Requiem for Relativity

More about the "61" relation and Mayan Long Count

Above, I noted that the Mayan Long Count is almost exactly 61 orbital periods of Uranus, and that also it is nearly a whole number of Saturn or Jupiter orbital periods. My preceding post shows that some numbers, such as 243, are related to more than a chance resonance of planetary orbital periods. Now let's show that 61 also is related to more than chance resonances. (The mathematical basis for this could be, Diophantine equations, arising from tilings or from Platonic solids, composing subatomic structure; or, integer eigenvalues of integrodifferential operators.)

The core sidereal rotational period of Jupiter often is given as 9.9250 days. The orbital periods of Jupiter's two biggest moons, Ganymede & Callisto, are 7.155 & 16.689 d, resp. If Jupiter itself were considered to be a moon in an orbit below that of Ganymede or Callisto, then I would, by analogy with the "243" relation in the previous post, expect the (integer plus half) relation to hold. Indeed it does:

61*9.9250/24 / 7.154553 = 3.526
61*9.9250/24 / 16.68902 = 1.512

The relation is even closer, when Jupiter's equatorial cloudtop sidereal rotation period is used:

61*9.8411/24 / 7.154553 = 3.4961
61*9.8411/24 / 16.68902 = 1.4988

Likewise, in total potential energy and in total angular momentum, Luna's geocentric orbit is "above" Earth's heliocentric orbit. Luna's sidereal period is 27.321661d, and Earth's sidereal period is 365.25636d, so:

61*365.25636/27.321661 = 815.4935,

again giving (integer plus half).

Finally, it is 61 which gives the best resonance between my "Barbarossa period", and Earth's precession period. Barbarossa's sidereal heliocentric orbital period was first estimated by me, as 6340 +/- 7 yr, from the four exactly coplanar sky survey positions. I refined it by consideration of the Egyptian calendar (with its beginning in, most likely, the summer solstice 4328BC and possibly ending, according to Seti I's inscription, at "the first day of winter, the start of eternity"!), of the Mayan calendar (ending at the winter solstice 2012AD) and of protoplanet resonances. The mutually consistent result is 6339.500 tropical yr (which I correct to Julian yr below):

61*6339.500*(365.24219/365.25) / 25771.5(precession period)
= 15.0050

So, the evidence for 61 as a physically special number, is no less overwhelming than the evidence for 243. Somehow, the Mayan Long Count, incorporates astronomical observations of accuracy at least comparable to our own, and a knowledge of astronomical cycles, and possibly the physical mechanisms underlying those cycles, even more advanced than our own. The contrived, convenient factorization (360*20*20*13 days) of the MLC (or rather, of a close approximation to the MLC) was an easy way to ensure that the MLC was used and remembered. The end date of the Mayan Long Count hardly can be frivolous.

Something will happen then. As I've explained above, crop circles strategically placed near astronomical megaliths in Wiltshire, England, often suggest astronomical events (transits, conjunctions, eclipses, even the solar system configuration exact to within a few days of Dec. 21) leading up to Dec. 2012.

Hi Joe, it sounds as if you have a little program do speed up you calculations, or at least a spread sheet. Have you done the same for orb periods around the barycentre? Which will place the sun in the group to look at, and I think that perhaps it might be an idea to put the asteroid belt in as well.

Thinking about the barycentre, won't it have to do a little double jump at some point in the protostar's evolution? A two component star has to dump angular momentum, and I think that sol dumped most of this onto the proto vega. This would slow vega's development, so it looks a billion years old. At some point in the collapse of sol, it dumps half of its mass in a ring around its equator. it's too early to be able to spit gobbets of mass out, as the density of the proto star is too low. Barbarossa will have to do the same a little later. The barycentre then has to do a little hop and skip between these two events. It's my hunch, that barie has to lose more than half its mass but I think we'd have to look at that, it might not be the case.

Both sol and barbarossa "know instantly" where the arycentre is, yet yet the changes in angular momentum are of finite speed, though very fast. Of course this throwing off of material due to disequilibrium in the protostar doesn't just happen once. Both sol and barbie will be "tapping the brakes" as they collapse.

So lets say we we draw the barycentre's movement as a superposed wave created by the die away curves of both sol and barbie. At some point both sol and barbie become very diffuse "liquids." now they can actually spit out gobbets of matter. These protoplanets will move into areas of the ejected disks where the density of matter varies. Barbarossa can eject proto planets that are captured by sol, or are flung into escape orbits from barbarossa. So we have to add in another pair of superposed signals to the barycentre oscillation. If that wave looks like "bode's law" then all well and good, if not then it's an interesting problem. A little touch of the harmony of spheres, I hope that it turns out that our solar system is great for playing the blues.

61 * Barbarossa period = 15 * equinox precession;
Mayan period is "tropical" Barbarossa period;
also, "61" for pulsars; "HAARP", "chemtrails"


Using Newcomb's precession value, 5025.64" + 2.22"*T per Julian century, where T is centuries past 1900.0AD, I find a value for 2013.0AD, of 360*3600/(5025.64 + 2.22*1.13)*100 = 25774.9 Julian yr.

61*6339.500*(365.24219/365.25) / 25774.9(precession period)
= 15.0030

So, 61 times the Barbarossa period, equals nearly a whole number of Earth precession periods.

Fricke, A&A 54:363-366, 1977, p. 364, thought +1.10" per century, should be added to Newcomb's 5025.64", giving 5026.74".

So the precession rate 6339.5 tropical yr (i.e. one Barbarossa period) prior to Dec. 21, 2012AD, is

5026.74 - 2.22*(63.39-1.13) = 4888.52" / Julian cent -->
period = 26511.08 Julian yr = 26511.61 tropical yr of date

An astronomer contemplating the 6339.500 trop yr sidereal orbital period of Barbarossa, also could compute Barbarossa's "tropical" period, i.e. the period for Barbarossa to return to the same longitude vis-a-vis Earth's equinox of date (on average; i.e., neglecting Barbarossa's orbital inclination):

1/(1/6339.500 + 1/26511.61) = 5116.12 trop yr of date (5116.02 Julian yr), very close to Uranus' period * 61:

84.0139*365.24219/365.25 * 61 periods = 5124.74 Julian yr.

Using Walter Cruttenden's estimate (from collected 20th century published data; see Cruttenden, "Comparison of Precession Theories", Aug. 12, 2003, p. 11), 3.49"*T, instead of Newcomb's 2.22"*T, as the changing term of the precession constant, gives

5026.74 - 3.49*(63.39-1.13) = 4809.45"/Julian cent -->
period = 26946.93 Julian yr = 26947.46 trop yr of date, giving a Mayan period of

1/(1/6339.500 + 1/26947.46) = 5132.14 trop yr of date (5132.04 Julian yr)

If the true rate of change of the precession constant, were halfway between Newcomb's and Cruttenden's surveys of the literature, then an astronomer in 4328BC would find that the Mayan period, 5125yr, equals the average period for Barbarossa to advance one cycle, relative to Earth's (retrograde) axis precession at its 4328BC rate.

Current theory says (see Wikipedia) that Earth's precession rate varies sinusoidally with period 41,000 yr (Milankovitch period) and is near an ascending node of that sinusoid. So if Cruttenden's line fit, to 20th century data, is accurate, then the change vs. 6339 yr ago, should be only sin(theta)/theta = sin(2*pi*6339/41000) / (2*pi*6339/41000) = 85.00% as great as the linear extrapolation 3.49"*T, i.e. equivalent to a linear extrapolation using 2.97"*T. Interpolating the above, shows that this most accurate extrapolation that I can make, of Earth's precession period, suggests that a 4328BC astronomer would derive a Mayan period ( = tropical orbital period of Barbarossa) of 5125.48 Julian yr. The Mayan Long Count is

360*20*20*13/365.25 = 5125.26 Julian yr.

How likely is it, that it would be possible to contrive a Long Count of days, with no prime factor bigger than 13, that would be within 0.22 yr ( = "tropical" period of Barbarossa) or 0.52 yr ( = Uranus * 61) of a desired number? Of the 100,000 numbers 1,800,001 through 1,900,000 (the Mayan long count is 1,872,000 days) 84 are factorizable using no prime bigger than 13. So in this interval, such days occur on average 3.26 yr apart, and the average distance to the nearest such day, is only 0.8 yr. The nearest other such days, to the Mayan Long Count, are 900d before, and 780d after it.

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For pulsar PSR B1913+16, johnstonarchive.net (updated 2004) gives a rotation period of 59.02999792988 msec, and an orbital period of 7.751939106 hr (error bars not given). Assuming these are for the same epoch, I find

7.751939106*3600*61/(59.02999792988/1000) = 28838317.59

again close to (integer + half), though the last digit is, at best, barely significant. Preservation of the (integer + half) relation would require either:

1. smooth but synchronized orbital and spin changes; or
2. unsmooth (quantized or jerky) orbital or spin changes, which latter indeed have been observed for at least some pulsars.

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The current issue of "Atlantis Rising" reports that sinusoidal (caduceus-like) inscriptions in stone on Easter Island and elsewhere, have been hypothesized in a recent mainstream, refereed electrical engineering article, to be depictions of space plasmas.

Maybe the HAARP project in Alaska (officially said to be "aurora research" able to transmit 3.6 megawatts of high frequency radio power, or alternatively, extremely low frequency) and the "chemtrails" (wide persistent contrails said by some to be composed of, or seeded by, barium salts and titanium and aluminum microfibers) are extensive practice maneuvers, perfecting techniques to protect the northern hemisphere from whatever the "insider" scientists think will happen in 2012. It's characteristic of the U.S. government to hide the true story from the public, though usually not with evil intent.

On the other hand, many in the U.S. were dismayed by lack of mass "civil defense" (typically amounting mainly to a rusty "fallout shelter" sign on the county courthouse) during the Cold War. The Soviet Union, not noted for posh treatment of its citizens, did make a good effort at civil defense, with, for example, heavy steel doors on Moscow subway stations so the subways could become bomb/fallout shelters (now that the springs on these doors are broken or stolen, they slam into commuters, causing serious injury and giving new meaning to the custom of holding the door for a lady). It might be that HAARP really only will be used to protect an elite sheltering in Alaska, and that the surviving U.S. "chemtrail" fleet, will withdraw to Alaska, abandoning the promises made to various Senators.

There is the new "seed bunker" in the Norwegian arctic, and behavior ("bailouts", "Madoff", etc.) by the government/financial sector, resembling looting at Pompeii. Stealing like there's no tomorrow, because they think there isn't?

There is a tomorrow, because Egypt's Pyramid Texts tell of the "eye of Ra" (associated with "Hathor"; whose "horns" are now the constellation Crater?) and "cobra snake of Ra" (the constellation Hydra?) exterminating mankind hither and yon, though the Egyptians happened to live to tell about it. Solon, according to Plato's Critias, was warned, by Egyptian priests, of both fire and flood. Maybe "fire" boils so much water from places in the oceans, that extreme rains occur.

Vice President Gore, like me a Harvard graduate, seems to have been "neutralized" by a fictitious rape accusation and "trial in the newspapers". Whatever else Gore is, he's a Harvard man, not a rapist. Most likely, when Gore, like the rest of us, discovered the frauds surrounding the global warming theory, Gore looked to regroup and salvage his efforts, by revising his meteorological warning, to something closer to the mark. And someone didn't want that to happen.

Mercury, the Sun and "61"

In 1968, Smith (BA Smith, Science 162:1275-1277) determined from groundbased photography that the sidereal rotation period of Mercury is 58.663 +/- 0.021 day. In 1975, Klaasen (J. of Geophysical Res. 80:2415,2416) determined from Mariner 10 photos, that it is 58.661 +/- 0.017. Then in 1976 Klaasen said (Icarus 28:469-478) that it is 58.6461 +/- 0.005, hence very close to 2/3 of Mercury's orbital period, 87.969/1.5 = 58.646.

But is it really that close to 3:2? Or did Klaasen have to talk himself into it? Measurement errors assumed to be independent, often aren't independent. Errors might systematically cancel, giving greater accuracy than standard error bars say. Smith's groundbased photo collection, and Klaasen's Mariner 10 photo collection, give suspiciously similar means and putative error bars. Maybe the true value is 58.662 +/- 0.001.

Of the five subgroups of photos studied by Smith (Table 2, p. 1276), four place the exact 3:2 rotation period, almost a standard deviation below expected (bottom 1-sigma: 58.641 to 58.643, and sigma 0.010 or bigger). As if this didn't make the exact 3:2 period unlikely enough, one of the groups (the group with the most observations - seven) puts the 3:2 value, 2.3 sigma below expected.

Recent published estimates of various kinds of averages of the Sun's equatorial rotation period, differ from Carrington's value by about +/- 2% (e.g. 24.90 d in Javaraiah et al, Solar Physics 232:25-40, 2005, p. 37; and 26.16 d in Howard & Harvey, Solar Physics 12:23-51, 1970, p. 44). Carrington's rotation value, 25.380 d (RC Carrington, "Observations of the Spots on the Sun", 1863, p. 221; on microfilm at Iowa State Univ.) is calculated not for the equator, but for Carrington's median (of 1414 sunspots observed over eight years) observed sunspot latitude of about +/- 14 deg. My simple weighted mean of Carrington's data (p. 224) gives 25.616 d, but Carrington went further and, essentially, found the median absolute sunspot latitude, then interpolated the value of the Sun's rotation period at that latitude. So I find

58.662*61/25.380 = 140.992

It is well known that Mercury also shows almost the same face to Earth, or opposite face to Venus, when it passes them:

1/87.969-1/365.25636 = 1/(2*57.939)
1/87.969-1/224.70069 = 1/(2.5*57.826)

So, other effects might cause Mercury's rotation period to fail to be in exact 3:2 mean resonance with its orbit.

Gobekli Tepe & Stonehenge: eternal recurrence

According to Wikipedia, the excavated ring of monoliths at Gobekli Tepe (50-foot high manmade "Belly Hill") in Turkey, was erected c. 11,000 yr BP ("Before Present") and then was intentionally buried c. 10,000 yr BP. (U. S. News & World Report's current Special Edition, "Mysteries of History", confirms the 11,000 BP figure, and mentions there are at least 16 other rings of monoliths buried nearby.) "The first structures at Goebekli Tepe were built as early as 10,000 B.C. [=12,000 BP], ..." (Archaeology Dec. 2008). So, there was major construction at Gobekli from c. 12000 to c. 10000 BP.

The sizes of the stones and diameters of the rings, at Gobekli and Stonehenge, are comparable. Both have good astronomical views. Stonehenge is in the big "Salisbury plain" with good views of the horizons; Gobekli is "1000 ft above the valley...[a] summit...above the surrounding landscape" (USNews&WR). According to www.stonehenge.co.uk , construction activity at Stonehenge was from c. 5100 BP to c. 3500 BP. Thus the beginning of Gobekli was "as early as" 12000-5100 = ~6900 yr before the beginning of Stonehenge, and the burial of Gobekli 10000-3500 = ~6500 yr before the end of major construction activity at Stonehenge.

The first major construction at Stonehenge ("Stonehenge I", apparently the erection of large timbers in chalk pit postholes) was c. 3100 BC, concurrent with the beginning of Egypt's First Dynasty, c. 3110 BC, and with the beginning of the Mayan Long Count, 3114 BC. One "Barbarossa period" earlier, would be 3114+6339 = 9453BC = ~11500 BP, and this seems to be about when major construction started at Gobekli.

Also, a date sometimes given for the completion of the Great Pyramid (or rather, the end of the reign of Khufu), c. 2566BC, suggests 4576+6339 = 10915 BP = ~11000 BP, for the end of the main construction at Gobekli, according to my cyclical theory.

Gobekli Tepe: oldest known star map, shows my Planet X "Barbarossa"

The Vulture Stone at Gobekli Tepe (upper left corner, p. 18, 2010 U. S. News and World Report Special Collector's Edition, "Mysteries of History") is a star map and calendar. It depicts a conjunction of my Planet X, Barbarossa (discovered by me on sky surveys, Feb. 2007) with the star Gamma Corvi, as they appeared in the sky at approximately 2012.97 AD - 2*6339.36 + 143.91 = 10,522.84 BC.

The three vulture heads have simple holes forming a triangle congruent to the triangle (clockwise from the biggest head) Gamma Corvi, Theta Crateris, Gamma Crateris. The congruence becomes more accurate, if correction is made for the oblique projection of the photo. The proper motions of the stars are too small to destroy the congruence in 11,000 or 13,000 years. The hole with a circle around it, rightward and slightly above the Gamma Corvi hole, is Barbarossa. The sizes of the vulture heads correspond to the visual magnitudes of the stars. The three stars are blue (Spectral Type or white (Type A). The Theta Crateris hole is lower, than normal position on a vulture's head.

A cataclysmic event likely would be symbolized by vulture heads. Today, and for Ptolemy, the constellation Corvus symbolizes a crow, but the vulture might have been altered to another carrion-eating bird, the magpie or crow. On the stone, the vulture containing Gamma Corvi, has a prominent wing; in Arabic, Gamma Corvi is called Gienah, "the raven's wing" (Jim Kaler, www.stars.astro.illinois.edu ).

The stone denotes the arithmetic unit ruggedly, as a triangle formed from nested Vs. The eleven small squares between the two top vulture heads, each denote five units, because under their row, are five of the triangles formed from nested Vs. The three big squares (rectangles) above, each denote fifteen small squares, because under their row, are fifteen of the triangles. The arches on the big squares symbolize handles, as if the big squares are boxes for carrying little squares. There must have been a missing top stone with a row of very big squares: there must have been more than one (one, would have been redundant) and fewer than three of these hypothetical very big squares (three squares, bigger than those that actually appear on the stone we have, would need a hypothetical bigger size stone on top). So, there is a missing top row of two very big squares, each denoting ten big squares, because by looking closely, I see that there are ten (not eight) triangles across the whole top edge of the stone. These triangles at the top edge, resemble the other rows of triangles.

The whole structure of triangles and squares covers most of the surface of the stone. At the bottom of this structure, is a picture of a gibbous Luna, resembling a U.S. football. The number above this Luna, is expressed in the maker's variable-base arithmetic as

5*11 + 5*15*3 + 5*15*10*2 = 1780

1780 synodic months (mean) = 1780*29.5306 days = 143.91 Julian yr

In my previous messages to Dr. Van Flandern's messageboard, I have marshalled evidence that a cataclysmic event occurs every 6339.500 tropical year (6339.36 Julian yr). The first such evidence that I found, was the sidereal orbital period, 6340 +/- 7 Julian yr, estimated from online sky surveys, of my discovery Barbarossa ( = Percival Lowell's actual Planet X). Barbarossa is always remote, but its period relates to the period of an unknown physical Solar System process. I refined the period, by consideration of Solar System resonances, Egyptian "Sothic" dates, and the Mayan Long Count.

My estimate of Barbarossa's orbit, shows that Barbarossa is in the constellation Crater at the end of the Mayan Long Count. At a time 1780 synodic months later, Barbarossa, on a map using ecliptic coordinates, is west and slightly north of Gamma Corvi. My estimate is, that the distance from Gamma Corvi is greater than shown on the Gobekli Vulture stone, but the directions agree. The orientation of the vultures' heads triangle, also agrees with ecliptic coordinates. So, the Vulture Stone shows where Barbarossa was, two periods before 2012.97 AD + 143.91 = 2156.88 AD.