Requiem for Relativity

Maurol, I don't have any fith in the current state of art reguarding astrophysics and stellar evolution so I'm very interested in proof that any of the major ideas you guys are kicking around is true or false. At this time some people say Sirius was red and now its white and other people say it was white and all those observers who reported Sirius was red were confused. I just want data proving one view of historical sightings-either Sirius was red or it wsn't.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 3)
by Joseph C. Keller, M. D., August 31, 2009

Degrees of freedom of the pyramid layout. The alignment of Sirius with Barbarossa's 2012 sidereal position point (i.e., the point in Crater) when the latter is on the celestial equator c. 8600BC, requires two degrees of freedom, in the position of Khafre relative to Menkaure. Equality of the Menkaure-Khafre peak-to-peak upward slope, to Barbarossa's 2012AD declination in the coordinates of the equinox of 2013.0, requires another degree of freedom. This implies that the Rigel & Regulus alignment of Menkaure & Khafre is accidental.

One of Khufu's degrees of freedom, relative to Menkaure, is used by the requirement that the break in the pyramid centers' ground line equal Barbarossa's ecliptic latitude. The alignment of Barbarossa's 2012 position, with Sirius, at Khufu and Menkaure (mentioned as excluded in Part 1, because the Barbarossa meridian position projects to the interior of Khufu) is statistically significant (see next section), therefore uses (net) another degree of freedom, if the time is arbitrary. Finally, the 2520BC alignment of Sirius & Arcturus (also statistically significant), at Menkaure & Khufu, uses (net) Khufu's third degree of freedom, if the time is arbitrary.


Statistical significance. The 8690BC alignment of Sirius with Barbarossa's 2012 point, has error 0.8deg, but at 8602BC, when Barbarossa's 2012 sidereal point is on the celestial equator, the calculated error of the alignment is 3.6deg. Also, there are two intersections where Barbarossa's 2012 point coincides with the equator, and with three pyramids, 3*2 = 6 ways to make the alignment. So p = 3.6^2 * pi / 40000 * 2 * 6 = 1/80. This overestimates p, because it doesn't consider that the error is much smaller, just before Barbarossa's 2012 point coincides with the equator.

The 7000BC alignment of Barbarossa's 2012 point with Sirius, has 0.7deg error but the time is presumably indeterminate, by consideration of the number of available degrees of freedom. During the 15900yr interval studied, the length of the track of Earth's axis is 23.5*2*pi*15900/25800 = 91deg; 91*0.7*2 = 127 sq deg. So roughly, p = 127/40000 * 6 = 1/50.

Likewise, the alignment of Sirius and Arcturus at 2520BC, with 0.8deg error, gives p = 1/40 (this star alignment is unique because they are the brightest stars in the southern and northern hemisphere, resp.). Overall, p < 1 / (80*50*40) = 0.0006%.

Rigel is the 6th and Regulus the 19th brightest star in the sky, according to one textbook. If any of the brightest 4 southern (Sirius, Canopus, Rigil Kent, Rigel)(for the meridian star) and brightest 10 northern stars are allowed, then the expected number of alignments, to 0.8 error, is 4*10/40 = 1. So, likely as not, the Rigel-Regulus alignment (to 0.5deg error) is fortuitous and uses no degree of freedom.


Barbarossa's 2012 ecliptic latitude, Sirius and the date of pyramid construction. The break angle in the line between the pyramids, was defined, by me above, essentially by projection of their peaks onto the horizontal plane. This definition requires measurement of the horizontal plane. Also, the horizontal plane would change if an earthquake tilted the Giza bedrock (synclinal activity); due to the different heights of Menkaure & Khafre, a rotation of a degree about the interpyramid axis, would change the (projected) break angle > 0.1deg.

An invariant way to define the break angle, is as the angle in space between the lines between the centers of their bases, including consideration of their differing base heights. Again, I take the center, as Petrie's "center of casing", which is the exact centroid of the corners of the casings, and in the case of Khufu, negligibly different from the centroid of the "sockets". The break angle by this definition is 11.493deg, corresponding to Barbarossa's ecliptic latitude at 5600BC (vs. 5960BC using the break angle, 11.461deg, as projected on the horizontal plane). Khufu's gallery points to Sirius on the meridian (i.e., 90 - 30 + Sirius' declination = 26.2778deg) at 5730BC.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 4)
by Joseph C. Keller, M. D., September 2, 2009


Luna's vs. Khafre's heights. In Parts 1-3, the degree of freedom given by the scale of the pyramids, was not used. Everything in Parts 1-3, applies to a larger or smaller scale model of them. The pyramid builders used the scale of the pyramids, to tell us Barbarossa's orbital period (i.e., the period between the Younger Dryas onset c. 10672BC per Brauer, and Year One of the Egyptian calendar, 4329 BC; and again between that and 2012AD).

"...secondary cycle...of perigee...lunar distance varies between 356,375 and 406,720km, the minimum being the 'proxigee' [cites FJ Wood, "Tidal Dynamics", 1986]."

- JH Duke, 2009, johnduke.com


Measuring from the base of Khufu (the biggest pyramid, and the one with the lowest base) the height of Khafre's apex (the highest pyramid) is 5664 +/- 13 inches (per Petrie) above Khafre's base; Khafre's base is 1011 cm (per Vyse) above Khufu's base, giving Khafre's total height as 6062.0 inches.

The ratio of Luna's "proxigee" (nearest perigee, as center-to-center distance) to Khafre's total height, equals the number of days in 6337 +/- 14 yr. My best estimate of Barbarossa's period (either from my four sky survey detections, or from my calculation of Year One of the Egyptian calendar from Sothic dates) is 6340yr.

Luna, and the Mayan Long Count. The 5125yr Mayan calendar cycle began 2012AD - 5125 = 3114BC. This also is, at least to within a few years, the beginning of Egyptian chronology; the Columbia Enc., 4th ed., gives 3110BC as the beginning of the First Dynasty. An earlier relationship mirrors this:

2012AD - 6340*2 = 10669BC; 10669BC + 5125 = 5544BC. The Great Pyramid seems originally to have been built approx. one Mayan Long Count cycle after the Younger Dryas disaster, or at least was designed to suggest that epoch: the slope of the gallery inside the Great Pyramid equals the altitude of Sirius on the meridian at 5730BC, according to the modern precession formula and proper motion. Perhaps more accurately, the break angle, in space, between the centers of the bases of the pyramids, equals the ecliptic latitude, in the ecliptic of date 5600BC, of Barbarossa's Dec. 2012AD position in Crater.

6340yr * 2 - 5125yr = 100,145 anomalistic lunar months (the change in month length over this interval is thought to be negligible; see Wikipedia "Month" article). So, the epoch indicated by the design of the Giza pyramids, might have been chosen to give the 100,000 anomalistic month hint. To give another hint, 5125yr again was chosen as the interval, before 2012, for the start of Manetho's Egyptian chronology and of the Mayan Long Count cycle.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 5)
by Joseph C. Keller, M. D., September 5, 2009


The truncation of the Great Pyramid. The usual "pyramidion", i.e. capstone, together with the top thirty feet of courses, is missing from Khufu's pyramid, or maybe never existed. The truncation of Khufu's pyramid allows it to have essentially two heights, for two different purposes. Khufu's geometric apex height (per Petrie), 5776 +/- 7 inches ( = 481.3ft) gives the best alignment, for Sirius on the meridian at Menkaure and Arcturus at Khufu: 0.8deg error at 2520BC; vs. about 1.2deg minimum error using Khufu's actual, truncated height. (For the other Khufu alignment, that of Barbarossa's 2012AD position on the meridian at Khufu, and Sirius at Menkaure, the difference is neglible.)

On the other hand, Khufu's actual, truncated height, gives another precise relation, between Barbarossa's orbital period, and Luna. Various online sources give its truncated height as 449 to 455ft. Petrie gives 5407.9 & 5409.2in for the NE & SW corners, resp. (mean 5408.55in = 450.7ft = 137.4m); Fakhry's textbook adopts this figure, 137m. At 30N latitude, Luna often is near enough the zenith, that differential atmospheric refraction is negligible, so I'll use Luna's 1737.4km radius given by the 2002 Astronomical Almanac (which says "0" flattening). The ratio of Luna's radius to Khufu's truncated height, is 6323.5 * 2. (Thus if Barbarossa's orbital period in years, were 6340, it would correspond to a height of 449.5ft.)


The DiPietro & Molenaar ("D&M") pyramid on Mars. Named for its discoverers, its base angles have been measured by professional cartographer Erol Torun of Massachusetts. The pentagonal base is divided into five triangles. The peak of the pentagon points 19.5deg east of Martian north. Clockwise from the peak, the base angles are:

Triangle 1: 60,60
Triangle 2: 49.6,45.1
Triangle 3: 55.3,55.3
Triangles 4 & 5: same as 2 & 1, resp. (there is approximate right-left symmetry, and apparently Torun assumed this symmetry, when determining the angles that best fit the image)

The altitude of Triangle 3 differs only 2% from that of Triangles 1 & 5. Torun gives his error as +/- 0.2deg. This 2% might be within that error. If the altitudes of Triangles 1,3, and 5 are equal, then whatever the height of the pyramid, the slopes of these sides are equal too. Bilateral symmetry causes the slopes of the sides above Triangles 2 & 4 to be equal.

If Sides 1, 5 (and 3, approximately) slope 45deg, then Sides 2 & 4 slope 48.67deg, and the pyramid is 953m tall, assuming an 1100 meter base for the equilateral triangles. Necessarily, if Sides 2 & 4 slope 45deg, then Sides 1, 5 (and 3, approx.) slope 90 - 48.67 = 41.33deg, and the pyramid is 838m tall, again assuming 1100m for the equilaterals.

The latitude of the common vertex of the five triangles, is 40.868 N. Presumably this is planetocentric latitude (i.e., angle from equator, viewed from the planet's center), which has been standard for Mars cartography for many years. If so, then using Mars' polar flattening, 1::136, the planetographic latitude (i.e., latitude w.r.t. local horizontal) is 41.31. Thus if any of the sides are sloped 45deg, then some of the remaining sides are sloped 45deg also, and the others are sloped at an angle equal either to the (planetographic) latitude, or colatitude, of the pyramid.

DeRoos et al, on their website, give the base of Triangles 1 & 5 as 1100m, the base of Triangles 2 & 4 as 1800m, and the base of Triangle 3 as 1500m. The height of the pyramid seems to be least accurately known; they give this as 900 +/- 100m.

It's long been known that the circumference of the Giza pyramids, especially the Great Pyramid of Khufu, approximately equals that of a hemisphere of the same height (the ancient Egyptians approximately solved the ancient Greek problem of "squaring the circle"). On a U.S. public television program, Egypt's director of antiquities, Hawass, noted that somewhat irregular pyramids are made naturally by wind erosion of boulders in the desert, and might have inspired the pyramid builders. If, as the Mars pyramid suggests, natural slopes are related to latitude, then natural pyramids at 30deg N latitude on Earth, might form slopes similar to the 52deg slope of the Giza pyramids.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 6)
by Joseph C. Keller, M. D., September 9, 2009


"...I went to Egypt a few years ago and people kept saying to me, 'If you're Welsh you're going to enjoy this soup'...'If you're Welsh you will like this monument.' I couldn't think what they were talking about, but then I began to discern similarities between Welsh and Egyptian in the family structures, the most marked being the preponderance of aunties common to both peoples."

- Alice T. Ellis, "A Welsh Childhood" (1990), p. 117, as cited by anonymous internet author


Stonehenge contemporary with Giza Pyramids. The building of Stonehenge, Avebury, etc., is said to have begun, according to C14 dating, c. 3100BC, comparable to the beginning of pyramid building in Egypt with the beginning of the First Dynasty c. 3110BC. (Likewise we have the Mayan Long Count starting 3114BC and the Kali Yuga said to start 3102BC.) Construction at Stonehenge, Avebury, etc., is said to have peaked c. 2500BC, the approximate date of the Giza pyramids. Stonehenge, Avebury, etc., are said to have become neglected after c. 1600BC, comparable to the ending of pyramid building by Amenhotep I near the start of the New Kingdom.


Stonhenge-Giza ethnology. Many authors have written about architectural, skeletal, serologic, cultural and linguistic relationships between some or all of (not necessarily limited to) the following: ancient Egyptians, ancient Minoans, prehistoric Iberians, prehistoric inhabitants of Britain and France, modern Berbers & Basques, and some modern inhabitants of Portugal, E. Crete, and S. Wales. The steepest successful very large pyramid achieved slope 56deg, by using the "bent pyramid" strategy. The tip of Cornwall is latitude 50N and Glasgow, Scotland, approx. 56N.

The Giza pyramids were accompanied by large, seaworthy buried longboats, and much Egyptian lore from Edfu and elsewhere says the Egyptians immigrated there from a distant land. It seems likely that the slopes of the Giza pyramids commemorate three megalithic homeland sites in Britain:

1. The latitudes of Stonehenge & Avebury are 51.178844N & 51.42861N, resp. (from Wikipedia; presumably someone's definition of the centers of the main rough circles). The mean of these is 51.3037N. A modern estimate of the overall slope of Menkaure's pyramid is 51.337deg (Lawton & Ogilvie-Herald, "Giza: the Truth", 1999, p. 121). Petrie gives 51.175 according to the granite courses (Petrie, sec. 81). Thus according to Petrie, the slope of the granite courses of Menkaure is 0.004deg (14 arcseconds) less than the latitude of Stonehenge.

2. Lawton adopts Petrie's value (Petrie, sec. 67) of 53.167 for Khafre's slope. Of the nine known "henge" monuments (dated c. 4000-2000BC) in Wales (RN Savory, "The Neolithic in Wales", in: JA Taylor, ed., "Culture & Environment in Prehistoric Wales", 1980, Fig. 5.4, p. 218) four are in NW Wales near Mt. Snowdon (a dangerous mountain; Hillary trained there for Mt. Everest) and four in SW Wales near Black Mountain. Measuring on Savory's map, I find that the four in NW Wales range from 53.171-53.247N, mean 53.214. Analogous to Menkaure vis-a-vis Stonehenge, Khafre's slope is only 0.004deg less than the latitude of the most southerly of these henges. The northernmost of the "Glyderan" peaks north of Mt. Snowdon, is Elidir Fawr, elev. 3031ft, lat. 53.13074N. Like many other peaks in Wales, Elidir Fawr has an unusual, sharply pyramidal profile in many photos.

3. Lawton gives 51.843deg for Khufu; Petrie (secs. 24, 25) gives 51.844 +/- 0.018 (50% confidence interval) for the north face and 51.867 +/- 0.033 overall. As I measure on Savory's map, the four henges in SW Wales range from 51.814-51.931N, mean 51.862. One of the henges is 51.836N, 0.008deg less than Petrie's likeliest slope of Khufu's north face. Black Mountain is the westernmost major peak in the Brecon Beacons range; it is not to be confused with the separate Black Mountain Range, also in S. Wales. The westernmost subsidiary peak of Black Mountain is Garreg Llwyd (a.k.a. Garreg Lwyd, a.k.a. Moel Gornach) which means Grey Stone, not to be confused with several other objects in Wales, named Grey Stone, or Garreg Lwyd. This peak's elev. is 2021ft and its lat. 51.84544N. It is topped by one of the largest prehistoric cairns in Wales. Lawton remarks that the Egyptians deliberately deviated from the arctan(4/pi) = 51.8540 formula in every case except possibly Khufu.


Avebury, Stonehenge and Barbarossa. According to my best estimate of Barbarossa's orbit, from the four sky survey detections, its latus rectum (distance c. Dec., 2012) is 216AU and its aphelion 554AU. Wikipedia gives 98m & 108m for the diameters of the N & S inner circles, resp., at Avebury, but I'll use Thom's estimate, that both are diam. 340ft = 103.6m (Thom & Thom, "Megalithic Remains in Britain & Brittany", 1978, Fig. 4.1, p. 33). Neglecting Earth's oblateness, the geodesic (i.e., great circle) distance from Avebury to Stonehenge is 91439ft, and the linear distance negligibly different. The radii of the outer Avebury circle, 3545ft/(2*pi) = 564.2ft (Thom et al, J. for the History of Astronomy 7:183+) and inner Avebury circles, subtend 1/162 and 1/538 radian, resp., at Stonehenge.

Stonehenge and Avebury lie 17mi apart across the Salisbury Plain. Because of the curvature of the Earth, if they were at the same elevation, someone with eye height zero at one place, just could see the tip of a tower 200ft high at the other. Stonehenge is 330ft above sea level and Avebury 520ft; 520 - 330 = 190. So, stones a few feet tall at one place would be visible to people a few feet tall at the other.

By simple trigonometric approximations accounting for the angle at which the ecliptic cuts parallels of declination, and for projection from the meridian onto the horizon, I find that those angles are the mean Earth parallaxes, with Barbarossa at latus rectum and aphelion, projected onto the horizon at Avebury, if Barbarossa's latus rectum & aphelion were 255 & 541AU, resp. The latter differs only 2% from my calculated orbit.

These same approximations give Barbarossa's declination as -19deg, at aphelion. Measuring from Thom's map, I find the slope from the center of the north inner to the center of the south inner Avebury circle, as 19.8deg E of S.

I estimate that Barbarossa reached its aphelion at 1603BC. This is approximately the time that interest in pyramid building in Egypt, and henge building in Britain, ceased.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 7)
by Joseph C. Keller, M. D., September 10, 2009


The steep, small pyramids, vs. Iceland. The lower slope of the "Bent Pyramid" of Snefru, is 54.46deg, but that of Unas, another bent pyramid which is less well preserved, is given as 56.3. This is the steepest successful large pyramid that I find, but several small "queen" and "cult" type pyramids successfully exceed 60deg (source: www.narmer.pl , by Dariusz Sitek).

The unfinished pyramid of Neferefre has slope 64deg30' but is only 7m high. Among finished pyramids, I find a cult pyramid (by Djedkare's pyramid) listed as 65deg slope, 16m high; the latitude of the highest peak of Iceland, Hofsjoekull, 1765m elev, is 64deg50'N lat.

Also near Djedkare's pyramid, is that of an unknown queen, listed as 62deg slope, 21m high. Queen Neith's pyramid has slope 61deg, 21.5m high.

Many small pyramids cluster near slope arctan(2). A cult pyramid by Teti's, is listed as 63deg, and has height and base both 15.7m, which if accurate in the last digits, implies slope 63deg26' +/- 9' (100% confidence) or +/- 3' (50% confidence). Another cult pyramid, of Pepi II, has about the same stated slope and base as the one by Teti's, but height not stated. The pyramid of Iput I, apparently a queen related to Pepi I, has 63deg slope and is now 7m high. Queen Wedjebten's pyramid has 63deg30' slope and 23.5m base. The latitude of the southernmost point of Iceland is approx. 63deg 23' N. Another hint that the pyramids' slopes encode latitudes, is their NS orientation.


The arctan(4/3) pyramids of Saqqara, vs. NW Wales. Sitek (see above for reference) lists the main pyramids of Pepi I (ruins only 12m high), and of Merenre I (a.k.a. Nemtiemsaf I)(both these pyramids are "badly [or "much"] damaged due to stone robbery") and of Pepi II (in pretty good shape) as 53deg 7' 48" = arctan(4/3). Petrie thought he could determine the overall slope of the Great Pyramid of Khufu, which is of better workmanship and less damaged than these, to +/- 2' (50% confidence). Ascribing that uncertainty to these pyramids, let's say their slope is 53.130 +/- 0.033. Also, Teti's pyramid has slope 53deg 13' = 53.217.

Of the four henges in NW Wales, two lie near each other at 53.220N lat, according to my measurements on Savory's map. Teti's Saqqara pyramid repeats the pattern noticed for the Giza pyramids in Part 6: its slope (though given only to +/- 0.008deg implied precision) is only 0.003deg less than the latitude of important henges.

Supposing that the slope of Pepi I&II and Merenre, really is arctan(4/3) = 53.13010, it is only 0.0006deg less than the latitude of that pyramid-like endmost Welsh peak, Elidir Fawr (see Part 6), 53.13074N.