Five pointed star revelations and revelries from the solar neighborhood


Two pointed star of NeptunePluto joins the five point star — there is Catseye looking at you, kid Eight pointed star chimes in — the eight sided octagon is from Mars and it is musical, you know, even though it is filled in counterclockwise
The eightpoint star also has a diagonal. Little discussed meaning of the diagonal gets into Note on the occult — cannot see it but you can figure it out
Intro 

Orbit ratios. Mayan astronomers first observed, measured, and applied the periodic relationship between the planet Venus and Earth. It turns out these two bodies have interlocked orbits in a ratio and that means that the planetary orbits of Venus and Earth are not independent of each other. 
Mayan stargazer. For better or for worse, Mayan Venus horoscope dealt with propitious times to wage war. 

The ratio is very close to 8:5  for every eight Venus orbits (cycles), our Earth completes five orbits (years). While this is not a source of orbit problems, the orbit's fixed ratio (interlock) allows Venus and Earth to become effectively a single planet in one orbit. The resulting merged planet is moving close to the midpoint between Venus and Earth because both of these planets are of about the same size (have about the same mass). From the Sun's point of view the positions of both Venus and Earth periodically occupy the same two spots on the solar plane and the merged planet is then also in a spot it occupied before. Every time Venus catches up with Earth the merged planet reaches its aphelion, the farthest distance from the center of the Sun. For such merged planet the time between aphelions happens every 1.6 earth years. The interlock of the two orbits merges both planets yielding one highly elliptical orbit that rotates and repeats every eight years  that is, the merged planet passes the same starting point every eight years while its path is curved. During these eight years the merged planet reaches aphelion five times, tracing a star with five points and taking 1.6 years between points. Historically, the aphelion is defined as the farthest distance from the Sun but you may have noticed that the aphelion for the merged VenusEarth planet is now defined as the farthest distance from the center of the Sun. The merged planet's orbit may possibly dip into the Sun. You can imagine the crisis in the horoscope circles as Galileo's and Newton telescopes begin to uncover new planets. There were seven planetary influences and seven is a sacred number. Horoscope casting is a serious business for some, so what is to be done? Presently, several mainstream science publications want to make Pluto a planetary outcast but nobody is arguing whether Venus or Earth is a planet or not. We could never think of Earth as not being a bona fide planet  yet the Sun has made the orbital decision for us. Sun sees Venus and Earth as one body that orbits in a five pointed star topology with a tight curlicue approaching the Sun between points. Perhaps there is a way to resolve all of this because Pluto's orbit is interlocked with Neptune as well. So now, planetary pairs merge computationally and each pair forms a unique orbit. While it may be difficult to prove that seven is the maximum number of independent orbits in our solar system, what this also means is that there could be more planets than there are independent orbits. Why not give each planet its own independent orbit? There may come a point where this is not possible. Any twobody system is tractable but a threebody system can become chaotic and intractable. An independent orbit calls for planetary separation that is great enough for each planet to be treated as a twobody sunplanet system. As big as Sun's mass is, there are but a limited number of orbits available. Orbit interlock allows merging of Venus and Earth such that the two bodies become one and the resulting body is always tractable with respect to Sun. A potential SunVenusEarth chaotic trio becomes a tractable duo. Giving Venus and Earth their own independent orbit could technically result in two twobody systems but would likely require greater planetary separation and greater distance from the Sun. Also, the orbital interlock of VenusEarth, say, could results in a smaller disturbance or wobble onto the Sun: Through the orbit interlock both bodies can be physically closer to the Sun and to each other. Tracing the merged pair of planets. Now, take the Venus and Earth planets as orbiting in the clockwise direction and start both planets at the top. The merged planet makes its first aphelion also at the top, which is the merged planet's first aphelion (point). As planets orbit, the merged planet skips every two points of a five pointed star because the the next time Venus and Earth are closest together is at the fourth point. The trace of aphelions moves from first (top) to fourth to second to fifth to third and back to the first point. The illustration of the merged planet trace is further down. [You may find a bit more in the illustration than just a trace  give it a slight tilt.] Being in the solar plane the star’s orientation does not have an appreciable social aspect, at least as far as the solar perspective is concerned. The five pointed star of this pentacle is intimately related to Venus and Earth.
Five pointed star: Pentacle with two rings  that is, orbits (not to scale) 





Symbolically and fairly close to reality, all points of the pentagram star are at midpoint between two circles that are the orbits of Earth and Venus. The dot in the center is the Sun. It is said Pythagoreans first used a circle around the pentagram (making a pentacle) but now you want to use two because you are working with two orbits. The concentric circles are paramount because the star owns its existence to two interlocked orbits. To add mystique, you can include alchemical symbols for the sun and the two planets. Also add a curlicue that may look like a lower case scripted 'e' for gals (Eves) or the Greek alpha for guys (Adams). You can keep it a pentacle but if you erase the circles you get the pentalpha or pentagram. My preferential name for a double circled pentagram is the cosmic pentacle  it exists in the macro but calling it the planetary pentacle is just as good. If you are into numbers then 5 and 8 and their ratio 8:5 (1.6) are relevant. When the ratio is slightly outside of 1.6, the star slowly rotates in the solar plane  and such is the case. Harmony. Why, then, would the planetary orbits be in the 8:5 ratio? Which ratios ought to be included and which ratios excluded, and why? The answer lies in musical harmony of planetary periods. (Harmony is also needed at the micro in case of atomic orbitals.) A period is a reciprocal of frequency and if we ratio the periods we are also rationing the frequencies. Empirically we find the planetary orbit ratios harmonious and give a great cosmic thumbs up to Pythagoras. (As to why and what makes a ratio harmonious is in the Quantum Pythagoreans book.) 
3rd4th century BC. Circled five point star coin or a talisman. 

Radius, radii. A question may come up as to the actual radii associated with rings that represent the interlocked pentacleproducing orbits. We know the orbital period of Venus and Earth, but what is the corresponding orbit radius? If Johannes Kepler were alive today he would likely have 'Dear Johan' column in the daily paper, much the same way Kepler worked in his time when he was the editor of an almanac making horoscopes and forecasts (sociopolitical forecasts at that). As it happens, Kepler is the author of the very equation we need for our calculation: T^{2}=kR^{3}. T is the orbit period (Time) and R is the radius. We do not need to know k (a constant that deals with mass) because we are interested in the ratio of the outer ring (orbit) radius to the inner ring radius. The ring ratio (multiplier) comes out of calculations and after selecting the outer ring's radius we obtain the inner ring radius by multiplying with 0.731. If the outer ring's radius (or diameter) is 11 feet then the inner ring's radius (diameter) is 8 feet. If you select the inner ring first then divide by 0.731 to get the outer ring's measure. If the inner ring is 9 feet then the outer ring is 12' 4". No matter what the mass ratio of the two planets may be, the pentagram will always have its points between the rings (orbits). The math in this geometry also means that these two rings are valid for planetary bodies of any size. 


Pentacle root properties. A pentacle is generally associated with protection, friendship and health. Pentacle's root is about a twobody orbit interlock (friendship) where the protection and health aspect is the ability to withstand chaotic environment. Similar associations lead to the acts of bonding and marriage. Pentacle's protection and interlocking qualities would also make a great seal. [The six pointed "Seal of Solomon" has no protection qualities and has other associations.] The pentacle is in the solar plane and each point is the closest VenusEarth approach: Pentacle orientation cannot corrupt its symbolism. The twodimensional aspect of the star also makes the pentacle well suited as a shield, which is generally any flat area or partition such as a curtain, door, cover, sticker, seal, table, plate, coin, or a window shutter. Perhaps the most misunderstood aspect is that a pentacle or pentagram may appear as "just an identification symbols." Pentacle, however, is a working tool and produces a strong reaction. In a somewhat crude analogy, a blade is sheathed as it is a serious tool. There are no easy or simple explanations for the pentacle, for its workings are applicable to both the cosmic and the atomic topologies. More you understand it, on the scholarly or practitioner level, more respect you will have for its properties. If you flaunt it, you likely do not understand it and nothing will come of it. 
Presently, Kepler is mostly remembered for the mathematical description of planetary orbits as ellipses. Yet Kepler's equations are also used for any and all satellites being launched into orbit  and 'satellite' is Kepler's word, too. We have a book review, Kepler's Witch in our archive.


Which way is up? The pentacle, pentagram and the five pointed star are powerful symbols. Many groups wish to claim them as their own. Up, down, or slightly tilted (Boston specialty). With circles, rays, flame, letters. Yet, with the array of attributes, the star cannot be owned by some and cannot be owned by all. 


Pentacle's revolution. Venus orbit period (time) around the sun is 224.70 earth days, while the Earth's orbit is 365.24 days. The actual EarthVenus orbit ratio is then 1.625  and the actual time between pentacle's points is 593.7 earth days. The EarthVenus interlock is not in the exact 8:5 ratio (1.60) and the pentagram issuing from the orbits rotates in the solar plane. Actually, every point slides forward by close to 9.3 days in excess of each perfect interval of 1.6 years (365.24x1.6=584.4 days vs. 365.24x1.625=593.7days). So, after 39.27 points (aphelions) the pentagram makes one complete revolution around the Zodiac. Now we take 39.27 and multiply by 1.625 for 63.814 earth years for a complete revolution. Because the pentagram has fivefold symmetry, we divide by 5 and that yields 12¾ (12.76) earth years before a point overlaps the next point. You are the best to apply this number. "Maturity" and "step" come to mind. From the Earth's perspective, when Venus is on the opposite side of Earth in the solar plane, the merged planet is on its closest approach to the Sun. There is much sophistication in the pentagram, much of it on the subconscious level, and it may take some work to bring it out. 
For parametric information about our solar system (Oss) and each of its planets and moons, visit University Corp. for Atmospheric Research web site. It has an excellent internal search. Light touch astrology for everyday living is at this Australian web site. They like planets as stars, for the future is in the stars, too.


Which way is the right way of drawing the Pentacle? That is, how to make a pentagram in the right order? This one is a bit easier to answer even though it may not agree with some books. If the opening (positive) direction is the clockwise movement of Venus and Earth, then every third point is traced (Venus catches up with Earth close to every 1.6 years) in the sequence shown below. 

This is the aphelion sequence for clockwise moving planets:

The aphelion sequence on the left results from two orbits, which are in the 8:5 ratio  that is, for every eight orbits of the inner (faster) planet the outer (slower) planet makes five orbits.
While the 'up' and 'down' cannot be differentiated in the solar plane, clockwise and ccw can be, and absolutely so. 

The aphelion sequence for counterclockwise moving planets is as follows:
You now have the root to compile a set of symbols associated with pentaanything. It is very potent. The meaning of the five pointed star of the pentagram is in the root of its creation. You now know who is speaking from indoctrination, from knowledge, from experience, or from a soap box. For example, if you were to create a flaming star as a way of heating up your relationship, you could indicate the rotation of the star when rendering the flame. However, it is also possible that the flaming star is some people's way of talking about a UFO, in which case the five pointed star has nothing to do with it, flaming or not. A flaming or a winged sphere is probably better. As for religious applications, you are, again, the best. [My take on the "new star in the heaven ushering new age" deals with the human making a significant intellectual advancement such as the Renaissance, possibly the Internet, and of course the hyperflight.] 


A crop circle showing macro and micro? The photo on the right is that of the crop circle discovered next to the Silbury Hill (Wiltshire) in England in 2002. I am not an avid crop circle chaser but I haven't seen a more revealing 5point star than the one presented here. The 13 "scales" or "fans" or "sweeps" (orbits, i.e., years) between points are interesting because, according to our calculations, the VenusEarth pentagram rotates in the solar plane and overlaps the next point in 12¾ earth years. There is a macro vs. micro view in the crop circle as well. In the macro we get orbits and in the micro (inner 5point star) we get the two kinds of the golden triangles for the orbitals (72, 72, 36 and 36, 36, 108 degrees). Still, beading around the periphery in the pentacle drawing on the left invokes a better representation of the pentacle's rotation. 64 beads would nicely show the number of years for the star to rotate around the Zodiac. Without the actual reference to the earth year, the number of beads around the periphery could also be 39.27 if you want to show ("point out") the rotating aphelions as they happen.



Here is the illustration of the actual pentacle trace in the making  the trace of the merged EarthVenus planet in the 8:5 orbit ratio. The straight (shorthand, simplified) 123451 sequence appears to be counterclockwise but the actual curved trace is always clockwise. Yep, there are five curlicues there in all and the illustration below shows the first one. In the second illustration the curlicue is the second one that happens 12¾ years later.
Pretty advanced shape. Am I the only one who sees a part of a human body in this shape?
Draw the star in the air, for that is how the Sun feels the dynamics of Venus and Earth. Chart the star in your heart and make a friend. 


TwoPointed Star pattern is made by Neptune and Pluto
If
you take Pluto away, you cannot play musical orbits. 



NeptunePluto orbits are also interlocked but in the 3:2 ratio  for every turn of the outside (slower) planet that is Pluto, the inside planet makes 1½ turns. The NeptunePluto duo can then be merged into a single planet with the resulting approximate orbit shown below. The combined planet makes a curlicue around the central sun before making the second point of a twopointed star. The combined planets' orbit completes and, therefore repeats, every two Pluto orbits. This orbit, tentatively named Catseye ("the eye of the pussy") also denotes stability similar to that of the pentacle. It can, of course, be applied if the outer planets are to be preferentially referenced. 



The making of the twopointed star is along the same mechanism as that of any multipointed star. Kepler's equation is again appropriate for obtaining the ratio of Catseyecreating radii. You may want to experiment combining three orbits into a triple ring  but consider that one orbit (one planet such as the Earth) would become the reference for the other two. All merged orbits are continuous in mathematical terms  that is, the points may be tight and sharp looking but all points are rounded. Having its ends curved may seem a bit of trivia  yet some difference exists when comparing the actual combined (merged) trajectory that has rounded points and the compass drawing of two intersecting circles with discontinuous transitions claiming to have "divine" geometry. In actuality, all planet made stars have rounded points and the geometric construction is a stylized representation of the actual (see below). Geometric ways and means, however, is the computing platform of the cosmos. You may enjoy the fact that the twopointed star is a bit of an enigma because the general updown direction may seem "not really a star." The threepointed star could be claimed to be the "lowest point star." Not so. With the extra curlicue and some width, there certainly is the two pointed star because the star exists in 2D. 


The eightpointed star is made with the Red Planet 

The octagon and thus the number eight is sourced from the EarthMars orbit relation. However, there are several ways of making the eight pointed star and that introduces the geometry of the diagonal. The number eight also continues its presence from the EarthVenus orbit ratio (8 Venus' orbits for every 5 of Earth). We are, then, dealing with several topics when working with the eightpoint star. 
This Mars Again design is from our nature inspired series. Also available in limited edition as a print in Euro A1 size. 

Octagon star Earth has an orbit interlock with Mars as well. This orbit ratio is 15:8 and it is the ratio of two notes of the musical octave. You will need to find two notes of the octave that, once put in a ratio, will yield the musical frequency ratio of 15:8. It is a ratio of two notes and that means they need to be played together. Why do these two numbers make a harmonious and pleasant sounding ratio? There are some mysteries left to be pursued and this is answered in the book. The fact that you and your friend agree that this ratio sounds harmonious is perhaps another mystery  but there is no reason the human brain would not inherently differentiate harmonious (pleasant) and disharmonious (unpleasant) sounds [we are, really, put together rather well]. The harmonious and disharmonious nature is absolute because we are able to agree on which is which. So far, the ratio of two notes that results in 15:8 (and that is musically harmonious) is in agreement with the ratio of the EarthMars orbits. Just as we did in the EarthandVenus case, the EarthandMars merged planet has aphelions from time to time and this happens when both planes are closest to each other. Connecting the aphelions results in the octagon. Because of the orbit ratio, the points of the octagon happen in the ccw fashion while both the Earth and Mars are taken as moving clockwise. The eight pointed star of the octagon then also represents a harmonious relation even though points happen counterclockwise. The trace of the EarthandMars merged planet happens clockwise but the aphelion points happen (peak out) in the counterclockwise sequence without skipping points. An eight pointed star that skips points, however, may or may not be harmonious. [This is more than a homework for the Muslims, for they do not seem to understand this.] There are several eight pointed stars. The octagon is traced in a sequence and different orbit ratios account for its clockwise or counterclockwise path. Skipping every two points draws every third point and results in an eight point star that could be called the octagram or octacle. Skipping every four points results in the identical octacle except that the order of drawing the points is different. No evenpointed star can be drawn by skipping a single point because only half of the points would be traced. Arithmetically, this deals with division such as when the attempt at drawing the 6:4 ratio actually produces the same star as the 3:2 ratio does. This could be a nice instance of applying the operation of division in nature. If you want to get into multipointed stars in more depth, the gateway question is: "How come 15:8 is harmonious (or musical) but 9:8 is not?" This will open up to other areas such as the absence of the six and seven pointed stars in orbit topologies. The true and harmonious eight pointed star comes from the 15:8 MarsEarth orbit ratio that is in the shape of the octagon. The eight pointed star is usually associated with Sun or Venus but you will need a better rationale besides just 'someone says' or 'someone wrote.' From the ancient carvings, the semicardinal directions are strongly differentiated from the cardinal directions. The eightfold symmetry does not have an equal weight or meaning when it comes to the diagonal. The point is that the "eightpointed" star is not necessarily about eight points. The cardinal and semicardinal separation takes precedence to "counting to eight," because the symbolism of the diagonal deals with the important aspect of transformation that is based on the geometry of the diagonal. It is likely that the "wavy" nature in the depiction of some of the diagonals is what leads some to think of "sun rays" and hence the Sun. Not so. We have depictions of other Venus stars  their diagonals have different graphics and do not support the symbolism of the Sun. Logically, the Sun is at the center and without an orbit the Sun cannot create a geometric star shape.

Diagonal is
about transformation Surprisingly, a scientist may have easier time with this because the diagonal of the Hermit (square) matrix has properties that hint strongly at the transformative aspect of the diagonal [think conjugation  and I mean this in the math context]. In the book Quantum Pythagoreans, another transformative aspect is invoked at the diagonal of the hyperbole, which is treated in the context of transitioning (and the necessary transforming) of data between the left and the right brain. In the East, the transformative aspect is in the virtual ("empty" or 'negative space') S shape that is in the middle of the Tao symbol. Preferentially it is composed of two gapseparated paisley shapes instead of a diagonal, which conveys the idea of 'not horizontal and not vertical.' The gap exists, for there must be a separation (and joining) between the real and the virtual domains. (Technically, a wave couples across the gap.) Whatever gets from one domain to another is subject to transformation. As a Tai Chi practitioner you might be ready to answer the question: "Why should I keep my foot at a diagonal?" At times the Tao symbol is shown with dots of the opposing color in the middle of paisley fields. This is an interesting addition even Buddhists fail to interpret in their literature. (Martial arts literature tends to discard the dots altogether.) It deals with alternate means of bridging the gap and you will need to get familiar with this site to understand it.


This symbol, while associated with Venus, is about the diagonal that is transformation. The idea, then, is to look to Venus for her transformative qualities. In general, a transformation deals with the exchange of real and virtual energies. As such, transformations can be personal or can deal with free energy extraction, Martial arts, space travel, or new computational modalities. [I've seen this star associated with Shamash, the sungod. Not so. Sin, the moongod was the chief who procreated Shamash the sungod as well as Ishtar, the goddessVenus and the star is definitely hers.] The Mesoamerican Venus symbols appear to be based on the number eight but the symbols make quite a distinction between the cardinal and semicardinal directions.

In the ancient Egyptian context, the god of wisdom and magic Thoth is depicted full of diagonals. We have a picture of him on a page dealing with the squaring of a circle.




Occult? Well, you cannot see the multipointed orbits but you can compute them. The shape of the shared orbits can never be observed but can be visualized or heard. The Sun indeed feels the shared obits gravitationally because the planets are computationally combined. The metaphysical question here is really the reverse: If you draw a pentagram, are you in fact computationally and subconsciously creating the two specific interlocked orbits? If you think geometry rules (and it does), wearing a steel helmet just might not work. Thinking that geometry and numbers are illusions just might not work. One way of drawing a pentacle is harmonious  think 8:5, which is also called 'invoking.' Another way of drawing a pentacle is disharmonious (closing)  think 7:5, which is also called 'banishing.' The ratios of 8:5 and 7:5 come from modulo math. Every time you draw the pentagram ccw you are creating the standing waves and every time you draw the pentagram cw you are dissolving the standing waves. (Some sources such as the Golden Dawn got it mixed up.)
One way of drawing
a pentagon is harmonious  think 6:5; Note that the pentagram and the pentagon have different modulo mechanics. The modulo math as it is known today takes one reference as fixed. In nature, however, everything is orbiting and in our case both the Earth and Venus are relating dynamically to each other. This generalization, or unfixing, of modulo math is described in one of our DSSP topics. 



NASA, as usual, cannot get there. When all planets are computationally combined, there exists one overall wobble onto our Sun. Unfortunately, the wobble (periodic deviation) of other solar system's suns cannot be correlated to the number, size and orbits of planets other solar system may have. That is, knowing the overall wobble, the wobble cannot be decomposed into specific planets and orbits, even if we know that the orbits are interlocked in musical orbit ratios. In fact, this is the primary mechanism behind the public key cryptography. Don't bother telling NASA, however, for they are busy telling us about the size and distance of a single "planet discovery" based on the overall wobble. If NASA can see a wobble of another solar system that is grossly out of kilter, they then also spend some more money misinterpreting it. 

Summary 
Q: We understand vibration and tones for making music. But you say that the gravitational force working the planetary (macro) bodies needs to subscribe to music as well. Is not the force of gravitation just a mindless force  this times this divided by that? A: For some, perhaps. For others, gravitation also organizes things into tractable topologies, particularly since this allows more than two bodies in the universe.


Music is vibrations. Orbits are periods that define vibrations. The Catseye orbit results from NeptunePluto interlocked ratio of 3:2 or 1.5. Interlocked orbits can make a number of star configurations but the planetary interlock usually does not exceed the ratio of 2.0. (Quantum Pythagoreans book has the ratios for planets and moons and the corresponding stars.) Because the musical octave spans orbital ratios from 1.0 to 2.0 then the Catseye ratio of 1.5 corresponds to the Sol note, which is a "fifth" played by C and G. (Music guys make it more complicated than it needs to be  and so we will stay with ratios.) Both notes need to be played to obtain the 3:2 (1.5) ratio and can be played at any particular octave. These tones then reinforce the symbolism of the Catseye. You can now construct the associative symbols of the Catseye that will acquire a symbolic meaning: numbers 3 and 2, their ratios, and notes of the (Western) octave C and G, and the eye shape itself. The eye shape can be rotated 90 degrees to resemble the cat's eye. [The shape then also begins to look like a winged sphere but I would not go that far.] The topic of Pythagorean celestial tones can get mystical, particularly if you get into chords and harmonics, which then reinforce and possibly create other orbits  some claiming to be able to hear the music. The correspondence of the pentagram's 1.6 ratio to a particular tone makes for a good exercise. Another ratio is 5:3 and this corresponds to notes C and A (ratio 12/3 or 1.66). If such orbital ratio were to exist (corresponding to musical ratio of notes C and A) then the merged planet would make a threepointed star orbit. Threepointed merged planet orbit does not exist in Oss [yet? or perhaps it exists at another solar system]. 

Additional things to consider arise when considering the 13:8 ratio. This ratio is not on the musical scale but, arithmetically, it is closer to the actual measurement of the VenusEarth orbit ratio, which means that the rotation of this star is slower than that of the pentagram. Both 8:5 and 13:8 are ratios of two consecutive terms of the Fibonacci sequence of numbers. It makes for a good exercise to figure out the star that issues from the 13:8 ratio and what advantage, if any, this star brings to the table. Fibonacci sequence grew from but a series of numbers into the golden ratio a:b when Kepler discovered that the ratio of two consecutive Fibonacci numbers converge toward (1+SQRT(5))/2. Normalized, the golden ratio is 1.6180.. to 1. Because the actual VenusEarth orbit ratio is very close to the golden ratio (1.625 and 1.618, respectively), any ratio of two consecutive terms of the Fibonacci sequence will make a ratio that is a very close fit with the golden ratio of 1.6180. Some examples: 8/5 (1.6), 13/8 (1.625), 21/13 (1.615), 34/21 (1.619), 55/34 (1.618), etc. If somebody proclaims that the eight or the thirteen or the twentyone pointed star represents Venus  you will know where he or she is coming from. 


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Enlarged with
NeptunePluto and EarthMars interlocked orbits, the original article
is available in Press
Releases as the pdf file. Last update May 29, 2013 