A Once Existent Earth Year of 360 days (Part 1)
Keith M. Hunter
360 Days as an Ideal Earth Standard:
If the ancients were right that at some point in the past the earth suffered a general increase to its orbital period, transforming the earth year from 360 days to 365.2421897 days, such a change, were it to have occurred, could not have done so without also causing various other celestial transformations. As indeed, it is well established in science that the physical motion of one astronomical body, so affected, can influence the characteristics of other nearby objects, or even aspects of its own self. One clear example of the former worthy of citation, and well known to astronomers, is that a change to the speed of the axial rotation of the earth directly affects the orbital distance between the earth and the moon.
It is exactly these sorts of changes that form the very basis of the proof of a once existent earth year of 360 days; specifically, by way of an intriguing set of physical associations found to link the proposed tropical year increase (from 360 days to 365.2421897 days), to an apparent increase in both the physical size of the earth, and also the mean distance separating the earth and moon - both of which are subtly hinted at as occurring alongside the earth year transformation, as detailed in the Egyptian myth, related previously. Indeed, as part of the proof, the 360 degree circle used in geometry itself, is also revealed to have been based originally upon 360 days; unit intervals completing a full ideal earth orbit.
In an evaluation of such changes, what actually brings the decisive mathematical connections to light is a distinct relationship that would appear to exist between the primary units of angular measure, as known to modern day geometers, and various real distance units of the imperial system. A careful examination of the earth tropical year with respect to both the physical size of the planet, and also the moon orbit, reveals the critical connections. Before proceeding directly though to the evaluation, a brief mention of the basic units of angular measure must be had.
Angular Measure: The Basics
In the modern age it is quite well established that the most fundamental unit of angular measure is the degree, which is taken to be 1/360th of the sweep of a circle; a 360 degree circle thus being the full completed form. More refined angular units are of course also used though to specify more acute angles. And this is done following a base-60 progression, through which degrees are split up into 60 smaller parts, each called a minute of arc, and still further, each minute of arc is split up into 60 even smaller parts, known as seconds of arc. A full circle may be composed then of either:
In general, one should of course realise that usually combinations of the above measures are used to specify a given angle. For example, the axial tilt of the earth is usually expressed as about 23 degrees, 26 minutes and 15 seconds (generally speaking this angle changes slightly every year); an angle responsible for the seasons.
What is of course important to realise is that in geometry, all of these expressed numerical values, set in accordance with a 360 degree circle (i.e. degrees, minutes, and seconds of arc), are angles, and thus are abstract in their nature. They do not refer to anything specific as such. Or at least, they are not thought to by modern geometers.
With respect to the physical geometry of the earth, angular measures composed of a primary 360 degree circle including minutes, and seconds of arc, are the primary unit intervals used to map the planet as a whole. Under this system, the equator of the earth is representative of zero degrees latitude, with the Greenwich meridian marking zero degrees longitude.
Within this matrix, one may thus specify any position upon the earth’s surface either north or south of the equator, and east or west of the Greenwich meridian. Of course, such a system could be applied to any planetary body of any size, using a 'template' of a 360 degree circle, due to the fact that it is based upon angular values, and not arc length measures that actually play out over the real surface of a given body. That being said, upon the issue of the ‘real’ measurements of a given form, one may indeed employ basic angular measures as a means to derive a set of real arc length values over such a body.
Respecting the earth, one may actively cite both the geographical mile and also the nautical mile as examples of real distance measures derived from angular ‘sweeps’ over the surface of the planet. In the case of the former, the geographical mile is the arc length distance swept out over the surface of the earth by a single minute of arc upon the circular plane of the earth’s equator; equal to 1/21600 of the earth’s equatorial circumference. By contrast, the nautical mile is a unit measure based upon the total circumference of the earth from pole to pole, which is elliptical in nature; being also 1/21600 of such a surface circumference.
Based upon the known dimensions of the earth, the actual values of these two noted measures may be calculated as follows:
Earth Equatorial Circumference = 24902.4 statute miles
Elliptical (pole to pole) Circumference = 24860.2 statute miles
Geographical mile = (24902.4 x 5280) / 21600 = 6087.25333…feet
Nautical mile = (24860.2 x 5280) / 21600 = 6076.93777…feet
As one can see, the nautical mile is just less than the geographical mile; a result of the planet being compressed along its axis due to its daily rotation, causing the earth to expand outwards at its equator. Indeed, the very dynamics of this readily accounts for the fact that the equator of the earth is circular and the polar circumference of the earth is elliptical. (The plane of the equator is at 90 degrees to the planet’s axis of spin).
With the above facts established, one is thus bound to suspect almost intuitively then that were indeed the earth to have once possessed a yearly orbit of precisely 360 days, then certain of its other primary physical characteristics, would also have been different; specifically, the physical circumference of the earth itself.
Moreover, in taking this point further; considering the exacting nature of an earth year of precisely 360 days one would suspect that were the earth in fact to have possessed such a year, it would also have simultaneously possessed a physical circumference of such measure, so as to actually be in harmony with the very value of its orbital period i.e that 360 days fully completes one full journey about the sun. And one would therefore expect also, what must be some sort of lawful association between an increase of the earth year (from an ideal of 360 days to its present value), and an accompanying change to the physical size of the earth.
But can this be demonstrated though?
A careful evaluation of the present-day value for the circular circumference of the earth at the plane of its equator, would appear to reveal the answer.
An Ideal Geographical Mile
Focusing upon the equatorial circumference of the earth, it can be seen that its fractional split into 21600 equal parts (minutes of arc), so generating the geographical mile, produces a value that when expressed in standard feet, does not appear too remarkable at all: 6087.25333…feet. And yet, were the earth to have once actively possessed 360 days per year, one would expect some sort of harmonic affinity between the value of its orbit and the actual size of the planet; an ordered correspondence of some sort.
To determine the truth of such an idea, one would be required to lawfully determine nothing less than precisely just what would have been the circumference of the earth, whilst under a year of 360 days. An examination of the primary distance measures of the basic Imperial System (as currently used in the United Kingdom and the United States) would appear to reveal the decisive breakthrough.
Of the Imperial system of measures, the most commonly used are the inch, foot, fathom, and the statute mile. In relation to one another, they are as follows:
12 inches = 1 foot
In reviewing these measures it can be seen that the progression from the foot unit to the fathom involves the multiplier 6. Indeed, in the case of the already noted units of angular measure, it can also be seen that they are similarly connected, via a base-10 multiple of this figure i.e. 60. The significance of this readily becomes apparent when one evaluates the current equatorial circumference of the earth expressed specifically in terms of the fathom unit:
Equatorial circumference = 24902.4 statute miles
With the equator so converted, one is able to bring a most remarkable mathematical association to light. For it can now be seen, that the reduction of this very value by the exact ratio between the current earth year and the suggested ideal of 360 days, produces a figure very close to precisely 21600000, which is of the same numeric sequence as the value given to the total number of minutes of arc that complete a full circle:
365.2421897 / 360 = 1.014561638
With: 21600000 – 21599586.64 = 413.3 fathoms
Also, comparing the ratios directly using the value 21600000 as a standard, one can derive the following:
365.2421897 / 360 = 1.014561638
From the above it can be seen then that there is an extremely accurate match between the noted ratios; from which one might draw two distinct conclusions. The first is that the primary distance units of the Imperial System would appear to have been established not in accordance with the size of the earth as it currently stands, but rather in accordance with an earth size reduced from its present, by the same ratio that governed the increase of the earth tropical year from an ideal of 360 days. Secondly, the very reality of this fact strongly implies that a general physical law of proportion exists linking the transformation of the earth year to the transformation of the physical size of the earth, upon its equatorial plane.
Given the truth of these two points, were the earth to have possessed a 360 day year, the physical equatorial circumference of the earth would have been precisely 21600000 fathoms, which would imply that a geographical mile at such a time would be exactly 6000 ft (21600000 x 6 and divided by 21600 = 6000). One may thus call such a unit measure an Ideal Geographical Mile, or IGM for short.
The claim hereby made, that a change to the earth’s tropical year is directly proportional to a change to its physical circumference, and that this is revealing of an actual physical law, is a bold one. However, it is one that does have support from within the realm of astronomy. Indeed, certain critical discoveries over the past few hundred years concerning the motions of the planets have demonstrated that proportional laws per se are without doubt operative within the universe. And furthermore, such laws of this type have been found to directly apply to all of the planets within the solar system. A slight detour in history is thus called for to demonstrate the reality of this fact.
The Physical Validity of Laws of Proportion
Without doubt, the greatest confirmation of the existence of the reality of proportional laws in governing various changes to certain aspects of planetary motion is to be found with the discoveries of Johannes Kepler (1571 – 1630 AD). During his lifetime Kepler was the first to discover the general principles that governed the planets and to explain the manner of their non-linear orbits about the sun. Thus was he able to correct many errors that had existed in the realm of astronomy even from ancient times. Today, the principles that Kepler uncovered with regard to explaining the motions of the planets are generally grouped into a set of 3 primary laws. Briefly, they are as follows:
1) Planets orbit the sun in elliptical orbits where the Sun is positioned at one of the two focal points.
2) A planet sweeps out equal areas in equal periods of time; the area being swept out from the sun itself and not the centre of the ellipse, which explains why they move faster in their orbits when nearest to the sun and slower when they are further away from it.
3) The time taken for a planet to orbit the sun (orbital period) is related to its distance from the sun at its mean point of approach (semi-major axis), by a very precise mathematical law; a law generally referred to as Kepler’s ‘harmonic law’, expressed as follows:
Mars Orbital period = 686.9297110 solar days
686.9297110 / 365.2421897 = 1.880751266
Mars Semi-major Axis = 81801193.26 x 1.523658277
According to the above result, Mars should have, in accordance with Kepler’s law, a mean distance from the sun of 124637065.17 IGM. And, actual observations do indeed reveal a figure very close to this; a fact that offers considerable support to the principled validity of the law:
From the above one can clearly see then the importance of Kepler’s Harmonic law for the planets of the solar system. Specifically, the character of the law implies that the orbital period of a planet determines its mean distance from the sun, and that the transformation of the orbital period affects a distinct change to its mean point of approach i.e. the length of its semi-major axis, as per the precise combination of powers built into the law.
But how though does the reality of Kepler’s law support that which was proposed earlier – that a change to the earth tropical year would cause a simultaneous change to the physical circumference of the earth?
The answer lies with an understanding of how the geometry of the orbits of planets is related to that of their outward physical form. Essentially, the geometry of a planetary orbit is exactly identical to that of the geometry of the physical form of a planet. Both are ellipsoid in nature. Thus, of the earth, the circumference of the planet on the plane of the equator is perfectly circular, whereas the circumference of the planet taken as a plane cut 90 degrees to the equator, passing through the axis, is elliptical (i.e. viewed from the ‘side’ the curvature of the planet is that of a 2 dimensional ellipse). Such facts also hold true for the very orbit of the earth, save only that the ellipsoid form of the orbit is invisible. And yet be that as it may, the mathematical geometry of both form and orbit is identical. Thus:
1) The actual elliptical orbital path of the earth is the mathematical equivalent of the earth’s physical (polar) elliptical circumference.
2) The mean distance of approach of the earth to the sun, known as its semi-major axis, is the mathematical equivalent of the equatorial radius component of the physical earth.
3) The circular (invisible) equator of the earth orbit at 90 degrees to its actual orbital plane is in fact the equivalent of the earth’s own physical circular equator. The former, one may thus designate the ‘celestial equator’ of the earth’s orbit.
With an understanding of the association then between the geometry of a planetary orbit and that of its physical form, one can clearly grasp the correspondence between Kepler’s law and that which was proposed earlier in this work.
Essentially, just as Kepler’s law relates a change in the earth tropical year to a change in the semi-major axis component of the earth’s orbit, via the noted powers of 2 and 3, the law described previously relates a change to the tropical year, to a (simultaneous) change also to the semi-major axis of the earth’s physical form i.e. its equatorial radius. In this latter instance however both components would appear to be transformed directly in proportion to one another, and thus the powers are 1 and 1. Given this, one may formally express the law as follows:
TY = Tropical Year (present) / Tropical Year (past)
As an equation this law has the following form:
TY = Tropical Year (Present)
The reality of the above stated law directly implies that were the earth to be ‘back-transformed’ to one containing 360 days from one of 365.2421897 days, then the physical size of the planet would also by necessity have to be reduced by exactly the same ratio as between these two orbital periods i.e. 1.014561638. And indeed, it is hereby suggested directly that such a back-transformation does reveal the state of the earth as was once manifest at some remote point in history, wherein there truly was an exacting harmonic correspondence between the value of its orbital period in days, and the value ascribed to the equatorial circumference of the earth in Ideal Geographical Miles; both of which conformed to the basic numeric sequence of the Babylonian measures: 360 & 21600, via a x60 multiplier.
The important to mention however, is that the numerical value of 360, nominally taken to be representative of a 360 degree circle (in geometry), does in fact represent 360 days of an ideal earth year, with the value 21600, actively representing the measure of the earth equator in ideal geographical miles.
From the above noted law one can now actually use the very measure of the tropical year to derive a value for the current equatorial circumference of the earth based upon a standard of 360 days:
365.2421897 / 360 = 1.014561638
Compared with what is the known measured value for the equatorial circumference of the earth, there is very little difference:
24902.87657 – 24902.4 = 0.4765 miles
Conclusions to be Drawn from the Above Evaluation:
1) The Imperial System of measures including the ‘angular’ measures (the 360 degree circle including minutes and seconds of arc) of the ancients were originally based upon the standard of an ‘ideal’ earth of 360 days.
2) The circumference of the ideal earth at the equator, expressed in units of Ideal geographical miles, was in harmony numerically with the total number of days in the earth tropical year via a ‘base-60’ multiplier i.e. from 360 days > 360 x 60 = 21600, expressed in units of Ideal Geographical miles.
3) The proposed stated law linking a change in the tropical year to a change to the semi major axis of the earth’s form (equatorial radius), will likely act in perfect unison with Kepler’s law, which itself would reveal how any change to the earth tropical year would affect specifically the earth’s orbital semi-major axis.
As a result of the evidence presented, it would appear then that there is strong - albeit indirect - support for the notion that the earth did indeed at one time possess an ‘ideal’ tropical year of 360 days in conjunction with an equatorial circumference of precisely 21600 ideal geographical miles. However, the evidence does not just rest upon the noted association between the tropical year and the physical size of the earth. Indeed, were one still to have any doubts, there is a further, utterly decisive connection, involving the orbit of the moon, that truly confirms beyond all reasonable doubt, a once existent earth year of 360 days. And this may be viewed in part two of the proof: