The Astronomical Basis of Ancient Mythology
Did the Earth once possess 360 days per year?
By Keith M. Hunter
Did the earth once possess 360 days per year? This is a question that has been considered by many people of late. It is of course well established that the earth currently possesses 365.2421897 (tropical year) days per year [1]. And yet, when we look back through the ages, there are a multitude of myths and stories from many different cultures widely separated geographically that speak of a time when the earth did once possess 360 days per year. Indeed, many past cultures established calendar systems based upon a 360-day year, including the ancient Egyptians, the Maya and the Babylonians to name but a few. Even in ancient times though, the astronomers of their age were well aware of and able to determine that the earth did not possess 360 days per year. Their own measurements were accurate enough to work out that it was indeed about 365 and a quarter and not 360 days. However they still used 360 in their reckoning. Both years were recognised and acknowledged. What the ancients believed was that the earth did indeed truly possess a 360-day year at some point in its past, but as a result of some unknown agency the earth gained an extra number of days. This was not something that was held to be good either. In fact the extra five days or so were thought to be ‘unlucky’ in the eyes of many. In effect, a 360-day year was thought harmonious and the current year was not. We have then, according to the ancients, deviated from an ideal orbital configuration to the present one.
Of course the very idea that the earth once truly possessed 360 days per year is regarded as preposterous and a nonsense by most scientists of the present age. It is dismissed out of hand as being something that cannot be proven. And yet, over the last year or so, my own studies have led me to a true physical proof that does indeed demonstrate the validity of this idea that the earth did once have a 360-day year. This proof also simultaneously reveals the basis for the angular system of measurement that has been passed down to us from the Babylonians, leading us to split the circle into 360 degrees. It has often been suggested by some researchers studying ancient systems of measure, that we split up the circle into 360 parts because the earth did indeed once possess this number of days per year. Whilst most dismiss this, there is very good evidence that it is true.
The purpose of this present essay is twofold. Firstly, it is an attempt to demonstrate why we use the units of angular measure we do, including degrees, minutes of arc and seconds of arc, and to explain how this very system of measure is in no way arbitrary; and secondly to demonstrate how this system, based in physical reality, allows us to account for an increased number of days per year from 360 to 365.2421897. I will attempt to make this essay brief and concise, but also I will attempt to explain important astronomical concepts that are necessary to the proof, as required. This essay should be well within the grasp of the layman.
To begin, I will recite a myth concerning the moon, and how this celestial object was thought to play its part in the earth gaining an extra number of days in its yearly orbit. This myth is the Egyptian version but it is a myth that is recounted in many cultures. The names are different, the story the same. Here is the Moon Myth…
How the
Moon lost its light
A long time ago, Re, who was god of the sun ruled the earth. During this time, he heard of a prophecy that Nut, the sky goddess would give birth to a son who would depose him. Therefore Re cast a spell to the effect that Nut could not give birth on any day of the year. Now, there were indeed 360 days per year at this time. To help Nut to counter this spell, the wisdom god Thoth devised a plan. Thoth went to the Moon god Khonsu and asked that he play a game known as senet. Thoth said that he wanted to play for the moon’s light. Khonsu was confident that he could win and agreed. However, he lost the game several times in succession such that Thoth ended up winning from the moon a measure of light equal to about five days. Thoth then took this extra time and gave it to Nut. This had the effect of increasing the earth’s number of days per year and allowing Nut to give birth on one of these extra days attached to the 360 already present. Losing its light had quite an effect on the moon, for it became weaker and smaller in the sky. It had to hide itself periodically to recuperate, and could only show itself fully for a short time before having to disappear to regain its strength. [2]
The above story includes many interesting features that are to be taken note of. Of particular importance is that the moon gets smaller in the sky as it ‘loses its light’. This, I interpret to mean that it increases its orbital distance from the earth, for being further away, it would be smaller to the eye. In addition to which this very action causes the earth to gain time. Also, the idea of the moon becoming weaker could very well imply that the moon radically changed its orbital plane to the earth with respect to the sun, during this event. These ideas may certainly fit the story, but can they be proven? The answer is yes, and to present this proof, I must address the basis for the Babylonian system of angular measure.
The
Origin of the Babylonian system of Geometry
In geometry, it is well known that we split up the circle into 360 equal parts called degrees. In each degree there are 60 smaller parts called minutes of arc, and within each minute of arc are sixty even smaller parts called seconds of arc. Thus, a full circle in angular measure possesses either:
360 degrees
21600 minutes of arc
1296000 seconds of arc
In geometry, these are all angles, and thus are abstract in their nature. They do not refer to anything specific as such. However, my own studies of the origin of this system have led me to conclude that the above were once based upon something very real. They each had as their origin a certain specific celestial phenomena. I theorize that these numbers were once based upon the following:
360 – number of days per year of
the earth
21600 – equatorial circumference of the earth in ideal geographical miles (6000
ft) [3]
1296000 – Orbital circumference of the Moon in ideal geographical miles, whose
plane of orbit about the earth is on the plane of the earth’s equator extended
into space.
Note: As the earth possesses a circular circumference at its equator, due to its being 90 degrees from its axis of rotation, I intuitively believe that the moon should also possess a circular orbit in the above proposed configuration; one that is exactly 60 times the physical circumference of the earth as measured in ideal geographical miles, on the very plane of the equator.
I theorize that the Babylonian system of measure that has been passed down to this present age, and whose numbers are today regarded only as a convenient way of specifying a series of abstract angles with ever greater refinement, were once understood to represent the physical configuration of the earth-moon system in an ideal and harmonious state. The 360 degrees were indicative of the earth when it once possessed this number of days (solar, i.e. 24 hours in duration) to one orbit about the sun. Furthermore, by mathematically multiplying this number by 60 we are given the actual physical circumference of the earth at its equator in units of 6000ft. In addition, by further multiplication by 60, we extend the plane of the equator to obtain the true orbit of the moon, being exactly 60 times that of the earth’s equatorial circumference. Thus, I propose that at some point in the past, this was a real earth-moon celestial configuration, wherein all of these orbital-physical features were indeed true both for the earth and the moon. As a result, we could move between these features simply by multiplying or dividing by 60, which was what the Babylonian system of measure was based upon. Indeed, theirs was a base 60 system. From this state of harmony, I theorize that the earth and the moon both ‘degraded’ their orbits, such that the earth increased both its number days per year and its equatorial circumference, the moon lost its circular orbit of precisely 1296000 geographical miles, increased its distance from the earth (semi-major axis) and left the plane of the earth’s equator; the latter two events resulting in the moon becoming smaller in the sky and weaker, leading to the creation of the phases of the moon that we now see and were spoken of in the moon myth.
The Proof
The theory that I have outlined above is proven in two parts. Firstly, by establishing a link between the number of days per year of the earth and its equatorial circumference, and secondly, in establishing a link between the distance of the moon to the earth and how a change of this distance affects the total time of the earth’s orbit. I shall deal with both in turn.
1) The number of days per year & equatorial earth circumference.
The first part of this proof rests upon a certain link between a unit of time and a unit of distance. There are studies that have been carried out to examine the rotational speed of the earth on its axis. It is known today that the earth possesses a day of 24 hours (86400 seconds). This is a standard solar day, and the length of time between the Sun returning to the same position in the sky on two successive occasions e.g. noon to noon. According to various scientific studies, some examining ancient records of eclipses, others the even more ancient geological fossil record, evidence appears to exist to support the conclusion that the earth has possessed a very stable solar day of about 24 hours exactly, stretching millions of years into the past. Of course, the data does show that there have been very slight fluctuations of a very small fraction of a second above and below 86400 seconds exactly, especially noticeable and recorded over very recent times [4].
However, this does not seem to be problematic, but really should be expected. Some researchers suggest that there has been a long-term trend of the earth slowing down its rotation on its axis by an extremely small fraction of a second per millennia, but this is not known to be certain, or whether if it is true, that it is not part of a long term fluctuation that will be corrected with a successive period of increase in axial rotation. Fossil records suggest for example, that the synodic month of the moon, about 29.5 days in duration, has remained remarkably constant over the last 50 million years, hardly changing at all. This is thought to indicate that the earth also has remained stable in axial rotation over this time period due to the link that exists between the synodic month and the earth’s solar day [5]. The important point here that I suggest is that the earth may be actively maintaining and seeking to maintain a 24-hour day. This could be an equilibrium point. As a result, it is my belief that if the earth were to have possessed 360 days per year in the past, each day then, would be as each day now; that is, equal to 24 hours in length. The earth may well fluctuate about an exact 24 hour day on its axis, with a very slight deviation of a fraction of a second above and below this mark, but this is independent of an increase in the actual total number of days in its year, which is something entirely separate.
With the above postulated, a definite link between a single solar day, as a unit of time, and a certain arc length in relation to the earth, can be established. I propose that 24 hours of time are equal to 60 geographical miles, each of which equal 6000ft in length. Thus, by simply multiplying the number of days per year of the earth by 60, whether it is 360 or 365.2421897, we arrive at a magnitude that must be understood to represent an actual arc length distance in units of 6000ft on the plane of the earth’s equator. Thus, an earth with 360 days per year will possess an equatorial circumference of 21600 geographical miles (6000ft), whereas the current earth will possess: 365.2421897 x 60 = 21914.531382. Indeed, this value is confirmed as being the current earth circumference at the equator. Converting from geographical miles (6000 ft) to statute miles (5280 ft), we get a more familiar answer: (6000/5280) x 21914.531382 = 24902.8765704 miles [6]. The relationship between the equatorial circumference of the earth and number of days per year is such that they increase in proportion, so long as the earth maintains a 24-hour solar day. Thus, according to this theory, the earth today must possess a greater equatorial circumference than when it only had 360 days per year. I propose that the total orbital time increase of the earth is proportional to the increase in the physical equatorial circumference of the planet. And thus I make the suggestion that the earth possessed in effect a sort of ideal circumference to match an ideal year of 360 days.
A further conclusion that must be drawn from this is that the ancient
civilisations of
2) Moon Orbital Radius and the Earth’s Total Orbital Time.
The second part of my proof establishing the origin of the Babylonian system of measure and the basis for the earth increasing its number of days per year, is similar to the above, and indeed strengthens it. In order to demonstrate a link between the distance between the moon and the earth, and how a change in this distance affects the earth’s orbit, I will need to summarise certain well-known astronomical laws, as they form the basis for my proof. The laws in question are those discovered by Johannes Kepler in the early 17th century. During this period Kepler developed 3 general laws governing the orbits of the known planets within the solar system. These laws are accepted as true today. They are as follows.
a) Planets orbit the sun in elliptical orbits where the Sun is positioned at one of the two focal points.
b) A planet sweeps out equal areas in equal periods of time. The area is swept out from the sun itself and not the centre of the ellipse, and this explains why planets move faster in their orbits near to the sun than when they are further away from it in their orbit.
c) The Harmonic law: This law is expressed usually in the form of an equation: p^2 = a^3. Essentially, the orbital period (p) of a planet i.e. the total time taken for the planet to complete a single orbit about the sun, is, when squared, proportional to the semi-major axis (a) i.e. mean distance of the planet to the sun, when cubed.
For those not familiar with these laws, I will attempt to explain them in more detail and to provide a working example of the third law. This example will be most helpful for the layman (and I count myself as one). It will most greatly aid the understanding of the proof I intend to develop.
A)
The Nature of an ellipse
An ellipse is constructed or revealed when a plane slice is made through a cone. Thus, if we take a flat circle as our base, mark out from the centre a line directly upwards a certain length, and imagine an infinite series of straight lines radiating from this apex point to all points on the perimeter of the circular base, then, we have a cone. With our cone, if we take several plane slices through it parallel to the base at various locations, then we will have a series of smaller circles. However, if we slice through the cone with a slight angle to the base, then we have an ellipse. An ellipse has the appearance of a slightly squashed circle, and possesses a two-way symmetry. The shortest point from the centre of the ellipse to the perimeter is called the semi-minor axis, and is at 90 degrees to the longest point from the centre to the perimeter, known as the semi-major axis. There are thus two of each and they form a cross radiating from the centre. Also, between the centre of the ellipse and the perimeter, along both of the semi-major axis lines radiating from the centre in opposite directions, there is a focal point. The semi-major axis is also found to be the distance between the point where the semi-minor axis touches the perimeter and either one of these focal points. It is at this position in its elliptical orbit, on the perimeter, that a planet (or a moon) is at its mean distance from either focal point. This distance, which is the semi-major axis of a celestial body, is that referred to as ‘a’ in Kepler’s harmonic law formula.
Kepler found that all of the planets known in his time (including those
not known) orbited in elliptical paths of various different eccentricities,
though most were very close to circular. The Sun was positioned at the focal
point of these orbits – the other being empty so to speak. The mean
distance/semi-major axis from the sun is that between the point of closest
approach (perihelion) and furthest approach (aphelion). In a circle, which is a
special case of an ellipse, the semi-major axis is also the radius of the
circle, as is the semi-minor axis, for they will both be of the same length.
The two focal points are also merged in a circle and have the same place,
whereas they are separate and separated in an ellipse.
B) The Harmonic Law: A working example.
The harmonic law allows us to relate the planets to each other and to discover their orbital characteristics. Kepler’s harmonic law relates all of the planets in the solar system. To verify this we need to take a planet as a standard reference. Any planet will do, but we usually use the earth. Thus, the total time for the earth to orbit the sun, is our reference p (period), in the equation p^2 = a^3. The earth will possess also a mean distance from the sun, that is its semi-major axis, a. The known total time for the earth to orbit once is 365.2421897 days (24 hours). The semi-major axis of the earth is about 81801110 geographical miles (6000ft), which is just short of 93 million statute miles. Using these values as our standard, we can assign a unit of 1, to each, and then use Kepler’s equation to help us to discover either the time or mean distance of any other planet in the solar system. An example would be mars, as follows:
Suppose we know the total time taken for mars to complete one orbit about the sun. From this information, we can then use Kepler’s law to determine the semi-major axis of mars, using the earth itself as our initial standard. The orbital time of mars is known to be 686.973 earth days (24 hours). Thus, according to the harmonic law, the procedure for calculating the semi-major axis of mars is as follows:
1) 686.973 / 365.2421897 = 1.88086978
2) 1.88086978 squared = 3.537671160
3) 3.537671160 cube-rooted = 1.5237222887
Just as the ratio between the orbital time of earth and mars is 1.88086978, Kepler’s law determines that the semi-major axis of Mars is 1.5237222887 that of the earth’s. If we then multiply 81801110 by 1.5237222887, the mean distance of mars is calculated to be 124642174.5539 geographical miles, or 141638834.7203 statute miles. This matches the actual semi-major axis of mars that is observed in the sky. Therefore, with this law we can calculate either the mean distance from the sun or the total orbital time of any planet, so long as we possess knowledge of one of these two things, the other being unknown; and, so long as we also know both of them for another celestial object, that will serve as a standard.
The Earth,
as Judged, Against Itself
Employing Kepler’s harmonic law, and the knowledge we possess about the
orbital time of the earth in its proposed ideal state as well as its present
one, we are able to judge the earth against itself, as if seemingly, it were
another planet in the solar system. The first assumption is that if the earth
were to have possessed 360 days per year in the past, each day would be 24
hours in length. The stability of the solar day stretching millions of years
into the past is supported by the scientific studies mentioned earlier.
Currently then, the tropical year is 365.2421897 days, each of these days also
being 24 hours long. Thus, we can determine, using Kepler’s law, what the
earth’s semi-major axis would have been for the proposed ideal earth because of
our knowledge of the earth’s orbital period at the time:
1) 365.2421897 / 360 =
1.01456163805
2) 1.01456163805 squared = 1.02933531741
3) 1.02933531741 cube-rooted = 1.009684349753
Therefore, the earth would possess a semi-major axis less than that which it currently holds by a ratio of 1.009684349753, were it to possess 360 days per year. The critical point to understand is that an increase in the earth’s orbital period by 1.01456163805, bringing it up to 365.2421897, is accompanied by an increase in the earth’s semi-major axis by 1.009684349753. Thus, the earth, were it to possess 360 days per year would have a mean distance from the sun of: 81801110 / 1.009684349753 = 81016517.7067 ideal geographical miles. It would be slightly closer than it is at present.
Hold the above in your mind, whilst we next turn to the moon.
Deviation
of the Moon from its Ideal Orbit
It has been proposed that the basis of the Babylonian system of measure was a specific earth-moon celestial configuration, wherein the earth’s number of days per year was 360, the physical circumference of the earth at the equator was 21600 geographical miles (6000ft), and the orbit of the moon in its ideal state was circular and equal to 1296000 geographical miles; all of the features of this system being present simultaneously at some point in the distance past.
If we examine the moon in its current orbit, we can see that it possesses an orbit that is elliptical much like the earth, though slightly more eccentric. It also has a specific semi-major axis or mean distance from the earth, which itself resides at one of the two focal points in the moon’s orbit, just as the sun serves as one of the focal points in the earth’s yearly orbit. Therefore, we can investigate the current mean distance of the moon against the proposed ideal mean distance, and their association with the orbital features of the earth.
The moon, were it in a circular orbit about the earth, would possess a semi-major axis equal to simply the radius of the circle, for the two focal points are merged, and the distance from the moon to the earth is the same at any point in its orbit. Thus, the ratio between the radius of the moon with an orbit of 1296000 geographical miles, and the current semi-major axis of the earth in its elliptical orbit can be determined. This is achieved with one special qualification, as I will explain.
PI fails where 22/7 succeeds
There is one important qualification to my theory. Indeed, without it, the theory collapses like a house of cards. Throughout much of my work into planetary harmonies, I have noted that certain relationships between the features of the earth, and other celestial bodies only seem to ‘work’, or reveal an important harmony when related by rational numbers, of which 22/7 is one of the most important. Another, which I will briefly mention is a ‘rational’ square root of 2, equal to 1 + 29/70. This is not to dismiss so called irrational numbers. On the contrary, they are all important. However, the physical theory that I put forward here rests upon 22/7 being valid, as it relates to the orbit of the moon. In one sense this is paradoxical and it seems obviously wrong to suggest that the ratio between a circle and its diameter is 22/7 and not PI. However, I maintain the validity of 22/7 against PI. Paradoxical or not, though I cannot fully explain why, PI fails where 22/7 succeeds in properly relating the critical features of the moon’s orbit to certain features of the earth. I will say no more about this issue for now, but move on with my proof and let the numerical/physical magnitudes that will be shortly revealed in support of it, speak for themselves.
The moon, were it in a circular orbit of 1296000 geographical miles on the plane of the equator extended into space, would possess a radius or semi-major axis of (1296000/(22/7))/2 = 206181.8181818181 (recurring…). The present mean distance from the earth to the moon is determined by observation. Currently, this is known to a high degree of accuracy. There are several references that I will cite. Most textbooks state that the mean distance between the moon and the earth is 384400 kilometres. However, this is an answer that I believe is rounded down. One specific source I can cite that gives a better answer and is more accurate is indeed Microsoft’s Encarta 98, which gives 384403 kilometres. However, a further reference is to be found in a book called, “The Exploration of the universe” (1987) by Abell Morrison, who states that currently the distance between the centre of the earth and the centre of the moon is 384404 kilometres, with an uncertainty of about 0.5 kilometres [7]. This is the distance then that I shall employ in the following proof. Firstly, it shall be converted into units of ideal geographical miles. According to the Supplement to the Astronomical Almanac (p.716), the conversion ratio between kilometres and Statute miles is 0.6213711922. The conversion ratio between Statute miles (5280 ft) and ideal geographical miles (6000 ft) is simply 0.88.
Thus: 384404 x 0.6213711922 x 0.88 = 210194.663154474944
We can now compare the mean distance between the moon and the earth when the moon possessed a circular ideal orbit, and the current mean distance from the earth to moon. What should be noted is the ratio of increase, which is determined as follows:
210194.663154474944 / 206181.8181818181 = 1.01946265198
This value of 1.01946265198 is then seen to be the ratio of increase of the moon’s radius from an ideal of 206181.81818181 geographical miles, in a circular orbit of 1296000, to its present semi-major axis / mean distance from the earth, of 210194.663154474944. If we recall the moon myth, the moon is said to become ‘smaller in the sky’ and that as a result it loses its light, and this somehow ‘transfers’ a measure of time to the earth. By a careful consideration of both the increase of the earth’s semi-major axis from an ideal as calculated earlier, and the increase in the axis of the moon as determined above, we can reveal the existence of a general law which appears to link these two orbital features. It turns out that with a simple mathematical function, the moon’s rate of increase and the earth’s are related. This is accomplished in the following manner:
1) Rate of increase in moon semi-major axis from ideal: = 1.01946265198
2) Square root of moon’s increase = 1.0096844318
3) Compare this with the increase in the semi-major axis of the Earth already calculated earlier, that must, according to Kepler’s third law, accompany a time increase from 360 to 365.2421897 days per year = 1.009684349753
The ratios of increase are identical to 6 places after the decimal point, and very close to seven. From a consideration of these two values, it appears that we may propose the existence of a deterministic law, similar to that of Kepler’s third law, but one that specifically relates the semi-major axis of the earth to that of the moon. This law, holding for the earth-moon system can be expressed as follows: Any change in the semi-major axis of the moon, is accompanied by a change in the semi-major axis of the earth, to the square root of the moon’s change:
a(e) = a(m)^2
a = semi-major axis, of either: (e) earth; (m) moon.
Implications of the Earth-Moon Harmonic law
The existence of such a general law if it is true gives powerful support to the theory that the Babylonian system of measure was originally based upon an ideal earth moon orbital configuration. Such a law physically explains exactly how an increase in the semi-major axis or mean distance of the moon to the earth is directly accompanied by an increase in the semi-major axis of the earth from the sun. Using Kepler’s law, this increase of the earth’s orbit, appears to correspond almost exactly with an increase necessary to transfer to the earth an extra 5.2421897 days to bring it to that total which it currently holds: 365.2421897. Moreover, with a strong belief in the reality of an ideal moon orbit of 1296000 geographical miles, the division of this number by 60 (in accord with the Babylonian system of measure) to return a true ideal equatorial circumference of the earth is given further weight. In essence, the two parts to my proof as presented, lend themselves to the following theory of how the earth increased its number of days per year:
From an initial celestial configuration in which the earth possessed 360 solar days (each, 24 hours in length) to one orbit about the sun, an equatorial circumference of 21600 geographical miles (6000 ft each), and an accompanying moon whose circular orbit was 1296000 gm, on the plane of the equator of the earth; through some unknown agency the moon significantly increased its semi-major axis from the earth. At exactly the same time, the earth increased its semi-major axis from the sun, to the square root of the moon’s increase. This in turn led to an increase in the total orbital time of the earth (as per Kepler’s third law) whilst it maintained a 24-hour solar day. In addition, the increase in the earth’s orbit led to an increase in the equatorial circumference of the earth directly in proportion to the total orbital time increase. As a result of this, the earth and the moon find themselves in their present configuration, a deviation from that which served as the basis of the Babylonian system of measure.
An intriguing Further Refinement
In the above section I demonstrated a link between the increase in the moon’s mean distance from the earth, and an increase in the earth’s orbital period based upon standard textbook values, in particular for the moon’s current semi-major axis. However, I now wish to present an intriguing refinement to this later component, which appears to be of special significance. The standard value quoted for the moon’s mean distance from the earth was 384404 kilometres, which in geographical miles = 210194.663154474944. From this, the ratio of increase was 1.01946265198 from the standard ideal radius of 206181.8181818181 for the moon, using 22/7 as a conversion between the circumference of the moon’s orbit and its diameter. It turns out however that if we take the reciprocal of this ratio, i.e. 1/ 1.01946265198, we obtain a value of 0.9809089112. On a hunch, I decided to refine this to 0.98090909090909 (recurring 09’s), which in fractional notation is 1079/1100. Reversing this value once again presents us with a new more refined ratio of increase of the moon from the ideal orbital radius. This value is 1 & 21/1079, or 1.019462465245 in decimal form. From this a new current semi-major axis for the moon is obtained, as follows:
206181.8181818181 x 1.019462465245 = 210194.62465245
Converted to kilometres = 384403.9295875.
From, this it can easily be seen to be a refinement that is still well within the bounds for our estimation of the mean distance from the centre of the earth to the centre of the moon. Recall that the best current estimate was 384404 kilometres with a margin of error of 0.5 kilometres.
What is intriguing about this new ratio of increase, of the reciprocal of 1079 / 1100, is that is has a remarkable affinity to a certain ratio present in basic geometry linking the form of a sphere to that of a cube wherein the diameter of the sphere is the side length of the cube. Consider the following:
1) 1 - 1079/1100 = 0.019090909090909… recurring 09’s.
2) 0.019090909090909 x 100 = 1.9090909090909… or 1 & 10/11.
The formula for the volume of a cube is: side length cubed, s^3.
The formula for the volume of a sphere is: Diameter x (1/6) x PI.
If a sphere sits inside a cube such that it touches without crossing each of the six sides of the cube with its own surface, then the diameter of the sphere is equal to the side edge of the cube. The ratio of volumes of these two forms using the above two formulas gives the following à Cube/Sphere = 1.909859317.
However, this answer uses PI in the formula for the volume of the sphere. If this is replaced by 22/7, the answer is exactly = 1.9090909090909… or 1 & 10/11. This then, in some way strengthens the link between 22/7 as a ratio and the orbital configuration of the moon-earth system. 22/7 must be used instead of PI, which fails.
I propose that just as the earth attempts to maintain a 24-hour day, that the moon attempts to maintain this ratio of increase, 1 & 10/11, from the ideal radius associated with a circular orbit of 1296000 geographical miles. Moreover, it would appear quite reasonable to assume that we can actively use the moon to calculate the earth’s orbital time, using this new ratio. The calculations are as follows:
1) Square root (1 & 10/11) =
1.009684339407915039
2) Cube (1.009684339407915039) = 1.029335285772665934
3) Square root (1.029335285772665934) =1.0145616224619704857
4) 360 x 1.0145616224619704857 = 365.2421840863093
This answer
differs only slightly from the textbook answer for the earth’s tropical year
that is equal to 365.2421897.
For any comments
or feedback, Keith’s e-mail address is:
References:
[1] ‘Explanatory Supplement to the Astronomical Almanac’, Edited by P. Kenneth
Seidelmann,
Page 698.
[2] This is a short summary of the key points of a myth taken mainly from one
source, to be found at: http://www.neferchichi.com/re.html. This is a web site
of Kevin Fleury.
[3] Ideal Geographical Mile: This is the term I use to describe a length of
distance equal to 6000 British ft. It differs from a normal Geographical mile
which itself is equal to 6087.2 feet and is determined to be the arc length on
the surface of the earth at the plane of the equator subtending an angle of 1
minute of arc. Throughout this essay I will often refer to geographical miles as
units of length. In all such instances I am referring to an Ideal geographical
mile of 6000 ft, never to a standard geographical mile of 6087.2 ft.
[4] ‘The Slowing Spin of Earth: Is Earth's Rotation Slowing Down Throughout
Time?’ An article, website: http://www.creation-answers.com/slowing.htm
[5] As above.
[6] Microsoft Encarta 98 gives: 24902.4 miles as the earth’s equatorial
circumference.
[7] This reference was itself cited in the book, ‘The Harmonic Conquest of
Space’ by Bruce Cathie, p.120