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:

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):

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.

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.

*********

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

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.

*********

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.

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:

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 B) 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.

Hi Dr Joe, Why not get better pictures of the map? Why use a pic in US News as a source when the real data still is at the site?

Hi Jim,

I agree, it is essential. A problem with pictures on the web, is that browsers might introduce additional distortions. If I use a magazine photo, at least others can be sure they're looking at exactly the same photo. Do you know of a source for hardcopy pictures?

Further results regarding the Gobekli Tepe star map

With correction for stellar proper motion (Hipparcos catalog) to the presumed date of 2012.97 AD - 2*6339.36 (Julian yr) + 143.91 = 2000.0 AD - 12551.84, and correction of the ecliptic to that date (1990 Astronomical Almanac formula), and adequate approximations giving the local angle between the ecliptic latitude lines and the declination lines, I find that the line from Gamma Corvi to Gamma Crateris should be sloped downward 32 deg, if the horizontal at the Gobekli Tepe Vulture Stone, is the ecliptic latitude line of date. (Ptolemy and other ancient astronomers usually used ecliptic rather than celestial coordinates; ecliptic coords. would be preferred by monument-making astronomers with knowledge of precession.) When I correct the US News&WR photo (see previous post) for an apparent 22 degree rotation of the right side forward (assuming an ordinary 35mm camera with a 50mm focal length and 37mm frame height) I find that about 5% must be added to horizontal dimensions. With this correction, the actual line on the Vulture Stone, from Gamma Corvi to Gamma Crateris, slopes downward 29deg (vs. 32deg predicted).

With the above methods, the line from Gamma Corvi to Theta Crateris, should theoretically slope upward 9deg; on the Vulture Stone, it actually slopes upward about 16deg. The ratios of the lengths,

theoretically are 1::1.019::0.675, and on the Vulture Stone (with the above correction for perspective) are 1::1.14::0.83. The unusual placement of the "eye" of the upper righthand vulture (Theta Crateris) suggests uncertainty about the position of that star. Theta Crateris lies across the path of Barbarossa; it already has unusually strong "interstellar" absorption lines, and Barbarossa's dimming of USNO-B catalog stars mainly occurs retrograde to Barbarossa's position. So, Theta Crateris might have been much dimmed, and confused with other stars.

My best estimate of Barbarossa's heliocentric position (really, barycentric including only the other planets with the Sun, which here is practically the same thing as heliocentric) 143.91 yr past Dec. 21, 2012 AD (which also should correspond to Barbarossa's position on the Vulture Stone, if I guessed correctly about the date, and if there is no precession or other disturbance of Barbarossa's orbit) is, in J2000.0 celestial coords, RA 184.396 Decl -15.794, distance 254.8 AU. Including the correction for Earth parallax at this presumed date of the Vulture Stone, Barbarossa should theoretically have been seen 1.973deg away from Gamma Corvi, at "ecliptic position angle" (i.e., azimuth counting clockwise from ecliptic north) 90 - 50.12 = 39.88deg. As I measure on the photo, Barbarossa actually is, with perspective correction, 0.67deg away, at ecliptic position angle 65deg. The circle around Barbarossa, on the Vulture Stone, suggests a nebula.

Dr Joe, The site is well stocked with science guys according to the Wiki. They must have a web site but it might be only in German because the dig is funded by a German university.

Dr Joe, The site is well stocked with science guys according to the Wiki. They must have a web site but it might be only in German because the dig is funded by a German university.

Hi Jim,

Two days ago I nonconfrontationally emailed four German Ph.D.'s associated with the Gobekli Tepe archaeological site. None of the emails bounced, but there has been no response. It's too easy for them to tell themselves, perhaps unconsciously, "Just a lone nut; I can get away with putting my guild's turf issues, before the taxpaying public's right to know."

My experience is, that professional academics never respond to anyone "not in the guild" regarding anything that involves two-way collaboration. One department chairman in astronomy, at a publicly funded U. S. university, even told me in an email, that he makes it a policy never to discuss research with anyone who isn't in the astronomy guild, i.e., a Ph.D., a doctoral student, etc.

Your taxes pay for it, but science is a "closed shop", and the "Freedom of Information Act" is a "dead letter". It seems that this is going to have tragic consequences for mankind.

Maybe you or someone else who reads this, could quietly email a few of them yourselves, and ask them to send me (or you) an accurate picture of the Gobekli Tepe "Vulture Stone" suitable for scientific study? If more than one person specifically expresses interest, then they can't say it's just a "lone nut".

Hi Joe, have you read this paper yet? I haven't but that stuff from my last post suggests that the angular velocity of the universe is about a third of the speed of light at 1.4E 26 metres. To get it to spin slower means an even larger big bang universe with G becoming vanishingly small.

"Models of a rotating universe have been studied widely since the work of Gdel, who showed an example that is consistent with general relativity. By now, the possibility of a rotating universe has been discussed comprehensively in the framework of some types of Bianchi's models, such as Type V, VII, and IX and different approaches have been proposed to constrain the rotation. Recent discoveries of some non-Gaussian properties of the Cosmic Microwave Background Anisotropies (CMBA), such as the suppression of the quadrupole and the alignment of some multipoles draw attention to some Bianchi models with rotation. However, cosmological data, such as those of the CMBA, strongly prefer a homogeneous and isotropic model. Therefore, it is of interest to discuss the rotation of the universe as a perturbation of the Robertson-Walker metric, to constrain the rotating speed by cosmological data and to discuss whether it could be the origin of the non-Gaussian properties of the CMBA mentioned above. Here, we derive the general form of the metric (up to second-order perturbations) which is compatible with the rotation perturbation in a flat #923;-CDM universe. By comparing the second-order Sachs-Wolfe effect due to rotation with the CMBA data, we constrain the angular speed of the rotation to be less than 109 rad yr1 at the last scattering surface. This provides the first constraint on the shear-free rotation of a #923;CDM universe."

After a quick read through of that paper, to get the angular velocities they're on about G has to be smaller, in the region of 1E-17, that means that the radius of the universe has to be larger. Now somewhere in this thread I worked out that the universe would be about eight thousand times larger than the 13.5 billion light year estimate. Trouble is I can't remember how I got that, all I can remember was that it had something to do with Wheeler and the idea that the universe "knows" in terms of the Compton wavelength.

6333 Gandharvas: Vedic knowledge of Barbarossa's period

Review: the disappearing dots I found on four online sky surveys, are consistent with a planet X, Barbarossa, with sidereal period 6340 +/- 7 yr. The "Sothic" (really, Arcturian) date of Amenhotep I points to an Egyptian calendar starting at the summer solstice 4328BC, 6339.5 tropical year before the end of the Mayan Long Count. The Mayan Long Count itself, 5125 yr, is the tropical period (Earth tropic) of Barbarossa, using the best available estimate of Earth's precession rate 6340 yr ago.

"The Gandharvas...observe all forms (or phases) of the Moon. ...(the Moon) lived among the Gandharvas...

"Their number is given variously as 27 and 6333.

"...Gayatri meter of the Rg Veda is an 8/3 meter. The Rg Veda declares that the Gayatri meter has different functions.

"...in the Rg Veda, the Gandharva is called Visvavasu or the universal Vasu, the term Vasu being associated with the number eight. It is specifically stated that the Vasus are associated with the Gayatri meter."

- B. G. Sidharth, "Precession of the Equinoxes and Calibration of Astronomical Epochs", pp. 5,6; arXiv.org (physics), Jan. 14, 2010

Sidharth notes that 27 is the number of whole days in a sidereal month. So, 27 Gandharvas symbolize the (shifting, because 27.3217 > 27) nightly stations of the Moon during the sidereal month. I think that likewise, 6333 (originally 6339 ? ) Gandharvas symbolize the yearly stations of Barbarossa during Barbarossa's sidereal orbit (6339.5 Earth tropical yr = 6339.254 Earth sidereal yr assuming the modern rate of precession). Sidharth also notes that 6333 synodic months = 6333*29.5306d = 512.0165 sidereal year = 8.00009^3 sidereal yr. If 8^3 is the "universal 8", then a "universal 8" of years, is 6333 synodic months. I think that originally however, 6333 signified years, not synodic months. The 6333 years of Barbarossa's sidereal orbit were analogous to the 27 days of the Moon's.

"The 'heavenly Gandharva' of the Veda was a deity who knew and revealed the secrets of heaven...generally had their dwelling in the sky...regulate the asterisms..."

- John Dowson, "Classical Dictionary of Hindu Mythology"

Hi Joe, I screwed up a bit on the spin rate of the universe, mixing up my degrees and radians per year. With a radius of 1.4E 26 metres, the velocity will be about a third of the speed of light, well the speed of light divided by pi. That gives me something in the region of 2.2E-11 radians per year.

Another reason I went askew there was I was after the radius where the universe is effectively not spinning at all.

Barbarossa period a fundamental physical constant; Hubble parameter related to Barbarossa period and acceleration due to moon gravity

The Hubble parameter's apparent value really might be peculiar to our solar system. Be that as it may, the root-mean-square speed of a proton in a given direction is sqrt(k*T/m) where k is Boltzmann's constant, we let T = 2.725 Kelvin (the current estimate of the "Cosmic" Microwave Background temperature is 2.725 +/- 0.001 K), and m is the mass of the proton. With a deceleration equal to H * c, where H is Hubble's parameter and c is the speed of light, the Barbarossa period, 6339.36 Julian yr, corresponds to the deceleration time, given a Hubble parameter of 77.16 km/s/Mpc. The current value of the Hubble parameter from the website, hubblesite.org, is 74.2 +/- 3.6 km/s/Mpc.

(Amendment August 31:

Fixsen, Astrophysical Journal 707:916+, recently combined all available data, and found for the CMB temperature, 2.72548 +/- 0.00057 K. By the above formula, this gives a Hubble parameter of 77.1729 km/s/Mpc; the error in this Hubble parameter prediction, is almost all due to the CMB temperature uncertainty, and amounts to about 1 part in 10,000.)

Posted here Aug. 16, 2010 because server would not accept new post:

Hubble parameter relationship to Luna's acceleration at Earth, Io's acceleration at Jupiter

I use the following values:

Luna mass: 7.34959736*10^25 gm (nssdc.gsfc.nasa.gov) Io mass: 8.9316*10^25 gm (solarsystem.nasa.gov) Luna semimajor axis: 238855 miles = 384400 km (2007 World Almanac) Io semimajor axis: 421700 km (Wikipedia) Luna eccentricity: 0.0549 (2007 World Almanac) Jupiter equatorial radius: 71492 km (Wikipedia) Jupiter oblateness 1-b/a: 0.06487 (Wikipedia) Gravitational constant: 6.6726/10^8 cm/s^2 (IAU, per Wikipedia)

In finding the acceleration at the center of Jupiter, Io's eccentricity is negligible, but Luna's eccentricity must be considered because it causes the time-average acceleration to be multiplied by 1.00151. In finding the average absolute value of the acceleration due to Luna on Earth's surface, the effects of Earth's diameter and oblateness are negligible, but Jupiter's diameter and oblateness cause the surface-average absolute acceleration to be multiplied by 1.00199. With these small corrections, the acclerations are:

due to Luna: 0.00332398 cm/s^2 due to Io: 0.003358 cm/s^2

Let's suppose that the Hubble parameter satisfies:

A*(fine structure const.)^2 / sqrt(6) = H*c

Then H (from Io) = 75.14 km/s/Mpc and H (from Luna) = 74.382 km/s/Mpc

These are close to the hubblesite.org value of 74.2 +/- 3.6.

The factor sqrt(6) comes from common Poisson ratios in solid mechanics. The Poisson ratio of glass and of phenolic laminates, is 0.25 (Fung & Tong, Classical & Computational Solid Mechanics, Table 6.2:1, p. 142), and "...Poisson advanced arguments...that the value of [the Poisson ratio, for most materials] should be 1/4." (Fung & Tong, p. 143). The Poisson ratio of hot rolled copper is 0.33, and other metals range from 0.29 to 0.35 (Fung & Tong, Table 6.2:1). If the ether (or "space" if the taboo word "ether" is to be avoided) contains elements resembling a perfect glass (Poisson ratio 1/4, volume decrease 1 - 2/4 = 1/2) or a perfect metal (Poisson ratio 1/3, volume decrease 1 - 2/3 = 1/3) with equal probability, then the overall effect could be the geometric mean of the two, 1/sqrt(6).

(Amendment Aug. 31:

Since Luna's time average absolute value acceleration at Earth's center, when multiplied by (fine structure const.)^2/sqrt(6), agrees with the recent hubblesite.org value for the Hubble parameter, let's find the time average absolute value (not root-mean-square) acceleration at Jupiter's center due to the Galilean moons; the other moons are negligible. For Io I use the values above together with the Wikipedia eccentricity 0.0041. For Europa, Ganymede & Callisto, I use the Wikipedia masses, semimajor axes, and eccentricities 4.8*10^25 g, 671100 km, 0.0094; 14.8*10^25, 1070400 km, 0.0011; 10.8*10^25 g, 1882700 km, 0.0074. One of the three integrations required, to find the time average, may be found from the (rapidly convergent, in this case) power series for a complete elliptic integral of Legendre's second kind. The other two integrations are by a two-dimensional trapezoidal rule. The time-average acceleration at Jupiter's center, corresponds, as above, to a Hubble parameter of 77.172 km/s/Mpc; the error, due to the implied uncertainty in Europa's mass, is about 1 part in 7500, and due to the uncertainty in the Gravitational constant, 1 part in 20,000. Summarizing:

Hubble parameter inferred from fundamental physical constants, CMB temperature, and Barbarossa period:

77.173 km/s/Mpc, 1/10,000 error due to CMB temp uncertainty

Hubble parameter inferred from Jovian moons' time-average absolute value of acceleration at planet center:

77.172 km/s/Mpc, 1/7000 error due to Europa mass and G uncertainty

and these two numbers differ only 1 part in 80,000. )

Addendum Aug. 17, 2010:

The modern fashion is not to publish epochs of observations, and not to share data with amateurs, but in old astronomical literature, epochs usually are published. Recently the Iowa State Univ. library moved most of the old astronomy journals to the storage building, where, because I'm not currently enrolled, I don't have access to them. Some old articles are available online but they are harder to browse than in bound hardcopy form. Anyway, I did find data on Hubble's parameter, that somewhat confirm that the measured value of the parameter, corrected for Earth's orbital motion, is proportional to Luna's gravity.

My Source #1 is Humason, Mayall & Sandage, Astronomical Journal 61:97-162, Table V, pp. 119-127. They measured the redshift of 300 galaxies, all with the same 36 inch prime focus reflector at Lick Observatory. The article doesn't explicitly say that the redshifts in Table V, col. 13, are corrected for Earth's orbital motion (regarding this detail, the reader is referred to another article which isn't available to me) but Zwicky's catalog copies the redshift values (e.g. for NGC 2366, NGC 4618, NGC 4753) as if they were corrected for Earth's orbital motion. The article is explicit that the redshifts in this column are not corrected for any solar apex motion, galactic motion, etc.

My source #2 is deVaucouleurs & deVaucoleurs, AJ 72:730-737, Table III, pp. 733-736. They measured the redshift of 113 galaxies, all with the same 82 inch prime focus reflector at McDonald Observatory. The article explicitly says that the redshifts in Table V, col. 14, are corrected for Earth's orbital motion. This column is explicitly not corrected for any galactic motion, solar apex motion, etc.

Only six galaxies are identified in both Tables: NGC 1058, 1232, 2366, 4618, 4753, 7640. Zwicky's catalog lists five of these; the photographic magnitudes given, range from +11.5 to +11.8.

Source #1 gives +80 km/s for NGC 1058, vs. +521 km/s for Source #2 and +518 km/s for Wikipedia. Zwicky apparently emended Source #1 to +480 km/s, but this emendation is doubtful because Source #1 itself, used the +80 km/s value to determine the galactic motion-corrected value. So, +80 is not a simple misprint.

Source #2 gives +847 km/s for NGC 4753, vs. the modern ne.jp value, +1724. Source #1 gives +1364 ( +/- 12, an unusually narrow error bar) and Zwicky used this value.

Four believable galactic observations remain. As a proxy for the reciprocal of the lunar distance, I use the lunar parallax (in arcminutes) listed in the [British] Nautical Almanac. Source #1 gives the epoch, presumably the midpoint of the plate exposure, to 0.1 day GMT. The exposures were several hours, therefore the midpoint had to be near local midnight, and indeed all epoch dates were x.3, x.4 or x.5 GMT, as expected; I interpolated the lunar parallax linearly from the daily tables. Source #2 gives the epoch only to 1 day GMT. The mean fractional day for Source #1 was x.37; the longitude difference would imply x.33 for McDonald Observatory. Instead, I used x.5 for Source #2, but 0.17 day never amounts to more than 0.1 arcminute change in lunar parallax.

NGC 1232/1820+-67/1723+-42/54.3/54.5 NGC 2366/194+-36/145+-18/56.3/56.4 NGC 4618/484+-47/562+-22/54.3/58.7 NGC 7640/423+-83/388+-28/61.1/56.2

Not only are the above redshifts given by Sources #1 & #2 believably close to each other; the errors given by Source #1 are roughly twice the errors given by Source #2, as expected from their telescope apertures.

For each of the four galaxies, I find the sum of all the likelihoods, for all the possible true redshift velocities, of giving the actual result (Sources #1 & #2, assuming normal error curve). Then I multiply the four sums, to find the likelihood of getting all four results. The likelihood ratio is 1.95::1 in favor of the hypothesis that the redshift is proportional to lunar acceleration, vs. the hypothesis that the redshift is constant.

Hi Joe, suppose we take that sqrt(kT/m) and rewrite it as kT = mc^2*(((1-sqrt(1-v^2/c^2))

Then interesting stuff happens when v^2 approaches c^2 and v^2 is vanishingly small. For instance it would man that an isolated hydrogen atom could ingest its electron by k capture and destroy itself as a hard gamma ray explosion.

But let's have v^2 go above c^2 Then we'll have a complex solution to the equation. A proton would have a positive temperature and a "i," or "j" if you prefer, temperature. If we go this route, just for the maths, then we have to deal with negative mass and energy. Or we could go with phase change. In which case we are talking about ordinary positive mass particles but in complex space which has a negative refractive index past light speed. That's an aether but it's not a static aether, it's a complex viscoelastic. I think there might be profit in considering the permeability and permittivity of the vacuum as being analogous to stress and strain.

Thinking about that equation a bit more sqrt(kT/m) We've got T = mc^2/k but I thik we need to multiply that by 1-sqrt(1-v^2/c^2)

We want rid of that root sign so square kT/m and have (kT/m)2 = c^4 C^4 = 8.0784215E 33 and it's reciprocal is going to be 1.2378655E-34 pretty close to barh.

Hi Joe, you wouldn't happen to know of an "idiots guide to Lie algebra" would you? The only stuff I could find just dives straight in at the deep end. I even went and joined Garrett Lisi's face book page but it's just a fan club. Pretty unhealthy actually, as I think that boat loads of people, without the foggiest idea what he's talking about, want to turn him into the next Einstein.