Bright Stars over the Pyramids: Atlantean Knowledge (Part 2) by Joseph C. Keller, M. D., August 29, 2009

Abstract. The relative positions and sizes of the three large Giza pyramids, together with two arbitrary dates, exploit a total of eight degrees of freedom, to specify two bright star alignments, and Barbarossa's 2012AD (or 4329BC) sidereal position; and, redundantly, Barbarossa's (approximately constant) ecliptic latitude, and Barbarossa's 2012AD declination.

Introduction.

"[Critias] replied: - ...one of the [Egyptian] priests...said: O Solon...There is a story, which even you have preserved, that once upon a time Phaethon, the son of Helios...burnt up all that was upon the earth... . Now this has the form of a myth, but really signifies a declination of the bodies moving in the heavens around the earth, and a great conflagration of things upon the earth, which recurs after long intervals;... .

"...after the usual interval, the stream from heaven, like a pestilence, comes pouring down, and leaves only those of you who are destitute of letters and education; and so you have to begin all over again like children..."

- Plato, "Timaeus" (Jowett transl.)(Britannica Great Books pp. 444,445)

Further results and discussion. In Part 1, I found that at 8690BC, Sirius could be sighted on the meridian at the peak of Menkaure's pyramid, while Barbarossa's 2012 sidereal position (a point in the constellation Crater) simultaneously was sighted at the peak of Khafre's. Now I also find that due to Earth's precession, this point in Crater, lies on Earth's equator, at 8602BC. It is like a code for this point of Barbarossa's orbit: the time to look, is given by the presence of the celestial equator at the peak of Khafre, when Sirius is on the meridian at the peak of Menkaure. At this time (c. 8600 BC), Barbarossa's 2012 position lies on the equator, and at the peak of Khafre. The cost of this information was two degrees of freedom in the arrangement of the pyramids.

The pyramids also were arranged (see Part 1) so that sometime when Rigel was on the meridian and at the peak of Menkaure, Regulus would be at the peak of Khafre; and sometime when Sirius was on the meridian and at Menkaure, Arcturus would be at Khufu. These dates could be accidental, not specified, and thereby provide another two degrees of freedom, in the time, so the net cost of this information is 2*2 - 2 = two degrees of freedom.

The remaining two degrees of freedom of the six available (i.e., the latitude, longitude and height of the second and third pyramids, relative to the first) were spent for redundancy in giving the position of Barbarossa in 2012AD. The ecliptic latitude of the Dec. 2012AD point, of Barbarossa's orbit, changes only a fraction of a degree during these millenia; this change is given by the formula at the bottom of p. B18 of the 1990 Astronomical Almanac. For 2000AD and 4329BC, the latitudes, of the 2012AD point, are -11.803 and -11.594deg, resp. According to Petrie's raw data (sec. 19), the break in the line on the Earth's surface between the casing centers of the pyramids, is 11.461deg. Thus Barbarossa's ecliptic latitude for 2012AD, is suggested with only 0.3deg error.

The angle upward from the peak of Menkaure to the peak of Khafre, from the data used in Part 1, is 9.472deg (neglecting the curvature of the Earth, which introduces error of order 0.01deg). My best estimate of Barbarossa's J2000.0 coordinate system declination on Dec. 21, 2012, is -9.381; in the coordinates of the equinox and ecliptic of date 2013.0, its declination is -9.453.

The dates of the pyramids. The pyramids might have been built c. 2500 BC and their layout calculated from an exact knowledge of Barbarossa's 4329BC position and sidereal orbital period, and of Earth's precession; or the pyramids might have been built earlier, maybe contemporary with the Sphinx, and merely refurbished in 2500 BC, with the addition of outer casings, sarcophagi, auxiliary temples and the like. Maybe the originals were smaller but to scale, and the final size built in 2500BC. The alignment of Sirius and Arcturus over the pyramids at 2520BC might have stimulated interest. The dates indicated by the star alignments might or might not be the dates the pyramids were built.

The purpose of the pyramids. The Rigel-Regulus and Sirius-Arcturus alignments serve to alert future scientists that "There is information about star alignments here." Then the future scientists would notice that the alignment of Sirius and the equator, implied a position where something might lie invisible, and that the Menkaure-Khafre-Khufu break angle, and Menkaure-to-Khafre peak-to-peak slope (ground, and air, geometry, resp.) of the pyramids confirm the (nearly constant) ecliptic latitude, and the 2012AD declination, resp., of this (now invisible) something.

quote:Originally posted by Maurol Around the 12th century CE, the date of Earth's solstice coincided with the date of Earth's perihelion. ... It could be interesting to study what other significative or rare astronomical events took place, particularly inside the solar system, around the 12th century CE.

What would lots more interesting is getting the mystery about the color of Sirius cleared up. If Sirius was red at 600AD and turned white by 1200AD it might be good to look for any mention of its color from any writing on the planet. The American Indians and many Asian sources my have noted this tidbit at some point during the time from 600/1200AD. But don't expect me to search that mountain of a haystack. Maybe someone has some info from other places.

What would lots more interesting is getting the mystery about the color of Sirius cleared up. If Sirius was red at 600AD and turned white by 1200AD it might be good to look for any mention of its color from any writing on the planet. The American Indians and many Asian sources my have noted this tidbit at some point during the time from 600/1200AD. But don't expect me to search that mountain of a haystack. Maybe someone has some info from other places.

Hi Jim you probably say this because you think that that's the only mystery that need to be resolved or cleared up, to maintain your actual worldview. If you begin to do your own research, you'll notice that there are many mysterious things in search for an explanation, not only this one. That is, actually your worldview is made consistent by virtue of ignorance, not knowledge.

To Joe Keller: Joe, when a theory is both correct and consistent, ALL the evidence tends to add up. When a theory is incorrect, on the other side, part of the evidence will tend to add up, and another part of it with tend to contradict it. If SOMETHING does not coincide with the predictions of the theory, it is enough to falsify the theory. It's not necessary to have an statistical distribution of misses vs. hits. It is enough with one miss, to nullify the theory, in its actual form at least.

Regarding Sirius: There is no knwon mechanism in stellar evolution theory that can account for the sudden(300 years) change of color of Sirius. We're providing a very plausible mechanism for it(Doppler shift due to change in velocity and direction), that is both gradual, and relatively quick, compared to the scale of changes in stellar evolution theory. If the change occurred gradually over a period of centuries, no one will have noticed it. To search the literature for a repentine change, happening in the order of days, weeks or even months or years, is preposterous, because such a thing should have been noticed and recorded everywhere.

Morevoer: that same mechanism be are proposing can be used today, to measure the degree of change of the star proper motion. By taking two pictures on the same epoch of the year (at perihelion, by example) and comparing its spectra, we can deduce the change in relative velocities of both systems, if there's a change, and establish that way scientifically that we are in an orbit with that star.

The American Hopi Indians talk about a blue star, Kachina, that must appear in the sky for their prophecies to be realized. Many different cultures and religions talk about a cycle of civilizations. The indians talk about Yugas, the Mayans about cycles of 13 Bak'tuns. Astrology talk about the Ages, the cycles of the zodiac, theosophists talk about "globes" and "great globes", and so on. Although different on their number, duration, and names, ALL of them coincide announcing the dawning of a new era, the end of Kali Yuga. The mayan had a calendar system, the Long Count, whose major cycle fits five times into the duration of the precessional cycle. The Hindus have a similar system of four Yugas, where each yuga has a different duration, and in total they amount to a cycle of 24000 years. The cycle of Zodiacal Ages is composed of 12 periods that, again, fit into the duration of the precessional cycle.

You can continue to deny the evidence, if you like. But as I said, your denial will be based in and related to ignorance, not knowledge.

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.

Bright Stars over the Pyramids: Atlantean Knowledge (Part 8) 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.

Maybe this is actually the debris from an exploded planet. According to Dr. Van Fandern's theories, this has happened several times in 5 billion years in our own system. The probability of seeing the aftermath of an explosion should be considerably higher than a mature system collision, if Dr. Van Flandern is correct.

Maybe this is actually the debris from an exploded planet. According to Dr. Van Fandern's theories, this has happened several times in 5 billion years in our own system. The probability of seeing the aftermath of an explosion should be considerably higher than a mature system collision, if Dr. Van Flandern is correct.

Thanks for this contribution! Maybe every 6340yr, an unknown force causes some asteroids to explode. Depending on which asteroid(s) exploded, and how they exploded, c. 12680 or 12900 yr ago, the fragments might have been too small to make big craters, and there might have been unusually little iridium for the quantity of nanodiamonds.

The most accepted values for the periods of Uranus and Neptune, are 84.01 and 164.79 yr, resp. If these are accurate to the last digit, then Uranus passes Neptune 36.994 times per 6340.0 yr Barbarossa orbit.

Barbarossa's incoming latus rectum was 1144AD. The interval after Ussher's creation date, 4004BC, is 5147yr, differing only 0.4% from the Mayan Long Count. Ussher's 4004BC is to Barbarossa's incoming latus rectum, about what the Mayan 3114BC is to Barbarossa's outgoing latus rectum.