laws
of proportion, strongly supports the idea that at one point in the
remote history of the earth-moon system, the following was true:
Length of earth tropical year = 360 days
Physical circular circumference of the earth = 21600 IGM
Celestial circular circumference of the moon = 1296000 IGM
1 Day = 1 solar day of 24 hours
1 IGM = 1 Ideal Geographical Mile = 6000 British Feet
The primary units of angular geometry would appear to have been originally based then upon a set of real physical magnitudes, with the truth of a once existent earth orbit of 360 days per year decisively confirmed.