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Tuesday, January 31, 2017

S&P 500 vs 24th Harmonic of Mercury's Right Ascension


Mercury is the closest planet to the Sun, and named after the god of commerce, travel, and thievery in Roman mythology, the counterpart of the Greek god Hermes who also guides the souls to the underworld. Mercury is the Celtic god Lugus, the Germanic god Wotan, the old Indian god Rudra, later known as Shiva, associated with magic, poetry, and warfare. In ancient Babylon Mercury was the god Nabu, the divine scribe and god of wisdom. To the Egyptians Nabu was Tehuti, rendered by the Greeks as Thoth. Nabu was one of the major gods of Egypt and personified the principle of reason. However, Thoth had no connection with the planet Mercury until the Greeks introduced astrology to Egypt, where the planet was regarded as belonging to the god Set, while Thoth presided over the Moon. Finally Hermes Trismegistus seems to be the syncretic combination of Hermes and Thoth.  

Mercury was attributed a divine messenger due to the fast speed across the sky. Mercury attains Inferior Conjunction with the Sun (nearest approach to Earth) every 115.88 Earth days (= average Synodic Period), but this interval can range from 105 to 129 Earth days due to Mercury's eccentric orbit. Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity. Mercury's axis has the smallest tilt of any of the Solar System's planets (about  1⁄30 degree), and its orbital eccentricity is the largest of all known planets in the Solar System. At aphelion, Mercury is about 1.5 times as far from the Sun as it is at perihelion. Because both Mercury and Earth are moving in elliptical orbits, the maximum elongation angle varies from one orbital revolution to another (HERE).

Enlarge
The Celestial Equator is the plane formed by the daily rotation of the Earth around its own axis. It is inclined to the Ecliptic at 23°26’. This angle changes very slowly. The position of a celestial body, e.g. Mercury, is measured with reference to the plane of the Earth’s equator. The Geocentric Equatorial Coordinate System is projecting the Earth's equator onto the celestial sphere (forming the celestial equator) with a primary direction towards the vernal equinox, and a right-handed convention. Hence the Right Ascension (in hours, minutes and seconds) is the angle of the planet in the Equator plane (RA), and the Declination shows how the planet is inclined to the Equator. 


 

In the above chart Mercury's Synodic Period of 105 to 129 days was divided by 24 (1 Synodic Period = 360° / 24 = 15° = 24th Harmonic). Therefore one oscillation of the Cosinus of Mercury's Right Ascension between -1 and 1 (= 15h) takes 4 to 5 Calendar Days, and considerably longer during the retrograde periods.

Stock Market Capitalization as a Percentage of GDI | 1925 - 2016


Total market capitalization (TMC) of the stock market as a percent of Gross Domestic Income (GDI) is 126%, the second highest in 100 years, only exceeded by 164% just prior to the 2000 tech bubble. This highlights the extreme extent of stock market distortion, which can largely be attributed to artificially low interest rates. Because stocks are an unusually large percentage of the economy, a stock market correction would undoubtedly stunt economic growth. Because the market is so high relative to GDI, corrections will have a greater negative impact on the economy. Furthermore, this ratio's lofty level illustrates just how overbought the stock market is in general, signaling the potentially precarious state of the markets (Chart: Ned Davis Research).

Monday, January 30, 2017

Sunday, January 29, 2017

A Theory of Astrology | L. Edward Johndro

In the 1930s electrical engineer and astrologer L. Edward Johndro (1882-1951) and astrologer Charles Jayne (1911-1985) simultaneously contributed to the development of the GEM Theory (Gravity, Electrical, Magnetism). In 1929 Johndro presented his Theory of Astrology as follows:

"Tesla demonstrated years ago that the earth is at a relatively constant electrical potential or charge of some seven million volts. It may now be accepted that all material bodies are in a state of relative charge, negative or positive, with respect to each other - man, atoms, earth, planets and stars, and that this manifests as love, cohesion, magnetism or gravitation, or their wholly illusionary opposite (repulse), according as the law manifests in a magnitude series ranging from the microcosm to the macrocosm.

[...] We cannot escape the fact that the earth is a charged body at a potential of millions or volts, nor can we easily escape the conclusion that the other planets are in a state of high charge. While that man is a charged body, with an accompanying electromagnetic field, is easily demonstrated by countless experiments [...] Suns and stars (not planets) are radioactive [...] they emit electromagnetic waves which, because of their exceedingly high frequency, we term light [...] The sun and stars, the planets, the earth, and man upon the earth are charged bodies, and that all their accompanying electromagnetic fields intersect and interact.

[...] The planets reflect light waves and they each, have a different natural frequency of oscillatory response to the solar and stellar light waves which constantly bombard them (consequently their reflected light is variously tinted) and that the phase angles of their field couplings, as their relative movements in space change them, changes the power factor at these frequencies; accept also the fact that these planetary frequencies, being of a far lower order than those of the sun and stars-a mere octave of lower harmonics, since they emit no light of their own, are within the range of man's sensibilities to subconsciously detect and respond to

[...] The solar waves continually directly bombard half the earth [...] they are also reflected to the earth by the Moon and planets [...] These waves constantly interact with the earth's electromagnetic field [...] as the inductive couplings of the earth, sun and planets change their mutual angular relations in space.
 
Tuning In Super-Heterodyne Man
By L. Edward Johndro
Author of "The Earth in the Heavens" and "The Stars, How and Where They Influence"
 
The science of radio and astrology are one. Their sole fundamental difference, as we know them today, lies in the frequency bands dealt with, the different distances involved in the radiation of electromagnetic waves, the relatively infinite difference in the length of those waves, and the supersensitivity of the human organism, as a receiver, as compared to the super-heterodyne receiver.
 
 
The importance of the laws of radio to the technical problems involved in the exposition of astrology as an exact science, in terms of physical science acceptable to scientists, cannot be overestimated. The reason for this is simple. As radio science advances, we find more and more that in the generation and conduction of high-frequency currents, and in the propagation of high-frequency electromagnetic waves through space, there is a gradual breakdown and reversal of Ohm’s law as higher and higher frequencies are dealt with. Dielectrics and conductors take on a reverse order as the wave length of light is even distantly approached.

This has to be predicated on the assumption that relativity is true, and this fact means that the time-honored objection to astrology on the grounds that the planets are too distant to radiate, by reflected solar light, any magnetic waves capable of setting up currents of response in the sympathetic nerve fibers and brain and body cells of the human race, is entirely unfounded.

A radio receiver wholly insensitive to a weak 700 kilocycle (450 meter) wave may be made to audibly respond to the same signal intensity on a 2000 kilocycle (150 meter) wave. A receiver limited to 500-mile reception on waves within the popular broadcast band may receive from the Antipodes by the substitution of short-wave tuning coils. In other words, a wave of 40 meters may be 1000 times as sensitive as one of 400 meters, as far as distance propagation and distant reception are concerned. Considering, then, that light waves are infinitely short as compared to even a 40-meter wave, we see readily that their straight-line propagation from planets, suns and stars, is far less diminished by millions of miles of interstellar space than are our radio waves by earth distances.

While long radio waves (low frequencies) have little as yet determined direct effect upon human health or "temperature," it is *Professor J. C. McLennan, of Toronto today, has found that certain long-meter waves so raise the body temperature as to promise a means of controlling fatal collapse in pneumonia cases. This wave acts on the sodium chloride of the blood.
Editor’s Note:—This article is INTELLECTUAL DYNAMITE! It is an answer to the time-honored objection to astrology on the grounds that the planets are too distant to radiate, by reflected solar light, any magnetic waves capable of affecting mankind. Anyone interested in astrology, equipped with information contained herein, may effectively refute the strongest argument put forth against astrology by orthodox scientists. While it is quite technical for the average reader, we feel that it is necessarily so, and that its importance justifies your reading it and the space we are giving it.
It is well known that waves of five meters and less, which are still a far cry to light waves, have a profound effect upon the nervous system, and that the high end of the spectrum (violet) affects the metabolism of some body tissues to a degree second only to the ultraviolet, X, alpha and beta rays. It can thus be said that astrology concerns itself with cosmic light-wave broadcasting from planets, sun and stars, and with a more sensitive receiver—the sympathetic neurons of homo sapiens.

I have already implied that electrical conduction and insulation that holds inviolate for direct current and low-frequency alternating current, and which gave rise to Ohm’s law, places all elements and their compounds in a definite progressive series. But let me again remind your writer that when we come to deal with radio, and higher frequencies than radio does yet utilize, this series undergoes for any given element or compound a gradual reversal as the frequency is increased. 
 
That is, conduction and insulation, which to direct current are characteristics arising out of electrical pressure or voltage only, are to alternating current variables depending on the frequency or time factor, varying and even changing places in the series as the “times are shortened” (frequency increased). The electrical properties of matter, so far as alternating current is concerned, being variable and dependent upon the current frequency, it is almost certain that radio facts will in time substantiate several of Einstein’s relativity claims.

To clarify the foregoing for the general reader, let us contemplate on the fact that copper, let us say, is a good conductor of direct current and for alternating-current power circuits. It is even a good conductor of radio frequencies, though its resistance to the latter is increased as the frequency is increased, due to “skin-effect” (unequal distribution of high-frequency currents in conductors). 
 
But copper is an absolute insulator to light or light frequencies, responding only to a lower harmonic of light in the form of heat. Thus copper is opaque to light. While it remains conductive to heat frequencies it acts as a dielectric or insulator to light. In contrast such a direct current or low-frequency alternating current insulator as glass, air or vacuum, automatically becomes an increasingly ideal conductor of light frequencies, and relatively poor to impossible conductors of heat frequencies.

The pertinent fact here is that “everything” is immune or resistant to some frequencies, but not to all frequencies, and that every frequency band, sufficiently separated, casts the elements and their compounds into a new series of relative conduction and insulation. Consequently, once proved that each planet has a different fundamental frequency response (plus the harmonics of that frequency), and that each planet reflects solar light at its own frequency or wavelength, it then becomes clear enough that each planet affects some things and not others. Thus their individual “relationship” (to revert to astrological terms) is explained.

That a purely physical (and this includes gaseous) body has a natural frequency is easily exampled. If common salt or ammonium chloride is dissolved in a glass of water, the glass when struck will sound a progressively lower note up to a certain point of solution density, then the pitch or frequency of the note will increase over two to three octaves till the point of saturation of solution is reached. 
 
This is not due to a change of density of the solution, for a sugar solution, for example, does not manifest a range of acoustical frequencies under the same test. I mention sodium and ammonium chloride because they show in the spectrum lines of the stars and are common in the earth. We know, too, that the reason one planet or star appears red, blue, green or white can be due only to the frequency or wave length of its reflected solar light.

The piezoelectric and pyroelectric properties of crystals, as discovered in recent years through intensive research in many quarters, particularly by the U. S. Naval Research Laboratory, and culminating in the present-day radio practice of utilizing quartz crystals as frequency controls in broadcast and marine transmitters, are direct evidence that the wave length and wave frequency of a body having definite (crystalline) electrical axes is relative to its diameter, circumference and mass, as well as dependent upon its substance.

Since the planets (not to mention the stars) are of widely different size, mass and density, the light waves they each reflect to earth carry a "sideband" wave of the lower frequency of the oscillating or vibrating planet, just as the carrier wave of a broadcast transmitter carries the superimposed audio-frequency of the program as a relatively "long-wave" wave or sideband, which is “unhorsed” by the detector tube of your radio and passed on into the loudspeaker of your program, while the "horse" (the carrier wave) goes galloping on.

It is thus to be seen that the inducement (electro-magnetic wave induction) of a planet exists neither necessarily, nor probably, by virtue of its reflected solar light upon us, but is due rather to the superimposed lower (and quite invisible) frequency of the planet as an oscillating crystal that rides that light wave to us over the great distances it would not be able to travel undiminished if it did not have the "light horse" as to ride by reason of the planet’s reflected sunlight. 
 
As a simple analogy we may say that Paul Revere (the planet), carrying his message (the planet’s own frequency), would have been tired out and failed in his purpose had he not had his horse (light frequencies) to ride the distance. For, as I have earlier pointed out, long waves or low frequencies, such as are necessary to carry a program and operate the audio circuits of a radio, meet too much resistance in traveling far through space unless they are carried "on the back" of a radio wave of sufficient shortness or high frequency to convert the ordinarily insulating ether into an excellent conductor by the reversal of Ohm’s law of resistance. This is not theory. Ask any radio engineer.

By passing the carrier wave of a transmitter through a quartz crystal cut to a definite diameter and thickness and with the proper plane with reference to its electrical axis, the broadcast station is held exactly to its authorized wave length. The only thing radio engineers and scientists in general are slow to accept is the fact that each planet is such a crystal reflecting sunlight, itself an electromagnetic wave, back to earth at a definite frequency that acts upon us through sympathetic nerve response in a different way and degree from the wave reflected by a larger or smaller planet oscillating at another harmonic of sunlight because of its diameter, mass, etc.

A second important fact about piezoelectric crystals, such as quartz, tourmaline, Rochelle salts, etc., is that when they are caused to oscillate in a high (as radio) frequency circuit they change their dimensions and shape, and if certain maximum electrical potentials (voltage) be exceeded the crystal heats and cracks on cleavage lines definite to its electrical axis.

If, now, we view the earth as a composite crystal and as possessing these piezoelectric and pyroelectric properties in its quartz, etc.; and if we consider the earth’s many electrical axes, and their shifts of stress due to the moving electromagnetic planes of the Sun’s and planets’ radial electric waves to earth, as they change positions in their orbits, as at once conclusive of the relation of earthquakes to planetary cycles, and obtain further mathematical approach towards a solution of their times and location.

Space will not permit adequate discussion of this subject; but it may interest students to know that oscillating crystals manifest three fundamental frequencies and that they are rich in harmonics. For example, five different samples of high-grade quartz show fundamental frequencies of 75, 105 and 450 kilocycles. These are familiar crystalline terms (astrologically ineptly termed "aspects") in terms of "degree of oscillation per 1000 miles."

It is the old story repeated. Whether we study astrology, astronomy, physics, electrophysics, radio or electromagnetism, however, men of supposedly "different"” sciences are now beginning to come together and compare and dovetail their findings, as never before.
  

Saturday, January 28, 2017

S&P 500 versus True Lunar Node's Speed | February 2017

Upcoming Signal Days and potential Market Turn Days:
Jan 28 (Sat), Feb 02 (Thu), Feb 09 (Thu), Feb 15 (Wed), Feb 21 (Tue), Feb 24 (Fri), Mar 02 (Thu), Mar 08 (Wed).

SPX vs Mercury – Venus Cycle | February 2017

Upcoming Cycle Aspects and potential Market Turn Days:
Jan 28 (Sat), Feb 16 (Thu), Feb 24 (Fri), Mar 02 (Thu), Mar 11 (Sat).

SPX vs Jupiter – Saturn Cycle | February 2017

Upcoming Turn Days are: 
Jan 26 (Thu), Feb 01 (Wed), Feb 09 (Thu), Feb 19 (Sun), Feb 21 (Tue), Feb 23 (Thu), Mar 02 (Thu).

Cosmic Cluster Days | February — March 2017


The basic assumption here is that heliocentric and geocentric angles between planets are related to financial market movements. A signal is triggered when the composite line of all aspects breaks above or below the Average Cosmic Noise Channel. Upcoming Cosmic Cluster Days (CCDs) are: Jan 25 (Wed), Feb 08 (Wed), Mar 05 (Sun), Mar 07 (Tue), Mar 13 (Mon), Mar 14 (Tue), Mar 18 (Sat), Mar 20 (Mon), Mar 23 (Thu), Mar 26 (Sun), Apr 06 (Thu). Previous CCDs are HERE

SPX vs Cosmic Cluster Days | February 2017 | Review & Preview

SoLunar Map | February — March 2017


This chart depicts the SoLunar bias for short-term movements of stock indices two months ahead. The markets are certainly influenced also by other planetary forces - especially longer-term - but a 3-5 day short-term rhythm and pattern is governed by the SoLunar forces (= 4 highs and 4 lows per lunar month). The SoLunar forces are a composite of Sun-Moon angles, orbital eccentricities, declinations and some long-term cycles. A Low in the SoLunar Map frequently is a High in the stock market and vice versa. Inversions occur, and if so, they should occur only once every 4 lunar months around a New Moon (max +/- 7 days). The SoLunar Rhythm is frequently disturbed by (1.) the FED, and (2.) by sudden solar activity, altering the geomagnetic field, and hence the mass mood. This can result in the skip and/or inversion of pivots in the SoLunar Map. An increasing number of sunspots and flares have usually a negative influence on the stock market some 48 hours later, and vice versa (Ap values > 10 are usually short-term negative). A rising blue line in the SoLunar Map means the bias for the market is side-ways-to-up, and vice versa. Highs and lows in the SoLunar Map also may coincide with the start and termination of complex, side-ways correction patterns like zig-zags, triangles or flags. 
 
Upcoming SoLunar Turn-Days are: Jan 31 (Tue), Feb 04 (Sat), Feb 07 (Tue), Feb 10 (Fri) = Penumbral Lunar Eclipse, Feb 14 (Tue), Feb 18 (Sat), Feb 22 (Wed), Feb 26 (Sun) = Annular Solar Eclipse, Mar 01 (Wed), Mar 05 (Sun), Mar 05 (Sun), Mar 09 (Thu), Mar 12 (Sun), Mar 16 (Thu), Mar 20 (Mon), Mar 24 (Fri), Mar 27 (Mon), Mar 31 (Fri), Apr 03 (Mon). Previous SoLunar Maps HERE

SPX vs SoLunar Map | February 2017 | Review & Preview

Saturday, January 21, 2017

SPX vs Mercury 0° and 180° Jupiter and Saturn | George Bayer

Upcoming events:
2017 Jan 16 (Mon) 17:50 = JUP 000 MER [H]
2017 Feb 09 (Thu) 00:46 = SAT 000 MER [H]
2017 Mar 13 (Mon) 12:10 = JUP 180 MER [H]
2017 Mar 24 (Fri) 01:49 = SAT 180 MER [H]
2017 Apr 16 (Sun) 14:49 = JUP 000 MER [H]
2017 May 08 (Mon) 11:23 = SAT 000 MER [H]
2017 Jun 10 (Sat) 05:41 = JUP 180 MER [H]
2017 Jun 20 (Tue) 11:12 = SAT 180 MER [H]
2017 Jul 15 (Sat) 14:08 = JUP 000 MER [H]
2017 Aug 05 (Sat) 09:55 = SAT 000 MER [H]
2017 Sep 07 (Thu) 10:14 = JUP 180 MER [H]
2017 Sep 16 (Sat) 20:34 = SAT 180 MER [H]
2017 Oct 13 (Fri) 15:51 = JUP 000 MER [H]
2017 Nov 02 (Thu) 08:19 = SAT 000 MER [H]
2017 Dec 05 (Tue) 13:59 = JUP 180 MER [H]
2017 Dec 14 (Thu) 05:58 = SAT 180 MER [H]
2018 Jan 11 (Thu) 19:57 = JUP 000 MER [H]

Friday, January 20, 2017

The Fading American Dream | Trends in Absolute Income Mobility since 1940

Raj Chetty et al. (NBER Working Paper No. 22910 | Dec 2016) - One of the defining features of the “American Dream” is the ideal that children have a higher standard of living than their parents. When children are asked to assess their economic progress, they frequently compare their own standard of living to that of their parents. 

Such measures of absolute income mobility – the fraction of children earning or consuming more than their parents – are also often the focus of policy makers when judging the degree of economic opportunity in the U.S. 

Around 90% of children born in 1940 across the entire income distribution earned more than their parents did at age 30. That percentage dropped each decade, with only about 50% of children born in 1980 earning more than their parents. The likelihood that children at age 30 had a higher inflation-adjusted income than their parents did when they were the same age has been dropping over the last several decades.

DJIA Performance during Presidential Terms | 1900-2017


Bespoke (Jan 19, 2017) - Through Thursday, the DJIA is up over 148% (not including dividends) since the close on [Obama's] Inauguration Day 2009, and that ranks as the fourth best return for the DJIA under any President since 1900. Calvin Coolidge presided over a gain of 251.7% during his time in office [...] followed by Clinton (227%), and FDR (197%) [...] Hoover presided over a decline of over 80% [...] the second George Bush saw the DJIA fall 22%.

Monday, January 16, 2017

An Aging World | Population Age 65+ in 2015 and 2050

Source: US Census
The social and economic implications of an aging population are becoming increasingly apparent in many industrialized nations around the globe. With populations in places such as North America, Western Europe and Japan aging more rapidly than ever before, policymakers are confronted with several interrelated issues, including a decline in the working-age population, increased health care costs, unsustainable pension commitments and changing demand drivers within the economy. These issues could significantly undermine the high living standard enjoyed in many advanced economies. 

As of December 2015, people 65 or older account for more than 20% of the total population in only three countries: Germany, Italy and Japan. This figure is expected to rise to 13 countries by 2020. A rapidly aging population means there are fewer working-age people in the economy. This leads to a supply shortage of qualified workers, making it more difficult for businesses to fill in-demand roles. An economy that cannot fill in-demand occupations faces adverse consequences, including declining productivity, higher labor costs, delayed business expansion and reduced international competitiveness. In some instances, a supply shortage may push up wages, thereby causing wage inflation and creating a vicious cycle of price/wage spiral.

Japan is home to the oldest citizenry in the world, with 26.3%
of its population being 65 years of age or older. The population
aged 15 to 64 fell by 4% between 2000 and 2010
(World Bank).
To compensate, many countries look to immigration to keep their labor forces well supplied. While countries such as Australia, Canada and the United Kingdom are attracting more highly skilled immigrants, integrating them into the workforce can be a challenge because domestic employers may not recognize immigrant credentials and work experience, especially if they were obtained in countries outside of North America, Western Europe and Australia.

Given that demand for health care rises with age, countries with rapidly aging populations must allocate more money and resources to their health care systems. With health care spending as a share of gross domestic product (GDP) already high in most advanced economies, it is difficult to increase spending while ensuring care improves and other social needs do not deteriorate in the case of publicly funded or government-administered health care systems. Additionally, the health care sector in many advanced economies faces similar issues, including labor and skills shortages, increased demand for home care and the need to invest in new technologies. All of these cost escalators make it more difficult for existing systems to handle the increased prevalence of chronic diseases, let alone sufficiently address the needs of large and growing senior populations. 

Countries with large elderly populations depend on smaller pools of workers in which to collect taxes to pay for higher health costs, pension benefits and other publicly funded programs. This is becoming more common in advanced economies where retirees live on fixed incomes with much smaller tax brackets than workers. The combination of lower tax revenue and higher spending commitments on health care, pension and other benefits is a major concern for advanced industrialized nations. Source: Investopedia. See also HERE

Monday, January 9, 2017

SPX vs 4.5 Degree Steps of Lunar Node to Lunar Apogee | 80th Harmonic

Upcoming aspects in this 18 Year Cycle:
Feb 04 (Sat) = 85.5 degrees, Mar 14 (Tue) =  90 degrees, Apr 13 (Thu), May 07 (Sun), May 26 (Fri),
Jun 19 (Mon), Jul 16 (Sun), Aug 22 (Tue), Sep 25 (Mon), Oct 21 (Sat), Nov 12 (Sun), Dec 02 (Sat),
Dec 26 (Tue), 2018 Jan 29 (Mon) = 144 degrees. See also HERE

Sunday, January 8, 2017

DJIA 2017 | Presidential Cycle + Seasonal Pattern + Decennial Cycle

Seasonal Cycle (1900-2016) Jan 01 - Dec 31 = +6.99%
1st Year of the Presidential Cycle (2017) Jan 01 - Dec 31 = +5.48%
7th Year of the Decennial Cycle (2017) Jan 01 - Dec 31 = +4.82%
"The Sun's position by itself in relation to the stock market can show you trends that are more
or less active for each year, as the Sun degrees are generally fixed. They fall on about the
same date every year. So this is why some periods of the year would be more of a pattern."

SPX vs 15 Degree Steps of Lunar Node to Lunar Apogee | 24th Harmonic

Upcoming aspects in this 18 Year Cycle:
Jan 12 (Thu) = 165 degrees, Mar 14 (Tue) = 180 degrees, Apr 28 (Fri), Jun 04 (Sun), Jul 16 (Sun),
Sep 17 (Sun), Oct 28 (Sat), Dec 02 (Sat), Jan 15, 2018 (Mon).
David McMinn (2016): 9/56 Year Cycle: Lunar North Node - Apogee Angles [5 p.]

Saturday, January 7, 2017

Harmony of the Spheres | Dance of the Planets


James Ferguson’s (1710-1776) representation of the apparent motion of the Sun, Mercury, and Venus from the Earth, based on similar diagrams by Giovanni Cassini (1625-1712) and  Roger Long (1680-1770). Taken from the "Astronomy" article in the first edition of the Encyclopædia Britannica (1771; Volume 1, Fig. 2 of Plate XL facing page 449). This geocentric diagram shows, from the location of the Earth, the Sun's apparent annual orbit, the orbit of Mercury for 7 years, and the orbit of Venus for 8 years, after which Venus returns to almost the same apparent position in relation to the Earth and Sun. In Arabic, Venus is called “El Zahra” - the flower. See HERE + HERE + HERE + HERE

Earth - Mercury Cycle.
This and all following graphics by John Martineau.
Earth - Venus Cycle:
Earth = 8 years x 365.256 days/year = 2,922.05 days
Venus = 13 years x 224.701 days/year = 2,921.11 days (ie. 99.9%)
Earth - Mars Cycle.
Earth - Jupiter Cycle.
Saturn - Uranus Cycle.
Jupiter - Saturn Cycle.
Venus - Mars Cycle.
The radius of the Moon compared to the Earth's is 3:11
Radius of Moon = 1,080 miles = 3 x 360
Radius of Earth = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5
Radius of Earth plus Radius of Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10

The ratio 3:11 is 27.3%, and the orbit of the Moon takes 27.3 days, which is also the average rotation period of a sunspot. The closest to farthest distance ratio that Venus and Mars each experiences in the Mars-Venus dance is also 3:11. The Earth orbits between them. The sizes of the Moon and the Earth is drawn to scale in the last illustration above, where the perimeters of the dotted square and the dotted circle are of the same length: The perimeter of the dotted red square is 4 x Earth’s diameter = 4 x 7,920 miles = 31,680 miles. The circumference of the dotted blue circle is 2 pi x radius = 2 x 3.142 x 5040 miles = 31,667 miles (ie. 99.9%).

Thursday, January 5, 2017

The Measure of the Circle | Math for Mystics # 2

Pi (π) is the ratio of the circumference of a circle to its diameter. 
As a fraction, its closest approximations are 22/7, 333/106 and 355/113.
Projection on the plane of the ecliptic of the parabolic
orbits of 72 comets, 1802. Engraving by Wilson Lowry after
Johann Elert Bode.
Circle of Fifths, and relationship of relative
minor keys to major key signatures.

"The circle is one of the noblest representations of Deity, in his noble works of human nature. It bounds, determines, governs, and dictates space, bounds latitude and longitude, refers to the Sun, Moon, and all the planets, in direction, brings to the mind thoughts of eternity, and concentrates the mind to imagine for itself the distance and space it comprehends. It rectifies all boundaries; it is the key to information of the knowledge of God; it points to each and every part of God's noble work."

John Davis (1845): The Measure of the Circle
[p. 12].