The Earth-Moon System Transformed

Keith Hunter

The Secret Ratio of Change Governing the Earth-Moon System

In all of the work so far presented, one is bound to wonder at the very significance of the increase to the earth year, and the extension of the moon orbit also. Indeed, just why exactly has the earth suffered a change to its tropical year to bring its orbital frequency to a rate of some 365.2421897 days, from 360 days? And what is the significance of the ratio of change of 1.01456163805?

Indeed, why also has the moon extended its orbital semi-major axis from an ideal of 206181.818181818 to some 210194.628959981772 IGM, and what is the significance of its ratio of change, 1.01946248613747773?

Upon face value, there does not appear to be anything significant in the extended values, or even the ratios. However, a most careful evaluation of the moon ratio of increase appears to reveal an incredible mathematical connection, one that not only confirms that the relative celestial extensions were not arbitrary, but also further confirms the physical validity of 22/7 over PI, to a level well beyond the arguments already considered in the previous essays.

The Sphere within the Cube – A Connection to the Earth-Moon System

In proceeding, let the reader recall then the length of the currently observed moon semi-major axis (as given in the previous essay, Imperial Measures: The Supreme Standard for Units of Length), and the ratio of increase from the noted ideal:

210194.628959981772 = Moon Semi-major Axis (current)
206181.818181818181… = Moon Semi-major Axis (Ideal)

Ratio of Change = 1.0194624861374777313038532649014

On the face of it, the numerical sequence of the ratio does not appear at all to possess any true significance. However, a certain geometrical relationship does indeed allow one to grasp its incredible importance. The relationship in question involves two shapes: a cube and a sphere.

If a sphere sits inside a cube such that it touches without crossing each of the six sides of the cube, then the diameter of the sphere is equal to the side edge of the cube itself. To determine the ratio of the volumes of each of the two forms, the following formulas are used:

Volume of a Cube = Side Length, Cubed.
Volume of a sphere = Diameter, Cubed x (1/6) x PI.

By way of example, one could determine a value for each of the noted forms in the above proscribed configuration by choosing a single distance unit that would simultaneously be equal to the side length of the cube, and also the diameter of the sphere housed within. And from this the relevant ratio could be derived. In the example shown below, the number 8 is chosen, though of course any number would achieve the same end:

Volume of a Cube = 8 x 8 x 8 = 512
Volume of a sphere = (8 x 8 x 8) x (1/6) x PI = 268.08257310

With these two values in hand, a simple division produces the following ratio:

512 / 268.08257310 = 1.9098593171027440292266051604702…

One should be aware that the very value as determined here is a mathematical constant respecting the arrangement of the noted forms. However, in examining the value itself, one can clearly see that in the formula for the volume of the sphere, one makes use of PI. However, as has been pointed out previously, PI has no validity respecting physical laws of proportion as operative within the universe, and one MUST employ 22/7 in its place. In doing so, the above example yields the following alternate answer:

Volume of a Cube = 8 x 8 x 8 = 512

Volume of a sphere = (8 x 8 x 8) x (1/6) x (22/7) = 268.1904762… = (268 + 4/21)

And: 512 / (268 + 4/21) = 1.909090909090909090909090909…

What is most intriguing about this alternate ratio is that via a simple set of manipulations, a numerical value almost an exact match to the ratio of increase of the moon semi-major axis is to be had:

1.9090909090909…/ 100 = 0.019090909090909...

1 - 0.019090909090909… = 0.98090909090909...(1079 / 1100)

1/ 0.98090909090909... = 1.0194624652455977757182576459685 (1100 / 1079)

One may compare this answer to the already derived ratio of increase for the moon semi-major axis:

1.0194624861374777313038532649014

The level of correspondence is astounding; precise to 7 figures after the decimal point. Moreover, if one uses the exact fraction of 1100/1079 as given for the moon ratio of increase, combined with 22/7, then one can derive a current value for the semi-major axis of the moon wherein it can be seen that the very ratio of increase itself is contained within the distance length separating the earth and moon, as expressed in units of IGM:

(1296000 / (2 x (22/7))) x (1100/1079) = 2101946.24652455977757182576459685 IGM

Setting aside the first numerical figure, which is a 2, and ignoring the placement of the decimal point, one can see the following:

Current Moon Semi-major Axis: 2 101946.24652455977757182576459685 IGM

Moon Semi-major Axis ratio of increase: 1.0194624652455977757182576459685

From these connections, there can thus be only one conclusion:

THE TRANSFORMATION OF THE EARTH-MOON SYSTEM FROM ITS IDEAL STATE TO ONE INCORPORATING ITS CURRENT MAGNITUDES WAS NOT ARBITRARY, BUT BASED UPON THE KEY FRACTION OF 1100 / 1079 – THE RATIO OF INCREASE OF THE MOON SEMI-MAJOR AXIS ITSELF, WHOSE PRECISE VALUE IS DERIVED FROM A CONSTANT LINKED TO THE FORM OF A SPHERE PERFECTLY CONTAINED WITHIN A CUBE, INVOLVING THE RATIO 22/7.

The Complete Values of the Current Earth-Moon System

As a result of the above associations, it is thus possible to derive a series of values for the current earth-moon system based purely upon the key fraction of 1100/1079, through use of the proportional laws as presented in the previous essays. Set beside the values of the ideal earth-moon system, they are presented as follows:

Ideal Earth-Moon System:

360 Days: Earth Tropical Year
21600 IGM: Earth Equatorial Circumference

30 Days: Moon Synodic Month
1296000 IGM: Moon Circular Celestial Equator
206181.81818181… IGM: Semi-Major Axis, Moon Orbit

Present-Day Earth-Moon System:

365.24218408630 Days: Earth Tropical Year
21914.531045178 IGM: Earth Equatorial Circumference

29.530585513798 Days: Moon Synodic Month
1321223.3549582 IGM: Moon Circular Celestial Equator
2101946.2465245 IGM: Semi-Major Axis, Moon Orbit

NB: 1 IGM = 1 Ideal Geographical Mile = 6000 British Feet.


Further Reading:

Concerning the issue of the transformation of the earth year and moon month, there are various studies that have been conducted to determine historically what values they each possessed.

A good site that reviews some of the scientific material related to this matter can be accessed at the following link, which gives further information on some of the more subtle aspects of the earth-moon system and its dynamics, specifically with respect to how a change in the spin rate of the earth, transforms the length of the synodic month.

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