In this article we will move into a discussion of the geometry of the solar system. We will begin by discussing John Martineau’s work, the geometric patterns of planets. In the next four articles we will discuss solar domains, extinction cycles, the precession of the equinoxes, cyclic history and the zodiac.
English author and biologist Rupert Sheldrake wrote, “I think much good will come from recovering a sense of the life of the heavens. We are coming to see the Earth, Gaia, as alive. I think we also have to take seriously the idea that the Sun is alive and conscious. If one wants a scientific rationale for this, it comes ready to hand through the discoveries of modern solar physics. We now know that the Sun has a complex system of magnetic fields, reversing its polarity every eleven years, associated with the sunspot cycle. With this underlying rhythm of magnetic polar reversals are a whole series of resonant and harmonic patterns of magnetic and electromagnetic change – global patterns over the surface of the sun of a fractal nature; patterns within patterns, highly turbulent, chaotic, sensitive, varied and complex. As electromagnetic patterns within our brains seem to be the interface between the mind and the nervous system, here we have a parallel in the physical behavior of the sun. It is perfectly possible that the sun has a mind which interfaces with the solar system itself as an organism. This is largely what astrology has concerned itself with.”
Geometric Patterns in the Solar System
Keitch Critchlow adds, “It is only by ‘standing outside’ moving time that one can see the pattern that the planetary cycles make.”
The work of John Martineau clearly shows the incredible patterns of the planets, and these patterns are all based upon the Platonic solids.
“The planets are apparently being held in place and driven through their orbits by the same geometric forces that very likely create atoms and molecules – as well as the global grid.”1
“[John Martineau] decided to make a close study of how the orbits of the planets relate to each other and how the patterns that can be drawn from them fit so precisely with things made down here on earth. He found many rather beautiful relationships…This is all pretty remarkable evidence that there is a mysterious unity in the patterns found throughout the whole of creation. From the smallest of molecules to the biggest of the planetary “particles” revolving around the Sun, everything depends for its stability upon an incredibly simple, very elegant geometric patterning – the grammar of harmony.”2
“The patterns traced by each of the planets were considered an essential part of the significance of the archetypal intelligence symbolically reflected in that planet, signs for the wise.”3
Clockwise from top: The orbits of Jupiter/Earth; Saturn/Jupiter; Mars/Venus; Earth/Mercury; Uranus/Saturn; Mars/Earth. Center: Earth/Venus
Plato taught that all the heavenly bodies were gods, were animate, intelligent, and had souls. It was their souls that generated the motions of the cosmos and the celestial bodies.
He wrote, “All the fixed stars were created as divine, ever-living beings, spinning evenly and unerringly forever”.
Furthermore, he said that these souls/gods are not capricious [as in Greek myth]. They always act for the best, and so will always act in the same manner.
Robin Waterfield tells us that “Plato employs a theory of harmony in cosmology: the spacing of the orbits of the planets is related to the musical scale. Musical notes can be expressed as the ratio between two numbers, as can the size of the planetary orbits.”
He goes on to note, “If we ask modern science why there are eight planets in the solar system, with specific spacing of the orbits and specific orbital speeds, the answer is likely to be that this is largely a matter of chance.”
As we will see, there is an awful lot of ‘chance’ and ‘coincidence’ that had to come perfectly together to form the solar system as it is. Add to this all the ‘chance’ and ‘coincidence’ of seeing these same geometries and musical ratios in so many other scales of the universe!
“As things are, however, the visibility of day and night, of months and the circling years, of equinoxes and solstices, resulted in the invention of number, gave us the concept of time, and made it possible for us to inquire into the nature of the universe. These in their turn have enabled us to equip ourselves with philosophy in general, and humankind never has been nor ever will be granted by the gods a greater good than philosophy.
That is, the gods wanted us to make a close study of the circular motions of the heavens, gain the ability to calculate them correctly in accordance with their nature, assimilate ours to the perfect evenness of the gods and so stabilize the wandering revolutions within us [the wandering movements of our minds].” Timaeus 47 a-c
Plato continues, as to “the thoughts and revolutions of the universe, these are what each of us should be guided by as we attempt to reverse the corruption of the circuits in our heads, that happened around the time of our birth, by studying the harmonies and revolutions of the universe. In this way, we will restore our nature to its original condition by assimilating our intellect to what it is studying and, with such assimilation, we will achieve our goal: to live, now and in the future, the best life that the gods have placed within human reach.” 90d
John Martineau – A Little Book of Coincidence
We will now explore the fascinating work of John Martineau from A Little Book of Coincidence published in 2001.
“Martineau realized that by adjusting the actual form of both physical body and orbit of each planet to their ‘mean’ size – that is, by not changing the mass or distance, only bringing them to their archetypal sphere or circle – he could reveal the extraordinary inner order underlying the outer facts.”4
To begin, as our solar system moves through space it moves in a helical (spiral) pattern, not a straight line.
The plane of our solar system is tilted at 30 degrees to the plane of the galaxy – our solar system actually corkscrews its way around the arm of the Milky Way.
Planets don’t move around the earth in simple ways – they lurch around like drunken bees, waltzing and whirling. Occasionally, when planets pass, or kiss, each appears to the other to retrogress, or go backward against the star for a time.
Johannes Kepler (1571-1630), the famous German mathematician, astronomer and astrologer, noticed three things about planetary orbits:
- First, that they are ellipses with the Sun at one focus
- Second, the area of space swept out by a planet in a given time is constant
- Third, the period T of a planet relates to R, its semi-major axis (average orbit), so that T2/R3 is a constant throughout the entire solar system
Looking for a geometric or musical solution to the orbits, Kepler observed that six heliocentric planets meant five intervals. The famous geometric solution he tried was to fit the five Platonic solids between their spheres.
Kepler noticed the ratios between planets’ extreme angular velocities were all harmonic intervals.
“…for there is music wherever there is harmony, order, or proportion; and thus far we may maintain the music of the spheres.” Sir Thomas Brown (1605-1682)
Wikipedia states, “He found that each of the five Platonic solids could be inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets – Mercury, Venus, Earth, Mars, Jupiter and Saturn. By ordering the solids selectively – octahedron, icosahedron, dodecahedron, tetrahedron, cube – Kepler found that the spheres could be placed at intervals corresponding to the relative sizes of each planet’s path, assuming the planets circle the Sun.”
Though this Platonist polyhedral-spherist cosmology was not precise enough to be 100% accurate Kepler nevertheless did not relinquish this model.
The seven traditional wanderers are so called because of their relation to Earth’s movement:
Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn
Two nested pentagons define:
- Mercury’s orbital shell (99.4%)
- The empty space between Mercury and Venus (99.2%)
- Earth and Mars relative mean orbits (99.7%)
- The space between Mars and Ceres (99.8%)
Three nested pentagons define:
- The space between Venus and Mars (99.6%)
- Ceres and Jupiter’s mean orbits (99.6%)
Planet’s orbital periods sometimes occur as simple ratios of each other, just like harmonic musical ratios.
There is a ratio of 2:5 of Jupiter and Saturn (99.3%) and the ratio of 1:2:3 for Uranus, Neptune and Pluto (99.8%).
Earth passes Mars 3 times for every 4 passes of Venus, revealing a 3:4 rhythm, or deep musical fourth being played around us all the time.
The Inner Planets
- Mercury – mostly solid iron; cratered, atmosphere-less world; 400° C in the sun; -170° C in the shade; no moon.
- Mercury has a highly elliptical orbit. One Mercury day is 2 of its years, a musical octave (1:2).
Mercury. Credit: NASA
- Venus – cloud-shrouded greenhouse world; 480° C on the surface; CO2 rich atmosphere is 90 times denser than Earth’s; no moon.
- Venus has the most perfectly circular orbit of all. It is the brightest point in the sky to Earth
- 1 Venus day is precisely 2/3 of an Earth year – a musical fifth (2:3)
- Orbits of Mercury and Venus
- If you put three circles of the same size together so they are touching, but not overlapping, the orbit of Mercury will perfectly pass through the centers of each circle and the orbit of Venus will enclose the figure (See page 21).
- Earth – one Moon
- Orbits of Mercury and Earth (page 29)
- The diameter of Mercury’s innermost orbit can be seen as a circle inside the pentagram (99.5%) and also happens to be the distance between the mean orbits of the two planets (99.7%)
- Mercury’s dance around Earth produces its synodic year of 115.9 days. Richard Heath discovered this is 618 times a musical fifth times a full moon (99.9%)
- 618 = 1 + phi
Keith Critchlow writes, “The triangle which emerges from this visible pattern represents the underlying archetype which is ‘outside’ time whilst Mercury’s path represents moving time.”
In one year Mercury loops 3 times around the Earth. The cycle of 22 loops occurs before Mercury returns to the same point in the sky.
Orbit of Mercury & Earth in 1 year.
- Orbits of Venus and Earth
- Venus passes Earth every 584 days.
- Venus draws a pattern around the Earth over exactly eight years (99.9%), or every 13 Venusian years (99.9%). This looks like a beautiful five-petaled flower.
- The periods of Earth and Venus (1.618:1) are closely related to the Golden Ratio. The perigee and apogee of Venus are defined by two pentagrams (page 25). The body of space one draws around the other is 1:2.618.
- The ratio between Earth’s outer orbit and Venus’s inner orbit is given by a square.
- Inner Three Planets
- Eight touching circles centered on Venus’ orbit produce Earth’s mean orbit (99.9%) (page 29).
- If we work in units of Mercury’s mean orbital radius and period, then Venus’ period times 2.618 is Earth’s orbit squared (99.8%).
- Mars – rocky, red world, just above freezing; ice caps cover the poles under a thin atmosphere; riverbeds suggest ancient long-gone oceans; two moons
- Olympus Mons, the largest volcano/mountain in the solar system is at ~19.5° Latitude.
- Orbits of Earth and Mars – page 40 – four-fold geometry (99.9%)
- Orbits of Mars, Earth, Venus – (page 35)
- The icosahedron and dodecahedron appear in the geometries between these 3 planets.
- They appear in bubble form suspended inside Mar’s spherical orbit. The dodecahedron produces Venus’s orbit as the bubble within (99.98%), while the icosahedron defines Earth’s orbit through its bubble centers (99.9%).
- Beyond Mars – the asteroid belt, dominated by Ceres, containing thousands of large and small tumbling rocks, siliceous, metallic, carbonaceous and others
- Ceres – about the size of the British Isles – produces a perfect 18-fold pattern with Earth (page 57).
- The Moon (See page 31)
- From the surface of the Earth, the Sun and Moon appear to be the same size.
- The size of the Moon compared to the Earth is 3:11 (99.9%).
- If you pull the Moon down to the Earth, then the circle through the center of the heavenly Moon will have a circumference equal to the perimeter of a square enclosing the Earth. This is ‘Squaring the Circle’.
The circumference of the blue circle is equal to the perimeter of the red square. Credit: Michael Schneider
- The Earth-Moon proportion is also precisely invoked by our two planetary neighbors, Venus and Mars – The closest:farthest distance ratio that each experiences of the other is 3:11. We orbit between them.
- 3:11 is 27.3%; the Moon orbits the Earth every 27.3 days, also the average rotation of a sunspot.
- The Radius of the Moon is 1,080 miles = 3 x 360.
- The diameter of the Moon is 2,160 miles = 6 x 360 = 18 x 1 x 2 x 3 x 4 x 5.
- The Radius of Earth is 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5.
- The Radius of Earth + Radius of Moon is 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10.
- The Diameter of Earth is 7,920 miles = 8 x 9 x 10 x 11.
- There are 5,280 feet in a mile = (10 x 11 x 12 x 13) – (9 x 10 x 11 x 12).
To Find the Number of Full Moons in a Year:
- Method 1: Draw a circle, diameter 13, with a pentagram inside. Its arms will then measure 12.364, the number of full moons in a year (99.95%).
- Method 2: Draw the 2nd Pythagorean triangle, with sides of 5, 12, and 13 (also the numbers of the keyboard and of Venus). Dividing the 5 side into its harmonic 2:3 gives a new length 12.369 (99.999%).
All of the current major time cycles of the Sun-Moon-Earth system can be expressed as simple combinations of the numbers 18, 19 and the Golden Section. Its values added to the magic number 18 produce 18, 18.618, 19, 19.618 and 20.618.
See chart page 33.
The Earth and moon rotate around each other – there is a component between them approximately 1/3 of the distance from the Earth to the moon acting as a pivotal point.
The Earth and moon rotate around this pivotal point in a helical pattern as they move around the Sun.
The Outer Planets
- Jupiter – the largest planet and its magnetic field is the largest object in the solar system; 90% hydrogen, built around a rocky core; metallic and liquid hydrogen surrounds the core; Jupiter has many moons including Ganymede and Callisto – one of the four largest, Io, is the most volcanic body in the solar system; another, Europa, may have warm oceans of water beneath its icy surface.
- Great Red Spot at ~19.5° Latitude
- Jupiter’s moons Ganymede and Callisto – page 41 – both the size of Mercury; produce one of the most perfect space-time patterns in the solar system.
- Orbits of Jupiter’s Moons – page 43 – Four groups of moons orbit Jupiter. First two groups have four moons; second group of four large moons is divided into two rocky worlds – Io & Europa – and Ganymede & Callisto; Each of the four groups has its own general moon size, orbital plane, period, and distance from Jupiter (the inclinations of the four orbital lanes of the four groups even add up to a quarter of a circle (99.9%)
- Orbits of Earth and Jupiter
- Jupiter has a pair of asteroid clusters that orbit with Jupiter, one 60° ahead of it, and one 60° If we join the spokes (page 45) to create a star tetrahedron, then two more 6 pointed stars will produce Earth’s mean orbit from Jupiter (99.8%).
- Exactly the same proportion may be created by spherically nesting three cubes, three octahedra, or any threefold combination of them inside Jupiter’s orbit (page 44). The tiny sphere in the center is Earth’s orbit.
- Orbits of Mars and Jupiter – 550 million km separate the two orbits; the orbits can be drawn from four touching circles or a square (99.98%)(page 41).
- Saturn – the 2nd largest planet; ring structure around planet; hydrogen and helium mix below the clouds; over 30 moons – the largest is Titan, the size of Mercury, has all the building blocks for life but warmth.
- Saturn – Hexagonal structure at pole
- Saturn, Mars, Neptune & Pi
- The radius of Saturn is the circumference of Mar’s orbit (99.9%).
- The circumference of Saturn is the diameter of Neptune’s orbit (99.9%)
- Orbits of Saturn’s Moons
- Most moons shepherd and tune the rings. The larger bodies are beyond the rings – giant Titan, tiny Hyperion, and far-out Iapetus; see page 43 for their orbits.
- Orbits of Earth and Saturn: Earth’s and Saturn’s relative orbits and sizes can be given by a fifteen-pointed star (page 29), which further produces the tilt of the Earth; Saturn also takes the same number of years to go around the Sun as there are days between full moons (99.8%)
- Orbits of Jupiter and Saturn
- There is a close 5:2 ratio of their periods – shown as a beautiful 3-fold harmonic (page 47).
- Jupiter’s and Saturn’s orbits are in proportion 6:11 (99.9%), the octave, or double of the 3:11 Moon: Earth ratio.
From Earth, this pattern is seen as an important triangular sequence of conjunctions and oppositions of Jupiter and Saturn, who come together every 20 years. Page 47 we see the hexagram created by these positions – with conjunctions marked on the outside of the zodiac and oppositions marked inside. The planets move counterclockwise around the circle of the ecliptic, shown here as a dotted line, starting at 12 o’clock, Jupiter moving faster than Saturn.
The phi ratio shows up in the relative speeds of the orbits of Earth, Jupiter and Saturn (see page 47). Earth orbits much faster than the other two and makes a whole annual circuit of the Sun (365.2 days) before lining up with slow Saturn again for a synod after 378.1 days. Three weeks later it lines up with Jupiter (after 398.9 days).
The Golden Ratio is defined here in time and space to 99.99% accuracy.
Reference Construction Lesson #81: Recreating the Proportions of the Planetary Orbits of Jupiter & Saturn
- Chiron – well-tuned comet-planet between Saturn and Uranus. Chiron measures out a perfect 25 in the Uranian sky (page 51).
- This ‘25’ relates to the 25 passes of Neptune and Uranus seen below.
- Uranus – orbits on its side; winds gust at the equator 6000 times the speed of sound; 21 known moons, faint system of rings.
- Uranus Rings – the bright outermost ring has a diameter twice that of Uranus itself, an octave (2:1).
- Orbit of Uranus and Earth
- Orbits of Uranus, Saturn and Jupiter – page 49 – uses a simple method for proportioning the outer, mean, and inner orbits of Uranus, Saturn and Jupiter using an equilateral triangle and an octagram.
- Neptune – like Uranus, an ice world of water, ammonia and methane; largest moon Triton – has nitrogen ice caps and spews geysers of liquid nitrogen high into the atmosphere; faint ring system.
- The Great Dark Spot is at ~19.5° Latitude
- Neptune’s Rings – the innermost ring is 2/3 the size of its outermost (99.9%), a musical fifth.
- Orbits of Neptune and Uranus
- Neptune’s orbital period is twice that of Uranus, an octave; they dance around each other to create the beautiful shape (page 51), which slowly spins so that every 4,300 years Neptune and Uranus both experience a perfect division of the zodiac into 25 passes.
- Pluto – tiny planet or ‘planetoid’ with one large moon Charon
- Orbits of Uranus and Pluto – Uranus’s orbital period is 2/3 that of Pluto – a musical fifth.
- Beyond Pluto:
- The primordial swarm of the Kuiper Belt
The Kuiper Belt. Jupiter (J), Saturn (S), Uranus (U) and Neptune (N) are indicated.
- 1/3 of the way to the nearest star is the Oort Cloud – home to the comets.
The Golden Ratio Phi in the Cosmos
Harmony in the Solar System:
The distance from the sun to Mercury plus Mercury’s distance to Venus equals the distance between Venus & Earth.
Also seen in the distances of the planets from the sun and each other:
- Mercury & Earth
- The relative physical sizes and the relative mean orbits of Earth and Mercury are φ2:1 or a simple pentagram (99%).
- Venus & Earth
- Venus draws a 5-fold pattern around the Sun every 8 years.
- The orbit of Venus around the earth is an 8 year cycle that transcribes 5 perfect phi spirals.
- 8 Earth years = 13 Venusian years. (8 and 13 being Fibonacci numbers)
- Venus perigree & apogee (furthest and closest distances to Earth) are defined as :φ4:1 (99.99%).
- Jupiter, Saturn & Earth:
- Jupiter & Saturn produce a perfect golden ratio from Earth.
- Line them all up toward the Sun and a year later Earth returns to where she started.
- 85 days later Earth is exactly between Saturn & the Sun
- 79 days later Earth is between the Sun & Jupiter
- These synodic measures exist in space and time and relate as 1:φ (99.99%).
Logarithmic/Fibonacci spirals are also, of course, seen in the spiraling arms of galaxies.
108 in the Solar System
- Sun diameter ~ 108 Earth diameters
- 108 Sun diameters between the Sun and Earth
- radius of the Moon = 1080 miles
- diameter of the Moon = 1080 x 2 miles (2160)
- 10080 miles = diameter of the Earth + Diameter of the Moon
- Distance from Sun to Venus = 108 million km
- Diameter of Mars = 1080 x 4 miles (4320)
- Diameter of Jupiter = 10800 x 8 miles (86400)
- Orbit of Jupiter = 1080 x 4 days (4320)
- Diameter of Saturn = 108000 km
- Saturn’s orbit = 10800 days
- Saturn’s hexagon edge length = 1080 x 8 miles (8640)
Note these synchronicities apply to both the standard measurement system and the metric system.
Celestial Harmonic Cycles
We will now discuss one more topic corresponding to the inherent harmony found in the solar system – the Constant of Nineveh.
Constant of Nineveh – “Great Constant of the Solar System”
This constant correlates to the revolution of all the bodies of the solar system, including satellites.
The constant is as follows:
195,955,200,000,000 (70 x 60 x 60 x 60 x 60 x 60 x 60 x 60)
It was first found on a clay Sumerian tablet with cuneiform found in the library of the Assyrian tyrant Ashurbanipal (669-626 BC).
Maurice G. Chatelain (1909-1995) was a French engineer and communications specialist. In 1959 he worked for the Ryan Aeronautical Company and was appointed head of the electromagnetic research group responsible for developing new radar and telecommunications systems. During this work he obtained 11 patents.
Later he worked for North American Aviation which had won the contract for the development and production of the Apollo spacecraft for NASA. Chatelain then built relay stations around the world in the tropics, each more than 200 feet in diameter so that they can communicate with each other and with the Houston flight center.6
Chatelain was the one who discovered the Constant of Ninevah to be in seconds. He calculated it to be 2,268 million days of 86,400 seconds each or 6.2 million years.
Chatelain writes, “Every period of revolution or conjunction of all the solar system bodies calculated by the Constant of Nineveh corresponded exactly down to several decimal points with the values given in the modern tables of United States astronomers… I have not been able to find even a single period of revolution or conjunction of a solar system planet or satellite that would not be an exact fraction down to the fourth decimal point of the Great Constant of the Solar System.”
It is to be noted that there are only tiny discrepancies in the cycles due to the tropical year shortening by 16 millionths of a second per year.
Within the Constant of Nineveh (N.C) include:
- Exactly 240 ‘Great Years’ of 9.450 million days each, or 240 precessional cycles
- 62 million year extinction cycle (Muller and Rohde) – 10 Nineveh constants
- 4 N.C = 24.8 million years – lines up with Raup and Sepkoski’s 25-26 million year cycle in the fossil record
- 40 N.C. = the 250 million year orbit of the galaxy, if the exact value is 248 million years (Official estimates are 225-250 million years)
- Halley’s Comet: 81,000 cycles in 1 N.C.
- Pluto: 24998 cycles in 1 N.C.
- After 24998 Pluto years the planets reassemble into an exact straight line (Pluto may act as the time-keeper of the solar system.)
- 3600 = # of seconds in 1 degree Lat/Long; 3600 to the 4th power (4 cardinal directions) give you 167961600000000 = 6/7ths of the Nineveh constant; same ratio as common cubit to Royal Cubit; ratio of days of creation to number of days (6 days of creation to 1 day of rest)
In this article we have seen a massive amount of data that backs up the idea that all the planets in the solar system are constrained by specific geometric patterns relating to the Platonic solids and regular polygons.
In the next article we will discuss the geometry of solar domains.
- Wilcock, David, The Source Field Investigations, Dutton, 2011
- Prince Charles of Wales, Harmony: A New Way of Looking at Our World, HarperPerennial, 2012
- Critchlow, Keith, Time Stands Still, Brecourt Academic, 2007