Requiem for Relativity

Bright Stars over the Pyramids: Atlantean Knowledge (Part
by Joseph C. Keller, M. D., September 11, 2009


Other arctan(4/pi) pyramids. Besides Khufu's, two small nearby "queen" pyramids, G1a & G1b, have slope about 51deg50'. The earlier Huni/Snefru pyramid at Meidum, already in ancient times robbed to its core, might have had this slope angle, too.

Later pyramids, of Neweserre at Abusir, and of Djedkare at South Saqqara, have slopes estimated at 51deg50' and ~52deg, resp. Two queen pyramids of this vintage, one intact, 17m tall, at Saqqara, and one ruined to 4m at Abusir, also have slope ~52deg.


The 43deg22' pyramids. Wikipedia gives the latitude of the Altamira caves as 43deg22'57"N, and the Cosquer caves as 43deg12'10"N. (The three other famous paleolithic painting caves are Lascaux, Chauvet & Pech-Merle.) Snefru's Red Pyramid, and the upper stage of Snefru's Bent Pyramid, both are said to have slope 43deg22' (though one source gives a range of about 42.5-44deg, for the Red Pyramid; I suppose the slope of the upper stage of the Bent Pyramid is about as vague).

Bright Stars over the Pyramids: Atlantean Knowledge (Part 9)
by Joseph C. Keller, M. D., September 16, 2009


Improvement of Janssen's theory. Bert Janssen (published online, approx. 2009) noted that the latitude of the Silbury neolithic mound; the slope of Khufu's pyramid; and the slope at Giza, of the surface geodesic (i.e., great circle) from Giza to Silbury, all are about equal. My spherical trigonometry shows that, assuming a spherical Earth, the differences between these quantities are about a degree or more. Correction for Earth's oblateness improves the fit only a little.

The fit is much better if instead of a geodesic on Earth's surface, one considers a geodesic (i.e., straight line) in space through the Earth between Silbury and Giza. Unlike the surface geodesic, the spatial geodesic can be found without calculus, for a spheroidal Earth. The geocentric colatitude of Silbury (i.e., the angle pole-Earthcenter-Silbury) equals the spatial angle pole-Giza-Silbury.

With a few further refinements and minor modifications of Janssen's theory, I find agreement between theory and observation, as good as can be expected from the accuracy of known data. Specifically, I substitute Stonehenge for Silbury and the slope of Menkaure's pyramid (its granite courses, according to Petrie)(and Menkaure's slightly different coordinates) for the slope and coordinates of Khufu's. I approximate Earth as an oblate spheroid with major::minor axes = 298::297.

I assume true north then was 5'40" west of our true north. This is Petrie's estimate of the Khufu pyramid's alignment. Petrie noted that this implied rate of pole shift, isn't much bigger than the astronomically measured rate c. 1800-1900AD; he said a major change in ocean current, would cause such a pole shift according to conservation of angular momentum (Petrie, sec. 94).

I assume the latitude of Khufu's pyramid then was exactly 30.0N, though some think the 1'15" discrepancy from exactly 30N, merely was to avoid sand north of the Giza plateau. Together with the 5'40"W polar alignment, the 1'15" latitude correction determines the pole exactly.


Improved Janssen theory, predicted vs. observed. Using the presumed ancient pole, the geographic latitude of Stonehenge is 0.066deg greater, than Petrie's estimate of the slope of the granite courses of Menkaure's pyramid. Petrie's 50% confidence interval here was +/- 0.022deg, so 0.066deg = 2.0 standard deviations.

The geographic colatitude of Stonehenge differs only 0.0011deg from the angle pole-Menkaure-Stonehenge. The biggest error in the data, is Petrie's +/- .0028deg (50% confidence) for the pole alignment (Petrie, sec. 93). Not only the slopes, but also the coordinates, of Khafre or Khufu, fit significantly worse: the angle pole-Khufu-Stonehenge is ~ 0.01deg greater.


British correlations of Khufu & Khafre. If latitude 30.0N were a requirement (my earlier paper on the Egyptian calendar gives another reason it might have been: namely the heliacal risings of Arcturus and Canopus on the summer solstice of 4329BC, at 30N) then there would have been only one degree of freedom remaining, in the choice of location for the Giza pyramids, assuming that their relationships to each other already were determined by the star alignments discussed in the previous Parts of this paper. The choice of longitude for the Giza pyramids, has been noted as somewhat abnormal and mysterious by other authors. This choice of longitude, would allow exact alignment with some pre-existing monument, such as Stonehenge.

Menkaure's pyramid (last but not least) aligns with Sirius on the meridian (see previous Parts of this paper) when Arcturus, or Barbarossa's 2012AD sidereal location in the constellation Crater, align with Khufu or with Khafre, resp. So, Menkaure would be the obvious choice to align with Stonehenge.

I found henges aligning with Khafre or Khufu, as Menkaure does with Stonehenge, but for Khafre or Khufu the alignment isn't much better than chance, considering the many British henges from which to choose. RN Savory plots nine henges in Wales, four of them in NW Wales. The southernmost of the four henges in NW Wales, has modern geographic latitude 53.171N, presumed ancient latitude 53.235, and henge-Khafre-pole angle (for straight line segments) = 90 - 53.383, vs. Khafre's slope, 53.167.

The "Giant's Stone" in Gloucester (Witts, "Archaeological Handbook of Gloucester") is the main remnant of a dismantled barrow which included hundreds of mysterious depressions. According to Danny Sullivan, a four mile long "ley line" (alignment of megaliths) starts at the Giant's Stone. Its modern latitude is 51.753N, presumed ancient latitude 51.815, and henge-Khufu-pole angle = 90 - 52.000, vs. Khufu's slope, 51.844.

Yesterday, I made this calculation with the planetary masses and semimajor axes given in the 2007 World Almanac; I neglected the masses of their moons. Today, I repeated it with the more precise masses and axes currently given online in Wikipedia; also, I included the masses of the known moons, according to the tables in solarviews.com. The results were about the same.

I found the planet's orbital period, in Earth sidereal years, by taking the semimajor axis to the 1.5 power. I adjusted for the effect of Earth and Mars, by adding their masses to the Sun's. I converted sidereal to Julian years.

Crouching tiger. Barbarossa's orbital period reveals itself in a resonance with Jupiter. From the World Almanac, or the more precise Wikipedia, semimajor axes, exactly 534 Jupiter orbits require 6339, or 6339.974yr, resp. My estimate of Barbarossa's orbital period, from the sky surveys, was 6340.0yr. My best estimate from the Egyptian and Mayan calendars (winter solstice 2012AD minus summer solstice 4329BC) is 6340.5yr. Brauer's lake varve study, combined with the calendars, suggests about 6342yr.

Hidden dragon. Mathematically, Jupiter + Saturn, or Jupiter + Saturn + Uranus, or Jupiter + Saturn + Uranus + Neptune, can be combined into one planet, with the sums, of the masses and orbital energies (potential + kinetic) of the constituent planets. The semimajor axis of the combined planet, is the reciprocal of the mass-weighted mean of 1/a, where "a" denotes a planet's semimajor axis. That is, it is the mass-weighted harmonic mean of the semimajor axes.

The World Almanac data (neglecting the moon masses) confirmed the results of the Wikipedia data, to within less than a year, the expected accuracy of the World Almanac results. The results from the more precise Wikipedia data were:

J+S: exactly 452 cycles in 6340.900yr
J+S+U: exactly 436 cycles in 6340.632yr
J+S+U+N: exactly 416 cycles in 6341.703yr

The mean of the four results (J, J+S, J+S+U, J+S+U+N) is 6340.802yr +/- SEM 0.358.

In my preceding post, I show that the various stages of outer solar system differentiation (proto - Jupiter, proto - Jupiter+Saturn, proto - Jupiter+Saturn+Uranus, & proto Jupiter+Saturn+Uranus+Neptune) all were in orbital resonance (534::1, 452::1, 436::1, or 416::1) with Barbarossa. The significance of this resonance depends on Barbarossa's actual exact period. The period 6430.0yr which I found from the four sky survey positions, gives cycles exact to p = 0.00109% overall. The period 6340.5yr suggested by ancient calendars, gives cycles exact to p = 0.00145%. The period 6340.802yr, the least-squares best fit to the phases of the cycles, gives p = 0.00054%.

Such resonance also occurs for the inner solar system, with Jupiter or proto - Jupiter+Saturn in place of Barbarossa. Calculating as in my preceding post, I find that the period ratio of the proto - Mercury+Venus+Earth+Luna+Mars, to the proto - Jupiter+Saturn, is 1::18.03196. The period ratio of the proto - Venus+Earth+Luna (I assume Mercury and Mars separated from Earth before Venus did) to Jupiter, is 1::15.03652. Taking it as given, that Mercury and Mars separated from Earth before, and Venus after, Saturn separated from Jupiter, the overall significance of these two resonances is p = 0.47%.

The current Wikipedia mass estimate for the asteroid belt, is 0.00055 Earthmass, +/- 10%. Some guess, that the asteroid belt originally had ~1 Earthmass. Be this as it may, inclusion, with Earth, of 0.004 Earthmass of asteroids (perhaps seven times the present mass) at Ceres' semimajor axis, 2.77AU, changes the ratios of the preceding paragraph, to 1::17.9942 & 1::15.0025, resp.

Would anyone like to use my registration to go to Walter Cruttenden's "Conference on Precession and Ancient Knowledge (CPAK)", October 10, 2009 (a one day event, a week from this Saturday) at the Univ. of California-Irvine? I've paid the $179 registration but can't go. You would have one duty for me there: to check that my poster stays up (I'll lend you a spare, so you can replace my poster if you notice it gets ripped off).

From the UCLA (U. of California - Los Angeles) website, regarding upcoming (December 2009) Astrophysical Journal article:

"Two terrestrial planets orbiting a mature sun-like star some 300 light-years from Earth recently suffered a violent collision, astronomers at UCLA, Tennessee State University and the California Institute of Technology will report in a December issue of the Astrophysical Journal...

"...whisked away. Thus, the dust-forming collision near BD+20 307 must have taken place rather recently, probably within the past few hundred thousand years and perhaps much more recently, the astronomers said.

" 'This poses two very interesting questions,' Fekel said. 'How do planetary orbits become destabilized in such an old, mature system, and could such a collision happen in our own solar system?'

" 'The stability of planetary orbits in our own solar system has been considered for nearly two decades by astronomer Jacques Laskar in France and, more recently, by Konstantin Batygin and Greg Laughlin in the U.S.A.,' Henry noted. 'Their computer models predict planetary motions into the distant future and they find a small probability for collisions of Mercury with Earth or Venus sometime in the next billion years or more.' "


Comment by Joseph C. Keller:

This isn't a dust-forming planetary collision. If this is a sun-like star, then the planets would be c. 5 billion yr old. If dust dissipation implies that the collision happened within the last 500 thousand yr, then ~ 10,000 sunlike stars with planets, would need to be studied, to find one like this. Not that many have been well studied.

Hardly that many even exist, within 300 lt yr. The apparent Visual magnitude of a sunlike star at 300 lt yr is approx. +4.83 (Sun's absolute magnitude) + 5*log(base 10)(300/(10pc * 3.26) = +9.65. The Henry Draper catalog (online VizieR search) lists only 33,000 stars in the entire sky, of this apparent magnitude or brighter, with spectral type "G" or "Gx" where x = 0,1,2,...,9 (of type G, only G, G0, and G5 appear in the Henry Draper catalog).

Some of those 33,000, lack planets. Some resemble our Sun, having planets but with small probability of late collision (according to the above study cited by Dr. Henry). So, for this finding to be statistically likely anywhere in the sky, many sunlike stars must have solar systems different from ours, specifically in that late planetary collisions are likely for them.

My alternative explanation is that this dust is due to a yet unknown recurring physical disturbance. I've presented evidence, on Dr. Van Flandern's messageboard, that such a disturbance recurs in our own solar system every 6340yr. In some solar systems, the disturbance produces too much dust to be swept away during the calm intervals.