The planets and other bodies of our Solar
System have profound interrelationships which go far beyond simple
Newtonian gravitational analysis. These
interdependencies include elements of electromagnetism, specific
orbital geometries, quantum-style laws, and other intriguing
characteristics. For example, viable theories of Quantum Physics (specifically: Superstrings, Zero-Point Energy, Vacuum Polarization, and Superconductivity) have now been shown to depend upon
hyperdimensions (i.e. extra dimensions in addition to the traditional
three dimensions of space and one dimension of time commonly thought of
as comprising the space-time continuum). The components of the Solar System, as well as their combined effect, may also depend upon such hyperdimensions.
The planets of our solar system (as well as
the satellites of these same planets and many of the other denizens of
the deep space) have several unique mathematical relationships which are
often ignored in astronomy textbooks. Such textbooks invariably include a discussion of Bode’s Law -- a thoroughly discredited attempt to fit the distances from the sun to the planets into a coherent scheme. Primarily known as an excellent example of the use of Fudge’s Factor and Finagler’s Theorem, Bode’s Law is a linear based rule (as opposed to cyclical)
and ignores the variable distances of each of the planets as they
circle the sun in elliptical patterns -- their actual distances varying
significantly. And yet Bode’s Law is still part of astronomy’s tradition, while the really interesting stuff is ignored.
A Book of Coincidence and the below tables provide, respectively, a geometric and algebraic treatment of the more “interesting stuff”. Table
1 considers the Earth-Moon system, where for purposes of clarity, it
should be noted that, for example, “7!” is known as “seven factorial”
and equals 7 times 6 times 5 times 4 times 3 times 2 times 1. (This
table is also included in Nines.]
| 1x2x3 | 6 | |
| 1x2x3x4 | 24 | Hours in an Earth Day |
| 1x2x3x4x5 | 120 | (see Genesis 6:3) |
| 3x120 or 720/2 | 360 | Degrees in a Circle |
| 1x2x3x4x5x6 | 720 | |
| 360+720 (or 3x360) | 1080 | Radius of Moon (miles) |
| 3x720 | 2160 | Diameter of Moon (miles) | *25,920 years/12 |
| 200x2160 | 432,000 | Length of the Kali Yuga) |
| 11x360 | 720+1080+2160 | 3960 | Radius of Earth (miles) |
| (radius/diameters of Earth and Moon have an exact 11/3 ratio) |
|
(radius/diameters of Earth and Mercury as well as their orbits, have a 2.618/1 ratio, i.e. Earth’s radius = (1 + f) x Mercury’s radius)
|
| 1x2x3x4x5x6x7 | 5040 | 3,960 + 1080 |
| 7x8x9x10 | 5040 | Earth radius plus Moon radius (miles) |
| 8x9x10x11 | 7920 | Diameter of Earth (miles) |
|
(11! / 7! = 7920, while 10! / 6! = 5040)
|
| 2160 + 7920 | 10,080 | Earth plus Moon diameters (miles) |
| 9x10x11x12 | 11,880 | Earth radius + diameter (miles) |
|
(also, 11,880 = 10,080 + 1,800 = 12! / 8!)
|
| 10x11x12x13 | 17,160 | |
| 17,160 - 11,880 | 5,280 | Feet in a mile |
| 11x12x13x14 | 24,024 | |
| 10x11x12x13x14 | 240,240 | Approximate Earth-Moon distance |
|
(which actually varies from 221,460 to 252,700 miles)
|
| 12! | 479,001,600 | Approximate Sun-Jupiter distance (459,800,000 to 506,800,000) |
*The period of time (years) for a complete revolution of the precession of the Earth’s axis.
The units employed in the above are based on the English system of measurements. This
is noteworthy, in that the more mainstream tendency to use the metric
system will result in many of the interesting features being missed!
Technically, units are arbitrary. That is, one defines a unit of distance (e.g. a yard) by what appears to be a totally arbitrary reason. However, once defined, the unit then is no longer arbitrary in measuring other dimensions. For example, miles, feet, and degrees can be considered to have been arbitrarily chosen. But
once “a mile” is defined as being, for example, equal to 1/7920 th of
the Earth’s diameter, then the unit of a mile is fixed thereafter for
other measurements. This means
that the product of the first seven numbers (seven factorial) equaling
5040 -- which turns out to be equal to the sum of the Earth’s radius
(3960 miles) and the Moon’s radius (1080 miles) -- is significant! In
other words, in the second case we are no longer dealing with an
arbitrary definition, having already defined the “mile” in the first
case.
[In Etymology, a “mile” supposedly stems from the Latin mille,
“one thousand”, which once referred to 1,000 paces of the Roman
legion’s formal parade step, left foot and then right foot, each pace
equaling 5.2 feet. This of course, yields only 5,200 feet, instead of the 5,280 feet we now use. Perhaps, there was a hop, skip, and jump added every 1,000 feet.]
More substantially, a review of Table 1 suggests that the English System of Measurements may be based on something not simply arbitrary, but on what could be construed as esoteric or other profound considerations. Furthermore, Table 1 suggests the Earth-Moon system may be obeying some heretofore unknown mathematical law or set of laws!
This is critically important! There
may be “physical restraints” on planetary dimensions and orbits (just
as in quantum physics where electrons can only take certain orbital
positions), and thus Sacred Geometry and/or other mathematical disciplines (such as Numerology) may be critical to a complete understanding of the “harmony of the spheres”, or of astronomy in general.
With respect to Table 1, it should be pointed
out that there is a minor flattening of the Earth at the poles such
that the radius of the Earth actually varies between 3964 and 3950
miles. The value of 3960 miles
is, however, considered sufficiently accurate -- particularly in light
of the fact that the Earth has mountains four and five miles high, and
thereby making any greater so-called accuracy, pointless in the extreme.
In comparing other planetary-satellite
systems within our solar system, modern astronomy has observed that the
Moon is far larger than might be expected for a planet the size of the
Earth. Our Moon is sufficiently
large, for example, that its apparent size in the sky (based on its
distance from the Earth) is virtually identical to that of the Sun
(which is why we are able to observe total solar eclipses from the
Earth’s surface). [Why do you suppose that is?]
The lunar disc subtends within the sky
an arc which varies from 29’ 22” to 33’31” (or 29.3666’ to 33.5166’)
for an average of 31.4416’ -- roughly equivalent to that of the Sun. Another
way of looking at it, is that the ratio of the Moon’s distance from
Earth to the Moon’s diameter varies from 102.53 to 116.99 (average of
109.76), while the ratio of the Sun’s distance from Earth and the solar
diameter (109 times that of Earth) is 107.68. This represents an error of from 0 to 8.65%, or an average of 1.9%.
It has been pointed out that the distance of
the Moon from the Earth (which varies from 221,460 to 252,700 miles)
very nearly equals 60 times the radius of the Earth. The
actual number is 60.27, which implies that the Moon is not precisely 60
times the radius of the earth by a “discrepancy” of some 1033 miles. Curiously,
this discrepancy may derive from the fact that the Moon is currently
receding from the Earth at a rate of a quarter of an inch per year. By
extrapolating back in time (a very risky proposition, but one to which
speculations are inclined to pursue), one can calculate that the Moon
will have receded 1033 miles in 261,803,520 years. Thus the exact ratio of 60 might possibly have been realized some 250 millions years ago. Probably on a Thursday.
This corresponds to approximately the time of
the Permian Extinction (when some 95% of the species on Earth suddenly
-- suddenly on a geological time scale -- became extinct). This also begins the Age of Reptiles --
the Triassic being initiated 250 million years ago, the Jurassic, 155
million years ago, and the Cretaceous, 130 million years ago. This
is, of course, highly speculative, but one can wonder if, perhaps,
there is a connection with the Moon being at a particular distance from
the Earth and the advent of the dinosaurs. This
speculation might also lead to some even more speculative conclusions
as to how the dinosaurs managed to stand -- their apparent weight being
too large for their legs. One
far-out view is that the force of gravity was less than now, and this
may be due to the location of the Moon with respect to the earth. This seems unlikely, but it is just the sort of thing that makes the universe “stranger than we can imagine”. (Keep in mind also that there may have been a time in Earth’s history When the Earth was Moonless! Or even a reason why there were once, respectable Lunatics.)
Things get even stranger when we also
consider the Precession of the Earth’s axis as it rotates every 25,920
years -- carving out a circle in the sky and periodically changing pole
stars from Polaris to Vega to Alpha Draconis. The
fact that 1/12th of 25,920 years equals 2160 years, while the Moon’s
diameter is 2160 miles, is nothing short of, well... amazing! Furthermore, the
idea that the size of the Moon is related to the Earth’s precession of
the axes is simply not obvious from any so-called “laws” of mainstream
physics.
Considering all of these “anomalies”, one might begin to think the Moon was customized for the Earth. This
statement doesn’t necessarily imply the Moon is artificial (but neither
does it imply it is not), but rather that the process whereby the Moon
and Earth came together as a unit, may somehow be obeying some higher
authority -- a law of physics not yet well understood, divine
intervention, or some other even more incredible reason.
The 11/3 Earth Moon ratio of diameters (and radii) is a case in point. For example, to a three decimal place accuracy, the Moon-Earth ratio equals ÖF - 1 [where F is the Golden Mean.] Or we can calculate: 11/3 @ 8 - 7f. This curious ratio is repeated in that the maximum distance between the planets Venus and Mars (the two planets which come the closest to the Earth), divided by the minimum distance between these same two planets, is equal (to within a 0.09% error) the same 11/3 value!
This intriguing circumstance of planetary
orbital characteristics having precise and similar mathematical
characteristics prompts us to look further into the matter. The
idea of a mathematical relationship between various planet’s orbits is,
of course, not new -- having been considered before in everything from Kepler’s “The Harmony of the Spheres” to the “Titus-Bode Law”.
However, the flaws in Bode’s Law are legion. First,
the formula which was developed before the outermost planets were
discovered, failed miserably in accounting for the orbital distances of
Neptune and Pluto. Two, the formula itself is heavily dependent up Finagler’s Theorem and Fudge’s Factor. Three, the concept of assigning a single number to a planet’s distance from the Sun may be a fundamental error. All of the planets, including Earth, have elliptical orbits with their distance from the Sun constantly varying. This
ranges from the nearly circular orbit of Venus (whose distance varies
from 66.7 to 67.6 million miles) to Pluto (whose elliptical orbit places
it anywhere between 2766 and 4566 million miles from the Sun).
However, a definitive measure of a planetary orbits can be obtained by discarding the linear thinking employed in Bode’s Law, and resorting to a cyclical mode of thought. Using orbits as our measure we begin dealing with the time it takes for the various planets to orbit the Sun, the orbital period, a very consistent measure. Table 2 provides several examples whereby the orbital periods of many of the planets are related by simple addition.
Table 2
Mercury Venus Earth Mars Error
0.2409 years + 0.6152 years + 1.0000 years = 1.8561 years @ 1.8808 years 1.31%
Earth Mars Jupiter Saturn
2 x [ 1.0000 year + 1.8808 year + 11.862 year ] = 29.4856 year @ 29.457 year 0.10%
Mercury Venus Earth Mars Saturn Chiron Uranus
0.2409 + 0.6152 + 1.0000 + 1.8808 + 29.457 + 50.682 = 83.8759 @ 84.014 years 0.16%
Ceres Saturn Chiron Uranus
4.6000 + 29.457 years + 50.682 years = 84.7390 years @ 84.014 years 0.86%
Saturn Chiron Uranus Neptune
29.457 years + 50.682 years + 84.014 years = 164.153 years @ 164.79 years 0.39%
Uranus Neptune Pluto
84.014 years + 164.79 years = 248.804 years @ 248.2498 years 0.22%
Ceres Athena Juno Vesta Jupiter Saturn
4.60 y + 4.61 y + 4.36 y+ 3.63 y + 11.86 y = 29.062 y @ 29.457 year 1.34%
Chiron Earth Pluto
5 x [ 50.682 years - 1.000 years] = 249.31 years @ 248.2498 years 0.06%
Note that while Chiron is currently considered to be a comet by mainstream astronomers, the fact remains that Chiron is in a planetary orbit (ranging between Saturn and Uranus), and is, therefore, justifiably included in the above formulas. At
the same time, if only the Mercury + Venus + Earth = Mars and the
Uranus + Neptune = Pluto equations were relevant, this would still be
impressive and intriguing data. Also note that Ceres is by far the largest asteroid, accounting for more than 50% of the mass of the asteroid belt. Thus its inclusion is also relevant.
The numbers shown in Table 2, however, are only the tip of the iceberg. A more complete set of relationships -- those between planets of our solar system -- are provided in Tables 3 through 6. Developed
by the author and based in part on the extraordinary geometrical
drawings and discussions in John Martineau’s classic volume, A Book of Coincidence [1],
these equations demonstrate that not only do the planets correlate with
each other via simple mathematical relationships, but they also do so
with an uncanny and profound association with various forms of The Golden Mean.
The Golden Mean or Golden Ratio is one of the most intriguing number in mathematics. It is commonly denoted by the Greek letter, phi, and is given in either to two forms by the equalities: F º 1.618033989... and f º 0.618033989... (where “...” means a continuation of the numbers -- See Transcendental Numbers). The
Golden Mean was known to the ancients (and moderns), who considered
these numbers so sacred that monuments from the Giza Pyramids and Greek
Parthenon to Notre Dame Cathedral and the United Nations Building in New
York City have been based on these fundamentals of Sacred Geometry.
Martineau [1] first pointed out the Golden Mean relationships between the outermost planets. The
additional formulas of Tables 1 thru 6 were derived, in some cases, by
converting Martineau’s geometries into algebraic expressions, and in
other cases, by observation. In all cases, the percentage error is less than one percent. The existence of any percentage error, however, may involve the possible nature of the Transcendental Numbers (F, p and e), and their apparent requirement for slight inequalities in making non-linear systems perform optimally.
Table 3
F = f + 1 = 1.6180339887... Error
1 Pluto (aphelion) / Neptune (aphelion) = 1.6255 0.46%
[Pluto (perihelion) / Neptune (perihelion) = 0.9993]
2 Pluto (perihelion) / Uranus (perihelion) = 1.6280 0.61%
Neptune (perihelion) / Uranus (perihelion) = 1.6292 0.68%
F2 = F + 1 = f + 2 = 2.6180339887... ( @ cos 36°/sin 18°)
3 Pluto (aphelion) / Chiron (aphelion) = 2.6112 0.26%
4 Chiron (mean) / Jupiter (mean) = 2.6331 0.57%
5 ½Ceres-Earth½max / ½Ceres-Earth½min = 2.6072 0.41%
6 Jupiter (mean) / Earth (mean) = 5.2032 = 2 x 2.6016 0.63%
[2 cos 30°]3 = 5.1962] [0.14%]
7 Earth (mean) / Mercury (mean) = 2.8540 1.32%
Earth (diameter) / Mercury (diameter) = 2.6141 0.15%
Note: Unless otherwise indicated, aphelion is a planet’s furthermost distance from the Sun, perihelion is a planet’s closest point to the Sun, and the mean is a planet’s average distance from the Sun. Also,½x-y½ is the distance between planet x and y, and may be further defined as the maximum possible distance between the planets or the minimum. In all of the above, the resulting numbers represent the ratios of the two distances.
Considering the Golden Mean
connections in Table 3, along with the correlation of the orbital
periods, the three outermost planets appear to be obeying some physical
law in which they move in essential harmony with one another. The
comet-in-a-planetary-orbit Chiron then connects these three (via Pluto)
to Jupiter, with Jupiter subsequently passing the torch to Earth. In the process, Ceres (the largest-by-far asteroid) is also included in the equations. Even tiny Mercury, closest to the Sun (while Pluto is the furthermost), gets involved. In this regard, equation 7 in Table 3 needs some additional clarification, i.e., Not only does a 5-pointed star connect Earth and Mercury’s mean orbits, but it also connects their physical sizes (as given by their radii)! Orbital period and planetary size!
This is incredible, but it is only the beginning of the truly astounding. As
Martineau [1] observed, not only does Earth have a Golden Mean
connection to the planet furthermost from Earth in the direction of the
Sun, but Earth also has a similar connection to Saturn, the visible
planet furthermost from the Earth in the direction away from the Sun. In this case (Table 5), Saturn’s mean orbital distance and physical size are both approximately 4F +3 times that of Earth. These observations, as shown by Martineau’s 5-pointed and 30-pointed stars, are important, and must not be dismissed as some random occurrence.
[In fact, the title of John Martineau’s book, A Book of Coincidence, should not be construed to imply that the
“coincidence” is to be defined as “a remarkable concurrence of events or
circumstances without apparent causal connection”, but rather that the
primary definition of “occurring or being together” more aptly describes
the multitude of examples in the book. These so-called “coincidences”
are thus examples of coinciding -- possibly, either with a purpose, or resulting from some physical reason and/or constraint. Also note that Martineau has recently published a follow up to his original effort, the new book entitled A Little Book of Coincidence, Wooden Books, Wales, 2001 (in the USA, Walker Books, New York). Inasmuch as A Book of Coincidence is out-of-print, the availability of the second volume is good news.]
There are many curious mathematical relationships demonstrated in these tables, but for the less mathematically inclined, it might be wise to skip to the conclusions below, do a quick trip to Satellites of Jupiter and/or Hyperdimensional Physics, or go directly to A Book of Coincidence, for a more graphic, visual description.
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
In Table 3, it is important to note that equations 1 and 2 have in common, ten (5 x 2) circle geometries, while equations 3 and 5 result from nested 5-sided pentagons, 4 and 7 result from a 5-pointed star, and equation 6 results from two, nested 5-pointed stars. The 5-pointed stars and pentagons also inevitably involve the ratio of cos 36°/sin 18°, which is equivalent to F2 (within a percentage error of 0.0000014%). We might also observe that equation 7’s ratio of the Earth/Mercury orbits (i.e. 2.5840), when squared, equals 6.6769. This is equivalent to (within a 0.47% error): 3 (F + f) = 3 Ö5. Finally, we must not forget the intimate Golden Mean connection between F and/or f and Ö5.
Finally, in Table 3, there is the relationship -- illustrated in equation 6’s Jupiter/Earth ratio -- between the nested 5-pointed stars and the 6-pointed, Star of David configuration. Using the latter, we derived the relationship of: [ 2 x cos 30° ]3 (shown in Table 3). This effectively connects the 5 and 6 geometries by the equation: 2 F2 @ [ 2 x cos 30° ]3. The latter is faintly reminiscent of Kepler’s Law of Periods, where the planet’s orbital period, T, is proportional to the planet’s mean distance to the sun, A, i.e. T2 = k A3, where k is the constant of proportionality.
Not shown in these Tables is the dodecahedron
which relates Mercury and Earth -- as well as Venus and Mars -- and the
icosahedron relationship between Earth and Mars. These three dimensional relationships are noteworthy because of the twelve, 5-sided
pentagonal faces of the dodecahedron, and the fact that the
icosahedron, with its faces of equilateral triangles, is derived by
taking lines from the adjacent centers of the dodecahedron faces, and is
thus considered the dual of the dodecahedron.
In Table 4, equations 8, 9, 10, and 11 are based on two nested pentagons, and equations 12 and 13 are based on four nested pentagons (as distinct from equations 3 and 5, which were based on five and three -- i.e. an odd number of -- nested pentagons, respectively),. Note
also that in the Venus-Mars connections (equations 13 and 14), which
includes both 3 and 4 nested pentagons, the difference is nothing more
than a factor of cos 36°.
Table 4
4 x f2 = 4 x (F - 1)2 = 4 x (1 - f) = 4 x (2 - F) = 1.527864... Error
8 Mercury (aphelion) / Mercury (perihelion) = 1.5185 0.62%
9 Venus (mean) / Mercury (aphelion) = 1.5409 0.85%
10 Mars (mean) / Earth (mean) = 1.5241 0.25%
11 Ceres (perihelion) / Mars (aphelion) = 1.5306 0.18%
12 ½Mercury-Mars½max / ½Mercury-Mars½min = (1.5262)2 0.21%
13 Mars (aphelion) / Venus (perihelion) = (1.5233)2 0.61%
8 (F + f - 2) = 8 (Ö5 - 2) = 1.8885... ( = 1.5278 / cos 36°)
14 Mars (perihelion) / Venus (aphelion) = 1.8954 0.36%
15 ½Mars-Earth½min / ½Venus-Earth½min = 1.8917 0.17%
16 Ceres (mean) / 2 x Earth (mean) = 1.8850 0.18%
17 Jupiter (mean) / Ceres (mean) = 1.8783 0.54%
18 2 x Uranus (mean) / ½Uranus-Pluto½min = 1.8943 0.31%
19 Pluto (mean) / Chiron (mean) - 1 = 1.8788 0.51%
It’s also curious that Earth’s nearest
neighbors (equation 15) allow for each of the closest point of approach
of either planet to obey a 3 nested pentagon pattern, while the Earth-Mars connection (equation 10) obeys a 2 nested pentagon pattern, and the Earth-Venus ratio of distances (equation 20, Table 5) obeys a more complicated 5-point star and pentagon combination. Finally,
the Pluto-Chiron connection (equation 19) is further amplified by the
ratio of Pluto’s orbital period in years to that of Chiron’s, which
turns out to equal 4.8984. This misses an exact multiple of 5 by a percentage error of 2%.
In Table 5, the Venus-Earth connection has multiple attributes (equations 20, 25, and 26). The first uses an enclosed 4-sided square between the two orbits, while the second uses a 5-pointed star/circle-inscribing pentagon combination and the third a series of 8 circles. This has the effect of relating the Golden Mean 5 to the 4 and 8 geometries. Meanwhile,
in equation 27, we have again encountered the 30-pointed star which
connects both Saturn and Earth’s distance from the sun and their physical sizes.
Table 5
F4 = (1 + F)2 = 3 F + 2 = 3 f + 5 = 6.85451... Error
20 ½Venus-Earth½max / ½Venus-Earth½min = 6.8684 0.21%
21 ½Jupiter-Earth½mean / ½Mercury-Earth½mean = 6.8515 0.04%
22 2 x Jupiter (mean) / Mars (mean) = 6.8281 0.38%
F5 = 5 F + 3 = 5 f + 8 = 11.09017...
23 ½Saturn-Mars½max / ½Sun-Earth½mean = 11.06 0.27%
3 - F = 2 - f = 1 + f2 = 1.3820...
24 ½Mars-Saturn½max / ½Mars-Saturn½min = 1.3799 0.15%
25 Earth (mean) / Venus (mean) = 1.3826 0.05%
26 Earth (mean) / Venus (mean) = 1 + sin 22.5° = 1.3827 0.05%
4 F + 3 = 4 f + 7 = 9.472136...
27 Saturn (mean) / Earth (mean) = 9.539 0.070%
[From a 30-pointed star: 1/sin 6° = 9.5668 0.029%]
Saturn (radius) / Earth (radius) = 37,449 mi/3,963 mi 0.024%
Slowly but surely it should be more and more apparent that these “coincidences” can not be thought of as random events. Clearly,
all of the planets (and an occasional comet) are profoundly connected
via the Golden Mean, and in a sufficiently strong fashion that one must
assume that physical forces are requiring some form of quantum limits to stable orbits. This latter point is extremely significant, and can not be overemphasized.
A curious aspect of Tables 4 and 5, is that
all of the planets are well accounted for except Saturn -- which appears
only in the more complicated relationships of Table 6. The need for the more unusual forms of F may call for some additional consideration -- particularly inasmuch as Saturn dominates Table 6, where p and trigonometry are used.
Equations 28, and 29 in Table 6, for example,
have the added connotation of relating the circumference of a planet to
another planet’s orbital radius or diameter. For example, the
radius of Saturn’s orbit equals the circumference of Mars’ orbit, while
the diameter of Neptune’s orbit equals the circumference of Saturn’s
orbit. Another Saturnian oddity?
Table 6
p = 3.14159265358979323846... Error
28 Saturn (mean) / Mars (mean) = 6.2592 = 2 x (3.1296) 0.38%
29 Neptune (mean) / Saturn (mean) = 3.1513 0.31%
10 ( p - 3 ) = 1.4159... (similar to a Square: 2 sin 45° = 1.4142... or just Ö2)
30 ½Jupiter-Saturn½max / 2 x Jupiter (mean) = 1.4159 0.00134% !
31 ½Jupiter-Neptune½ / ½Jupiter-Neptune½ = 1.4183 0.17%
32 Earth (aphelion) / Venus (mean) = 1.4162 0.02%
3-sided Triangle: 1 + cos 30° = 1.8660
33 Venus (mean) / Mercury (mean) = 1.8687 0.14%
7-sided Polygon: 1 + 2 x sin 360°/14 = 1.8678...
34 Venus (mean) / Mercury (mean) = 1.8687 0.05%
9-pointed Star: 1 / sin 10° = 5.7588...
35 Neptune (mean) / Jupiter (mean) = 5.7774 0.32%
The relationship between p and the square form (equations 30 to 32) is also worth mentioning. But perhaps more importantly, is the near equality of the Venus-Mercury connection to both the three and seven geometries (equations 33 and 34). We have already seen how 5-sided geometries connect with 4 and 8-sided geometries, and with 3 (and obviously 6 and 9) relating to 7-fold geometries and 5 to 9-sided geometries, it becomes clear that all of these
geometries are connected in some manner, and typically via one of the
transcendental numbers -- in these cases, either F or p.
The unusual nature of Saturn’s relationships
to the other planets is also observed in the Saturnian satellites and
their respective distances from the mother planet -- especially when
compared to the Satellites of Jupiter.
Finally, another 4F2 relationship which was not included in Table 5, concerns the tilt of the Earth’s axis! This
wholly unrelated -- or what has thus far passed scientific muster as
wholly unrelated -- physical characteristic of the Earth is
extraordinary to say the least. The
basic concept is that by projecting from the viewpoint of the pole, the
Tropic of Cancer (or Capricorn) onto a plane located at the equator,
one is then able to measure the radius, r, of the projection and compare it to the radius, R, of the equator. The ratio of the two is: R = r x 1.5278... = 4F2 r. The identical relationship holds for the larger projected circle of radius R = 4F2 R (of the equator). The
Tropics of Cancer and Capricorn are, of course, the result of the tilt
of the Earth’s axis of rotation with respect to the plane formed by the
Earth’s orbiting the Sun. (The angle of this tilt is 23.45229°, and is the major factor in the Earth having seasons.) A Book of Coincidence shows this fact in a much more graphical fashion.
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Conclusion (Skipping Stop Point)
Clearly, the ratios of orbits of the planets and moons of our solar system depart slightly from precise equalities. This, in fact, may be a requirement or constraint of planetary quantum geometries, and directly related to Heisenberg’s Uncertainty Principle -- which, in principle, limits the degree of accuracy for which an electron’s position and momentum can be simultaneously determined. In effect, without a recognition of the need
for slight inequalities or minute departures from precise symmetries in
the design of mechanical and/or electromechanical new energy systems,
the devices may simply not work in the optimal condition envisioned. It’s as if without slight imperfections, there can be no interaction with other entities. [I.e.,
if one has a rotating perfectly smooth, perfectly spherical sphere,
then it cannot mechanically interact with anything else. It’s like trying to change directions on a perfectly smooth surface, such as an icy surface. Skates work only because they mar the smooth surface with a nick, which is used to push off on.]
It appears that the planets of our solar
system, the moons of Jupiter, and other orbiting bodies have strong
preferences for discrete distance and inclination windows -- similar to
the quantum physics requirement of electrons existing only in discrete
energetic orbital levels within atoms. Accordingly,
it might then well behoove the National Aeronautics and Space
Administration, i.e. NASA (an acronym also for “Never A Straight
Answer”) to consider that orbiting artificial satellites might undergo
significantly less “degradation of their orbits”, if they are situated
in orbital windows which are more conducive in allowing the satellites
to stay in their assigned orbits for much longer periods of time. In other words, harmonize with the Harmony of the Spheres! Duh!
For Quantum physicists, applying these principles of Sacred Geometry might elicit some additional understanding
of the geometrical restrictions on everything from electrons in orbit
around atoms to nucleons within a nucleus to internal spin
characteristics of any and all elementary particles to Superdeformation of heavy nuclei.
http://www.halexandria.org/dward115.htm
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου