Paradoxes Resolved, Origins Illuminated - Requiem for Relativity
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Joe Keller

959 Posts

Posted - 11 Mar 2009 :  23:24:46  Show Profile  Reply with Quote
Ugo Buoncompagni (Gregory XIII) and Joseph Scaligeri: Men of Atlantis

My new, eccentric, calculation of Barbarossa's orbit little affects Barbarossa's present 1/r^3, but halves its average 1/r^3. The present (i.e., epoch 1976) tidal force is proportional to 1/208^3 vs. the previous estimate 1/198^3; to compensate for this and give the same present tidal force as estimated previously, Barbarossa's mass needs to be only (208/198)^3 = 1.16x bigger.

The orbital time-average, of 1/r^3 i.e. u^3, is the average with respect to theta of u^(3-2), divided by the average w.r.t. theta of u^(-2). The denominator can be found from the binomial series in eccentricity (only even terms have nonzero time average), replacing all but the first five terms with an approximating geometric series. The time-average 1/r^3 is only 0.50x 1/(latus rectum)^3; i.e. Barbarossa's mass needs to be 2.01x bigger (Barbarossa now is near its latus rectum). So, maybe the orbital precession frequencies of Neptune, Pluto and the classical Edgeworth-Kuiper belt, due to the known solar system :: due to Barbarossa, aren't 3::1, 2::1 and 1::1 resp., but rather 6::1, 4::1 and 2::1. (Other explanations are possible.)

In my earlier post, I said my orbit estimate for Barbarossa had perihelion only 13 yr before 1583.0 (Pope Gregory's reformed calendar began with a jump to Oct. 15, 1582). I also said that Joseph Scaliger's 1583 system of Julian dates, sets JD 0 = 4713.0 BC, 6295 yr earlier than 1583.0 (my estimate of Barbarossa's period is 6340 yr).

Maybe Buoncompagni and Scaliger had Atlantean knowledge. The young Clavius (who published an 800 page book about it) and other leading astronomers collaborated for a decade on the Gregorian calendar reform, yet the Gregorian leap year reform wasn't urgent: the Julian calendar error had been accumulating for 1600 yr, Protestant countries still were getting around to adopting the Gregorian reform almost 200 yr later, and Russia after almost 400 yr. The promulgation of a new calendar in 1582 (at Barbarossa's perihelion as then known from hermetic sources?) might have been a beneficent "time capsule".

The Gregorian calendar is set to the tropical year, so from 1600 to 2000, Earth's perihelion date (neglecting Earth's perihelion advance) would have moved forward 400/25785*365 = 5.7 days; including the perihelion advance, it would be 6.9. That is, if perihelion was Jan. 3 in 2000, it would have been Dec. 27 in 1600. Christmas, Dec. 25, originally was set nearer to perihelion than to the solstice, though the perihelion has been moving forward because it depends on the anomalistic year (about the same as the sidereal year), not the tropical year. Pope Gregory's committee seemed conscious of perihelia, as anchor dates for calendars.

Plato's "Critias" testifies that Egypt had special knowledge of Atlantis and America, though modern experts note that some of the events told by Critias, seem confused with the eruption on Thera and the fall of the Minoan Empire to the Hellenes. Solon was, in part, educated in Egypt; there he learned about Atlantis. Solon passed the knowledge of Atlantis on to his fellow Athenians as oral tradition, until it was written down by Plato.

Heyerdahl and others have given evidence of an Egypt - Mesoamerican connection. Maybe the Mayan calendar ends, or rather has a major terminus, at the 2012 winter solstice (I gather that Mayan calendars used a 365 day year but little heeded leap years, equinoxes or solstices) because of an Atlantean plan to post a warning. Indeed a stone carving (Monument 6, Tortuguero, Mexico) warns of literal disaster then, when a God of war (but this God also is a God of creation and of a symbolic nine-foot tree) descends, named "Bolon" (Prof. Robert Sitler of Stetson College, chapter in a book called "2012", by an anonymous editor).

The Egypt chronology in the Columbia Encyclopedia ("Dynasties" table in "Egypt" article) begins at 3110 BC, 5121 yr before 2012 AD. The Mayan "long count" (the Mayans had several parallel calendars) of 13 "pik" cycles, is 5200 years of 360 days (though parallel Mayan calendars had 5 extra days per year) = 5125.25 yr (several chapters in the abovementioned editor-less "2012" book explain the Mayan calendar, about as well as it can be explained, I suppose). Maybe Egypt got started with essentially the same calendar, also ending a long cycle in 2012.

The medium Edgar Cayce gave 10500 BC as the date for the ultimate destruction of Atlantis (Adrian Gilbert's "2012"). This date might be contaminated somehow by the consciousness, of Cayce's questioners, that Plato had said c. 9500 BC. However 2012 AD - 2*6340 = 10669 BC. If I use Scaliger's period instead of my own, it's 2012 - 2*6295 = 10579 BC.

My Barbarossa has perihelion 133.9 AU. Little happened at the last perihelion in 1569 (my est.) or 1582 (hermetic estimate of Pope Gregory et al?). I suspect that the outgoing latus rectum is disastrous. At the latus rectum, the radial acceleration toward Earth, d2r/dt2, is zero; that is, dr/dt is maximum. Nearby the acceleration achieves small multiples of H*c, the Hubble parameter times the speed of light. This acceleration value also is observed for millisecond pulsars: it is physically important. Small multiples of this relative acceleration might cause an "ether soliton" ("ES").

Barbarossa is unique. It is massive, nearby, and yet outside my proposed Solar "ether island" of radius 52.6 AU. By my estimate, its orbital latus rectum was passed 2003.94, but Barbarossa's d2r/dt2 will be 2*H*c, on 2012.96. (Dec. 21, 2012 is 2012.97.)

Alternatively, using the first day of the new Gregorian calendar, 1582.79, as perihelion, and Scaliger's period, approx. 6294.79 yr, then getting the area between perihelion and latus rectum from exact integral calculus assuming my eccentricity estimate e=0.610596 (probably my most accurate calculated parameter) I find that the latus rectum will be passed 2013.98, at the solstice a year later.

Adrian Gilbert, "2012", shows diagrams of trios of pyramids in Egypt (the three great pyramids of the Old Kingdom) and Mesoamerica, which are congruent in their positions, to the slightly nonlinear geometry of Orion's three belt stars. My program finds Barbarossa's descending node (orbital inclination to ecliptic: 12.93 deg) of the center of mass of Barbarossa/Frey, to be RA 112.654, Decl +21.817. This point on the ecliptic is in Gemini. The argument of perihelion is 180-25.022=154.978; i.e., the perihelion is 25.0deg west of the descending node, as measured along the orbit. Though arctan(0.5) = 26.6deg often would arise in architecture, when one side of a right triangle is half the other, this angle (said by Robert Temple to be common at Giza) also might have astronomical significance desired to be built into durable structures as a mnemonic so that Barbarossa will be recognized quickly when it returns.

The perihelion is ~30deg due North of Orion's belt (roughly true now as well as in ancient Egypt, despite some pole precession). (As given earlier, the semimajor axis is 343.840 AU, the eccentricity 0.610596 and the period 6339.93 yr.) At the most recent presumed destruction, in 2013 - 6295(Scaliger's period) = 4283 BC, the vernal equinox would have been (using Newcomb's precession rate) at J2000 ecliptic longitude 87.402, so Barbarossa's descending node would have been at ecliptic longitude 110.952-87.402=23.55deg relative to the equinox of date. Barbarossa's perihelion would have been only ~5deg North of the equinox ("first point of Gemini" in those days).

A catastrophic physical phenomenon occurring at or just after the outgoing latus rectum, that is, near Barbarossa's present position, could brighten Barbarossa to about magnitude -5, if it is, as I suspect, about the size of Earth (though 10x the mass of Jupiter) and it became heated to the temperature of the Sun. This part of the orbit is almost parallel to the ecliptic, so Earth parallax mainly moves it back and forth along its orbital track. It would be easy for Egyptian or Atlantean astronomers to extrapolate the visible part of the orbit to the ecliptic, the usual home of wandering stars.

Calculating the perihelion would be harder, but could be done by "second differences" of the seasonally-adjusted angular speed. Orion's belt is the easiest marker of this spot.

The previous disaster, perhaps 2013 (13, an unlucky number) - 6295 = 4283 BC, is about the right length of time ago, for us to have the legends of universal floods, extermination and other destruction that we have: legends much less complete than, say, the Iliad. Also, the root Indo-European language, according to the American Heritage Dictionary, dates from the 5th millenium BC (4000-5000 BC) suggesting that something happened c. 4500 BC, which only one clan survived in a large area covering much of Europe and central Asia. (Alternatively, maybe Aryan tribes were busy expanding into the retreating glacier areas, until this retreat slowed markedly c. 4100 BC, and they had to scatter to look for new territory. See next post.)

The Sphinx might be Atlantean, predating 4300 BC, then remodeled during the Old Kingdom. If Atlantis had the level of civilization of 16th century Europe, its main residue would have been stone buildings, which would have been dismantled to make other buildings.

Atlantean astronomers as advanced as Brahe and Kepler, might have observed the Barbarossa system if it were greatly brightened by whatever disturbance occurred as it passed the latus rectum. Stonehenge (c. 2000 BC), Avebury (bigger and older than Stonehenge) and the like, might have been aids to accurate naked eye astrometry based on averaging many measurements by many observers. Atlanteans would have correlated the "new stars" with comet strikes or other physical disasters, causing enduring interest in astronomy and astrology far beyond agricultural needs. The damage might come not from Barbarossa per se nor even from comets influenced by it, but from this disturbance in the ether between the Solar and Barbarossa systems: the ES.
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Joe Keller

959 Posts

Posted - 13 Mar 2009 :  15:12:44  Show Profile  Reply with Quote
(email sent today, Friday, March 13, 2009, to "Coast to Coast" radio program producer)

Dear Sir:

I'd rather not appear solo on Coast to Coast, but I'd like to debate either Phil Plait, Dr. Neil Tyson, or anyone else who will take the negative position, or all of them together, about the existence of Planet X. I've already challenged Dr. Tyson, to a debate about Planet X on Coast to Coast, in an email to him. I've been censored from Phil Plait's messageboard, "Bad Astronomy".

I've amassed evidence that Lowell's Planet X, which I call Barbarossa, exists, including quantitative information about its orbit, and its location on all four relevant red and optical infrared emulsion sky survey photographic plates (from online scans). The details are on my posts to the messageboard of Dr. Tom Van Flandern, at, in the "Requiem for Relativity" thread, under my name, Joe Keller.

Don't heed any simple dismissal of my views. I'm familiar with the usual objections and can rebut them in depth. I'm a 1977 graduate of Harvard College, B. A. cumlaude in Mathematics.

Joseph C. Keller, M. D.

cc: Candace Lowell; Andy Lloyd
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1871 Posts

Posted - 16 Mar 2009 :  13:52:21  Show Profile  Reply with Quote
Dr Joe, While we are waiting for some telescope time can we kick around the impending results of a look see? What if nothing is found after a search do you change the calculations or challange the math that lead to all this fuss? It seems to me your ideas are based on a model and if the calculations are right something else is wrong. As you can see I'm hoping nothing is found but either way its a good project that should generate a new discovery.
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Joe Keller

959 Posts

Posted - 17 Mar 2009 :  18:57:35  Show Profile  Reply with Quote
Climate Change vs. Phase of Barbarossa Solar Orbit

Though Ice Age data have been correlated with small-amplitude astronomical cycles of Earth's precession, obliquity and eccentricity (Hays, Science 194:1121+, 1976) it's been necessary to invoke positive feedback schemes to explain the magnitude of the climate change. Maybe these cycles are effects, not causes. Ice Ages end suddenly. Again some try to explain this with positive feedback, but maybe Ice Ages are regulated by some larger event.

IW Jones et al, Global & Planetary Change 33:139+, 2002, show in Figs. 4, 6, 8 & 9, that bicarbonate, germanium & silicon studies locate the last spike in glacial melt to have been the entire period from 6000 to 12000 yr ago. This is between one and two orbital periods of Barbarossa ago, but these charts are not precise enough to show whether the endpoint was the latus rectum or the perihelion.

Thom & Roy, Journal of Sedimentary Research vol. 55, 1985, say in the abstract that sea level rise, as measured at Australia (a geologically stable continent with little human disturbance) ended c. 6500 (by 14-Carbon dating) yr BP. SM Flanagan (article on, 2003 or later, according to the bibliography) says terraces at Cape Liptrap on the Australian coast, formed ~125,000 yr and 5570 +/-40 yr (the latter by 14-C) BP, are strange because after formation they were partly uplifted, deformed and faulted, though on a "passive continental margin".

Burbridge et al, Quaternary Research 61:215+, 2004, studied sediments in two lakes in the Bolivian Amazon. About 39,000 yr BP ("Before Present"), sediment deposition in Laguna Chaplin declined to ~ 1/3 normal, and declined in Laguna Bella Vista (LBV) to almost nothing. Then 11030 +/-80 "14-Carbon" yr BP, deposition resumed in LBV, but it was only sand, until 9820 +/-70 BP, when fast clay & mud deposition gradually began to occur. Corrected for the difference between calendar and 14-C yrs (following Klaus; see below) the start and end of this "sand" period (presumably torrential seasonal Andean snowmelt) correspond to the "Younger Dryas", said to have been 12900(?) to 11550(+/-20) BP (Wikipedia, etc.).

Citing Prof. Glynn Custred, Academic Questions 13:12-30, 2000, Wikipedia's article, "Kennewick Man", says that for this skeleton, 8400 "14-C yr" equalled 9300 calendar yr. Following Custred, I convert the (possibly younger) sample from the (possibly subsequently) anomalously deformed coastal terrace at Australia's Cape Liptrap to 6170 +/-40 BP; this uncertainty would be that of the "14-C date", not of the calendar date.

KF Klaus et al, XVI INQUA Congress Paper No. 83-12, 2003, equate 12350 14-C BP to 14300 calendar BP, for Swiss pines. Following Klaus, I convert Lake Bella Vista's sand interval to 12770 +/-80 BP (start) - 11370 +/-80 (end).

Klaus (op. cit.) says:

"The absolute chronology developed by the Hohenheim lab is based on German oak for most of the Holocene and dates back to 10,340 yr BP. The older part, based on pine samples also from Switzerland, extends the absolute record back to 12,454 yr BP. In the pine series we observe a drastic growth reduction at c. 11,590 yr BP, which we associate with the YD/PB [Younger Dryas / Preboreal] transition. ...between 10,850 and 10,600 BP, [there is] only one tree sample which has 245 annual rings, while there are several specimens that fall within the interval between 10,600 BP and the start of the absolute chronology."

Klaus' tree ring chronology, unfortunately does not go back to the beginning of the Younger Dryas.

Science 2 January 2009
Vol. 323. no. 5910, p. 94
Nanodiamonds in the Younger Dryas Boundary Sediment Layer
D. J. Kennett et al

"We report abundant nanodiamonds in sediments dating to 12.9 +/-0.1 thousand calendar years before the present at multiple locations across North America. ...These diamonds provide strong evidence for Earth's collision with a rare swarm of carbonaceous chondrites or comets at the onset of the Younger Dryas cool interval, producing multiple airbursts and possible surface impacts..."

On "Physics Forums" I found this abstract:

Luecke A & Brauer A, 2004
Biogeochemical and Micro-Facial Fingerprints of Ecosystem Response to Rapid Late Glacial Climatic Changes in Varved Sediments of Meerfelder Maar (Germany)
Palaeogeography, Palaeoclimatology, Palaeoecology 211:139+

"The response of a lacustrine ecosystem to climatic changes from 13,500 to 10,800 BP was studied in a varve dated sediment profile of Lake Meerfelder Maar. ...A prominent transition took place within two decades at the AL/YD boundary (12,690 - 12,670 BP). ..."

Though many sources say 12900 BP, this definitive study found 12680 +/-10 BP, i.e. 12688 = 2*6344 yr before 2012. This compares well to my orbital period calculation for Barbarossa, 6340 yr. However, the anomalous deformation in Australia possibly ~6180yr before 2012, suggests an anomalous terrestrial, not a meteoric, phenomenon.
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208 Posts

Posted - 17 Mar 2009 :  23:28:12  Show Profile  Visit shando's Homepage  Reply with Quote
It might be appropriate to check out "Lost Star of myth and time" by Walter Cruttenden, if you have not already done so, Joe. He has made a pretty good case for so-called "precession" to be due to our sun being in a binary orbit with some other star, such Sirus.
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United Kingdom
964 Posts

Posted - 18 Mar 2009 :  04:22:23  Show Profile  Reply with Quote
It is distinctly possible that our solar system formed by dumping angular momentum into the dust cloud that would later become Vega. Vega then takes longer to form into a sun. We're heading towards Vega but Vega is also moving in the same direction, though I think I might have to check that.

Okay so we've really got the barycentre of the solar system at the equinox but we think it's close to the sun and in line with Jupiter. We want to measure the parallax of some star and we measure it again after six months. The distances we get for spring and autumn sightings are going to be right but are going to be out for summer winter sightings.
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Joe Keller

959 Posts

Posted - 18 Mar 2009 :  17:24:42  Show Profile  Reply with Quote
Barbarossa Affects Planetary Axis Tilts?

Predicted geocentric J2000.0 celestial coordinates of the Barbarossa/Frey c.o.m.
for the 2012 solstice, 11:53 UT Dec. 21, 2012:

RA 11:28:44.38, Decl -9:29:19.4

same, heliocentric J2000.0 ecliptic coords.:

ecl. long. 176.36900 deg, ecl. lat. -11.80277 deg

From the 2009 Astronomical Almanac, I got the celestial coords. of the planets' rotation axes (from the 2006 IAU report), then used the free online conversion at (tip: it requires decimal RA in hours, not degrees) to get ecliptic coords. The ecliptic longitudes of the planets' N poles are:

Mars 353 (approx. correction to planet's own orbital plane: 355)
Jupiter 248
Saturn 80 (corr. to planet's own orbital plane: 84)
Uranus 258 (corr. to planet's own plane, still 258)
Neptune 319 (corr. to planet's own plane: 316)
Pluto 317 (corr. to NEPTUNE's orbital plane: 317)

Neptune's & Pluto's axes have much different ecliptic latitudes, but the longitudes, if both are expressed in Neptune's orbital plane, differ only 1.0 degree. Maybe Pluto and Neptune were formed together, or at least were together, and therefore had the same spin axis. Torque on the planetary bulge (mainly from the moons, which are nonequatorial; but also considerable from the Sun at this time scale) should continuously change the longitude of the pole. Yet apparently the poles' longitude has changed exactly the same amount, possibly zero, since the planets Neptune & Pluto separated. Their spin seems stuck, and perhaps for this reason, the moons (Neptune's Triton & Nereid, and Pluto's Charon) are in wild orbits.

The big moons of Saturn & Uranus are almost exactly in their equatorial planes, but the Sun should cause these planets' spins to precess in 10^8 or 10^9 yr, resp. Saturn's autumnal equinox is only 2 deg less than Barbarossa's 2012 longitude; Uranus' vernal equinox only 8 deg less. Maybe Saturn & Uranus are stuck there. (If corrected to Jupiter's orbital plane, the longitude of Jupiter's small axis tilt seems unrelated to Barbarossa.)

Mars' spin precession period has been measured at 171,000 yr, near the Newtonian theoretical prediction. Trying to explain Mars' Ice Ages with Milankovitch cycles analogous to Earth's, Barlow, "Mars" (Cambridge, 2008), p. 197, cites calculations that Mars' obliquity (i.e. axis tilt) should range from almost 0, to > 80deg, 42deg most probable. These calculations must be faulty. Mars' present obliquity happens to be almost exactly the same as that of Earth, Saturn and Neptune, all ~25deg. If 42 is "most probable" for Mars, then surely various other numbers are "most probable" for Earth, Saturn and Neptune. So, why are all four, 26+/-3?

What if something happens to Mars too, when Barbarossa reaches its latus rectum? At this 2012 event (whatever that event turns out to be) Barbarossa is only 1deg from Mars' winter solstice. This is analogous to the event one Barbarossa period ago, in ~4300 BC, when Barbarossa was only ~1deg from Earth's summer solstice: the subsequent 6000 years were good for mankind on Earth. Maybe the next 6000 years will have favorable conditions on Mars.

Barbarossa's period, ~6340 yr, differs only 2%, from (1/4)x Earth's precession period, so for a long time, Barbarossa "events" will be at Earth solstices or equinoxes. Earth's Ice Melt period, extending from 10000 to 4000 BC (see my previous short post) started after a Barbarossa "event" when Barbarossa was near Earth's vernal equinox. At 171,000/4 = 43,000 yr ~ 6340*7 = 44,380 yr ago, Mars would have had a Barbarossa event when Barbarossa was near Mars' autumnal equinox.

Maybe this was Mars' last wet period. Kargel, "Mars: a Warmer Wetter Planet" (Springer, 2004), p. 361, says "...the crispest flow and sublimational forms [on Mars]...are probably < 100,000 yr old...".
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Joe Keller

959 Posts

Posted - 18 Mar 2009 :  18:59:42  Show Profile  Reply with Quote
Ice Age Cycles: Beats of Precession with Barbarossa Period

The Enc. Britannica "Geochronology" article, Macropaedia vol. 19, Fig. 41, p. 861, shows that the last three Ice Age clusters ended at intervals of ~115,000 yr apart, with a trend toward somewhat shorter intervals, for the last few before that (the downward slope's intersection with baseline, at the end of the Ice Age cycle, is most distinctive, so that's what I considered to define those intervals). Fig. 42, p. 863, shows an interval of ~130,000 yr between the last two Ice Age clusters, if one considers the distinctive upslopes of the upper two charts.

Hays, Science 194:1121+, 1976, found four dominant sinusoidal periods in his analysis of Ice Age temperature & isotope data from the last 468,000 yr. These periods are 100,000 yr (50% of variance), 42,000 yr (25% of variance), 23,000 yr (10% of variance), and 19,000 yr. The ~23,000 yr cycle was the first discovered by geologists and has been assumed to be related to Earth's (at present) 25,800 yr precession cycle. Cycles in astronomical parameters (Milankovitch cycles) have been claimed to have the same periods Hays found, though the small amplitude of Earth's astronomical cycles is problematic.

I find today that all four of Hays' periods, are generated by Earth's precession period interacting with Barbarossa's orbital period. I note that Barbarossa's period, 6340 yr by my calculation, is almost 1/4 * Earth's precession period. Let x be Barbarossa's frequency in cycles per millenium, and y Earth's precession frequency. At present, Barbarossa when at its outgoing latus rectum, is always near an Earth solstice or equinox point on the ecliptic. Due to the slight difference between x and 4*y, a beat frequency arises: call the beat frequency z = x - 4*y. The time between these synchronizations, of Barbarossa's outgoing latus rectum (or any other fixed point on its orbit) with Earth's solstices & equinoxes, is 1/z = approx. 100,000 yr.

Thus the main Ice Age periodicity seems to be due to the beat (probably the interaction mechanism is not merely gravitational) of Barbarossa's orbit with Earth's precession. The second harmonic of this process, 2*z, also is likely large, because the process is periodic but not necessarily a pure sinusoid. Let's guess that the other frequencies arise from the product of this beat wave or its second harmonic, with the sine wave describing Earth's precession. One of the harmonics resulting from such a product, is y - 2*z = approx. 1/72 millenia; this harmonic is not mentioned by Hays. Likewise the pure second harmonic 2*z = approx. 1/50 millenia, is not mentioned by Hays. The other harmonics are:

y + z = 1/23
y - z = 1/42
y+ 2*z = 1/19
and the original equation z = 1/100

According to my estimate of Barbarossa's orbit, x = 1/6.34. Given this x, all of the four equations, which, if satisfied, give the periods that Hays observed in Ice Age data, are approximately true with the same value of y. For the four equations, the implied values of 1/y are

27.08, 26.63, 26.26, 27.54 millenia (vs. Newcomb's precession period, 25.785 millenia).

The square root of the variance of these five values (including Newcomb's)(defining variance as: sum of squared deviations, divided by 5) divided by their mean, is 5.1%. Here I have statistical evidence from period analysis, that Barbarossa interacts with Earth's precession and climate. This adds to the likelihood of Barbarossa's reality, and adds to the importance of upcoming special points on Barbarossa's orbit.

Let's find the value of Barbarossa's period, for which the four equations above, for the observed harmonics found by Hays in Ice Age data, give precession periods most consistent with each other and with Newcomb's (for our purpose, Newcomb's value, 25785 yr, will turn out to be practically the same as very current values such as 25771.5). The simplest way, is to choose Barbarossa's period so that the five (including Newcomb's) implied precession frequencies, "y", minimize sqrt(variance) / mean. That period is 6210 yr; it slightly improves the fit, to 4.6%, from the 5.1% implied by my orbital program's period, 6340 yr.

Perhaps the most valid way, is to weight each "y" proportionally to the frequency of its corresponding sinusoid (dividing the observation interval, 500,000 yr, by the sinusoid's period) and also proportionally to the variance in the data explained by that sinusoid, according to Hays (I roughly estimate this as 5% for the 19,000 yr sinusoid). The "y" determined by higher frequency components, effectively samples more values of the precession frequency during the 500,000 yr data set (Hays calls his interval of observation 500,000 yr in the title, 450,000 yr in the conclusion and 468,000 yr in the text). The "y" determined by a component explaining twice as much variance, essentially reflects twice as many data. Both weighting factors are reasonable, they are independent, and both can be applied. Newcomb's value amounts to one sample of the frequency but, in a sense, explaining all variance at that one time; so this value gets a weight factor of 1*1=1.

Weighting both the mean and the sum-of-squared-deviations formulas appropriately, the best fitting Barbarossa period is 6284 yr, if Newcomb's precession 25785 is used, and 6282 yr, if the very modern precession value 25771.5 is used. These are remarkably close to Scaliger's presumed Hermetic value: 6294 yr.

If I assume the observation interval 468,000 yr instead of 500,000, then the very modern precession value 25771.5, gives 6273 yr. If I then change the variance due to the 19,000 year period, to 2.5% (a better guess, I think) instead of 5%, I get 6267 yr.

I can further accurize this by estimating the precession rate that would correspond to the theoretical all-time mean obliquity, 23.497deg according to the 41,000yr sinusoidal formula (Wikipedia; citing Wittman, Astronomy & Astrophysics 73:129-131, 1979). Newcomb's obliquity was 23.452deg, in good agreement with the modern time-dependence polynomial, and the modern obliquity is 23.439. If +0.013deg of obliquity change is associated with 13.5yr longer precession period, then the all-time mean obliquity might be associated with precession period 25771.5 + 0.058/0.013*13.5 = 25831.7yr. This gives a best fitting solar orbital period, for Barbarossa, of 6278yr.

Let us recall that Pope Gregory's calendar reform was, by my estimate of Barbarossa's perihelion, 13yr past perihelion. (Gregory became Pope in 1672 and began his calendar reform initiative right away.) Thus Scaliger's choice of JD 6294yr for 1582AD, makes JD0 occur only 6294-13-6278 = 3 years before Barbarossa's perihelion, if I use the orbital period inferred from climatological data.

(Continued March 23, 2009)

The six periods above, would come from the function

(a + b*sin(2*pi*y*t+phi1)) * (c*sin(2*pi*z*t+phi2)
+ d*sin(2*(2*pi*z*t+phi2)))

where a, b, c, d and phi1, phi2 are unknown coefficients and phases. This is a sinusoid in Earth's precession period, multiplied by a second order Fourier series for a symmetrical periodic function of the angle between Barbarossa's perihelion and the preceding solstice or equinox.

The other two frequencies above, 1/72 & 1/50, which don't appear in Hays' article, do appear in other articles. The standard text, Muller & MacDonald, "Ice Ages & Astronomical Causes" (Springer, 2000), has Sec. 8.12 entitled "The 'Unexplained' 70kyr Peak". Deep sea cores from 20-25 Myr ago (Science 292:274+, 2001, Fig. 2A, p. 276) show these periods of statistical significance p<5% for at least one of the isotopes 13-C or 18-O:

406Kyr, 125, 95, 54, 41, 23, 20, 19.

The 54 is close to the 50 predicted by my model above but not found by Hays. If y=1/25.8 and z = x-4*y = 1/110, then my model, if extended to the fourth order Fourier series, predicts a frequency of y-4*z = 1/417, matching the 406Kyr period. Both the 19 and 20Kyr periods might arise from the y-2*z term, if z, which is a sensitive function of y, changed during the 5Myr interval.

Still needing explanation, is the split of the 100Kyr term into 95 & 125. Also needing explanation is the sudden reappearance of the ~100Kyr period, at ~1Myr BP (Science 277:215+, 1997). Both the split and the intermittence are explained if the constant term "a" in my formula above, is replaced by the augmented term


where u=1/792Kyr is Barbarossa's presumed spin precession period. This splits the 100Kyr (or rather 110Kyr) period into 95 & 125 Kyr periods, and splits the 55Kyr second harmonic into 51&59 ~ 54. The ~100Kyr periods appear or not, depending on whether Barbarossa is precessing or not. Thus because of some unknown physical interaction, Barbarossa's and Earth's spins appear symmetrically in the first factor of my augmented formula.

[Update March 28, 2009: In an early Icarus article, Oepik rightly complained that it's hard to know whether the match is significant, when a theory like Milankovitch's generates several periods. On the other hand, in making my case I should show every match. The Greenland GISP2 ice cores (Stuiver, Quaternary Research 48:259+, 1997; p. 264) show a 1470yr 18-O cycle approximately corroborated by other studies, and ~10x bigger before the Holocene, than now; using the precession period (25831.7yr) corresponding to the mean obliquity during the 41,000yr Milankovitch cycle, and my presumed Barbarossa anomalistic year (6341.5yr) in the notation above, y+2*(x+4*y)=1/1506yr, matching 1470. (When the frequencies x and 4*y interfere, the beat frequency is x-4*y and the carrier frequency is x+4*y.) Also, y+(x+4*y) & y-2*(x+4*y) are 1/2847 & 1/1705yr, resp., roughly matching the period of Dansgaard-Oeschger events, 2000-3000yr (Bond & Lotti, Science 267:1005+, 1995). If it makes a difference, whether some special timed point on Barbarossa's orbit, is aligned with an Earth solstice or with an equinox, then there should be the period y+(x-2*y)=1/8405yr; this matches the period of Heinrich events, 7000-10000yr (Lott & Bondi). ]

Presumably Barbarossa has a nearby moon, Freya, of ~0.0001 solar mass, at ~0.1 AU. If Barbarossa were just like Earth, Freya would cause Barbarossa's spin to precess in 26Kyr*3.2(Sun causes 1/3.2 of Earth's precession)/0.0001 * 0.1^3 = 800Kyr. The main moon, Frey, has been observed on four sky surveys; its orbit is eccentric, e = 0.6 (and the c.o.m. implies it has 0.0002 solar mass). Likely Freya is eccentric too. Its inclination would vary (Kozai phenomenon) conserving its Tisserand parameter. The Tisserand parameter involves semimajor axis, eccentricity and inclination. The semimajor axis is conserved to second order (progressively conjectured and proved by Lagrange, Poisson & Tisserand) but e and i teeter erratically between big eccentricity with small inclination, and vice versa. When i is small, Barbarossa doesn't precess.

Barbarossa may well be Earth size, but its mass is ~3600x more. If it spins with 60x the frequency, it has the same shape as Earth because 60^2=3600. It would have 60x more angular momentum per unit mass then, so Freya would need to be 60x more massive, or 4x closer (4^3=64) or some of each. If Barbarossa bulges 8% (similar to Jupiter, 6%, or Saturn, 10%) instead of 1/300 like Earth, it needs to spin yet sqrt(8/(1/3))=5x faster (P=24*60/60/5 = 5 min) but, with 25x the bulge, Freya can be 25/5 = 5x less massive (e.g. 0.0012 solar mass at 0.1 AU).

Using Paul Wesson's constancy of J/M^2, an Earth-size Barbarossa with the same "J0" (mass profile) as Jupiter would need to spin with 1000x the frequency, i.e. P=10hr/1000=36sec, which is far beyond any stability limit. Barbarossa, like the Sun, must have given most of its angular momentum to its satellites.

Barbarossa is like the Sun's binary pulsar. Taylor's 1995 pulsar catalog shows that 39/45 binaries have e<0.3 but 6/45 have 0.6<e<0.9, so Barbarossa conforms in eccentricity.

Worley's 1983 visual binary catalog (N=933) shows that (lumping all spectral types) the eccentricity histogram doesn't drop off much until e>0.65 (Barbarossa = 0.61 for its solar orbit, and ~0.6 for its binary orbit with Frey). Aitken, "The Binary Stars", gives for double stars with Type G primaries (N=54) ave. e=0.52, ave. P=84yr. Worley's catalog lists only two double stars with Type G primary and Type M (the closest I can come) secondary: these have e=0.78, P=693yr, and e=0.90, P=2205yr.
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Joe Keller

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Posted - 20 Mar 2009 :  15:06:10  Show Profile  Reply with Quote
(email sent 19:01h UT March 20, 2009)

To: Vice President Albert Gore (ret.), Scheduling Requests,

cc: editor, "Atlantis Rising"; also posted to messageboard, (Dr. Tom Van Flandern, founder); & interested members of Lowell family

Re: Scheduling Request

Dear sirs:

I wish to schedule one or two of Mr. Gore's scientific advisors to come to my house to visit with me about global warming. In two years of research, I have discovered that imminent climate change will be even more drastic, than the projected change of which Mr. Gore has warned with such dedication.

My recent letter about my discovery was rejected immediately by about a dozen relevant scientific journals, with neither peer review nor any reason. The exception was the editor of "Icarus", who complained that my letter was too short, but was unwilling to correspond further; I supposed he was "giving me the runaround".

A friend warned me not to "lead with my credentials", but otherwise you likely will not read further. I was graduated from Harvard College, B. A., c. l. in (pure) Mathematics, 1977. Recently I worked part-time for a year under an NSF grant, doing the math and Fortran programming for a graduate/faculty Engineering group at Iowa State Univ., whose leader got a statewide award for that project. I mention these achievements only to make it plausible that I might make the discovery of which I am about to tell you:

In 2007 I discovered Percival Lowell's "Planet X".

[ It is perhaps the size of Earth, but there is much indirect evidence that it is very cold, partly "gravitationally collapsed", with about 10x Jupiter's mass. Its orbit is moderately eccentric but never comes near Earth, and is now slightly beyond 200 A. U., slightly south of the constellation Leo. A novel astrophysical theory of mine, had localized this object, Barbarossa, to within a few degrees, so I was able to search the online photographic sky survey plates until I found Barbarossa (named from the prologue to a novel by Berry Fleming) on all four of the red and "optical infrared" band plates. I found fewer than 100 starlike candidate objects in my searching, so it's unlikely that these four would chance to lie so perfectly on an orbit.

[ I find Barbarossa on none of the four relevant blue band sky surveys. In the prospective astrophotographs I have persuaded amateurs and institutions to take (none with telescopes bigger than 17 inch) the longest, clearest exposures with the biggest of these telescopes, show Barbarossa at about the right extrapolated coordinates, but too faint to convince mainstream astronomers, who perhaps expect too much of small telescopes with CCD cameras and data-wasting "stacking" image processing. Details are posted on Dr. Van Flandern's messageboard under my name, Joe Keller.

[ According to current astrophysics, Barbarossa should have practically no direct effect on Earth, but might influence comets. Barbarossa might influence Earth through a new, non-gravitational force, such as the unknown force which causes millisecond pulsar decelerations (as observed from Earth) to cluster near the value of the Hubble parameter. ]

This month, I discovered that Barbarossa's perihelia almost coincide with the promulgation of the Gregorian Calendar, and before that, with "Julian Day Zero". In the 16th century AD, scholars such as Pope Gregory XIII, Christoph Clavius and Joseph Scaliger pursued ancient "Hermetic knowledge". An estimated 90% of Hellenic literature was lost with the fall of Classical civilization. Also one might, like Giordano Bruno, be burned at the stake for saying too much. It seems that nonsensical "cover stories" were provided, both for the urgency of Gregorian calendar reform, and for the choice of JD 0.

The Mayan "long count" calendar begins in almost the same year as Egyptian dynastic chronology. A physically significant point on Barbarossa's orbit will occur within a few days of the Dec. 21, 2012 end of the "13th pik", i. e. "long count" cycle, said on Monument 6 at Tortuguero to be the "descent" of "Bolon".

Ice Age and warming cycles (Hays, Science 194:1121+) have been attributed to low-amplitude astronomical "Milankovitch cycles" of similar periodicities, but incalculable positive-feedback mechanisms must be supposed to account for the magnitude of the Ice Age changes. Alternatively, the Milankovitch cycles themselves might be effects, not causes. This week I found that the "beat" between Barbarossa's orbital period, and Earth's precession quarter-period, or the second harmonic of the beat, when multiplied by a sinusoid in Earth's precession period, yields six frequencies, four of which are the same as the four climate change frequencies found by Hays.

My sky survey "Barbarossa" identifications imply Barbarossa's orbital period is about 6340 yr. The presumed "Hermetic knowledge" placed into the calendar by Pope Gregory XIII and by Joseph Scaliger, as obvious clues, implies a period of 6294 yr. The best simple fit to Hays' climatological periods, occurs for a Barbarossa period of 6320 yr.

Joseph C. Keller, M. D.
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Joe Keller

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Posted - 24 Mar 2009 :  17:17:31  Show Profile  Reply with Quote
Surprising Accuracy of the Periods

My computer program uses the four sky survey detections to find 6340.0yr for the solar orbital period of the Barbarossa system's c.o.m. The ultimate accuracy limit of this approach, is ~0.5" / 0.1 radian * 6000yr = 2mos.

Another approach is to accept Brauer et al's German lakebed chronology (which the popular press reported in 2008, had been refined to, exactly 12679yr prior to 2008AD) for the sudden onset of the Younger Dryas; and to accept the 2012 Mayan calendar date as "Hermetic knowledge" because, according to remaining historical records, not until 16th century AD Europe (or possibly 12th century AD India which, I deduce from the Wikipedia article, possessed an accurization of the Hellenic measurement of equinox precession) was the tropical year well enough quantified, to admit a calendar which reliably ends 1500 years later on a solstice. In this approach, the disaster interval is (12679+(2012-2008))/2 = 6341.5yr.

A third approach is to accept my computer program's latest Barbarossa perihelion, 1569AD (which should be more accurate, than the program's value, of the period); and to accept as Hermetic knowledge, Joseph Scaliger's placement of JD 0, 6281yr prior to that perihelion, as though secretly basing the astronomical calendar on Barbarossa, much as the Gregorian calendar reform had moved Earth's perihelion to near New Year's. In this approach, Scaliger's 6281yr period is corroborated by climate time series analysis, which in my best effort (see above) gives a period of 6278yr.

These approaches can be reconciled:

1. Keller's sky survey/computer fit period, 6340yr, is Barbarossa's sidereal year.

2. The German "Younger Dryas" / Mayan calendar period, 6341.5yr, is Barbarossa's anomalistic year.

This amounts to perihelion advance of 5 arcmin / period. Adapting the apse precession formula of the last section of Roxburgh, Icarus 3:92+, 1964, I find that a second Barbarossa of comparable mass and major axis to the first, would give the 1/r^4 time-average gravitational force term needed for this. Two Barbarossas would restore the (3::1)::(2::1)::(1::1) outer solar system precession ratio (see above) and if opposite, might cancel the Sun's acceleration in interstellar space vis-a-vis pulsars.

3. The Scaliger / Buoncompagni period, presumed 16th cent. AD Hermetic knowledge, accurized at its latter terminus to Keller's (sky survey based) perihelion date, is Barbarossa's tropical year, 6281yr. It is corroborated within 3yr, by climate time series period analysis.

Time series analysis (see above) suggests that much of the time, Barbarossa's (variable) precession period is 790Kyr. A sidereal period of 6340yr becomes a mean tropical period of 6281yr, when the precession period is 680Kyr; slower precession suffices if the tropical period is with respect to an equinox or solstice on the farther portion of Barbarossa's orbit.

A brightening of Barbarossa, like a cataclysmic variable, at a certain season of Barbarossa's year, would have let ancient astronomers know its tropical year w.r.t. that season. Barbarossa's orbital radius at that season, would change little during civilized history, because of Barbarossa's ~700Kyr precession period. This tropical year would become Hermetic knowledge which somehow influenced Scaliger to set JD 0 appropriately.

On the other hand, drastic Earth climate change seems to correlate with Barbarossa's precise orbital position at some point not far from the outgoing latus rectum. The interval between occurrences of this position, is Barbarossa's anomalistic year.
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Joe Keller

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Posted - 25 Mar 2009 :  23:21:52  Show Profile  Reply with Quote
(March 25, 2009)

On March 6, 2009, the same philanthropist who arranged the February 16 photo, arranged another photo with the same telescope. The March 6 photo is 50 stacked 30sec ( = 25min) clear filter exposures, apparently in quick succession; anyway the start was 05:08 UT & midpoint 05:22:30.

I looked for Frey at the linear extrapolation of Frey's positions on the philanthropist's (midpoint 05:16) 2/16 photo (200+ min, red filter, >16 inch aperture) and Genebriera's ~01h 2/23 photo (20 min, red filter, 16 inch aperture, Tenerife)(see coords. above). The predicted Frey position is

11:26:45.0, -9:18:36

Indeed an object is detected at

11:26:44.7, -9:18:30 pixel coord. (112, 415)

The discrepancy is about the net error of the linear extrapolation (which includes Frey's binary orbital motion).

This photo lacks built-in coordinates but does have built-in pixel "counts". When I use the "histogram equalizer" in the "fv" viewer, the higher the "count" the brighter the pixel, within a given small area. I chose the brightest 3x3 pixel array which contained the brightest pixel in the area (I don't know the "seeing" for this photo, but the U. of Iowa in S. Arizona typically has 2.5" Full Width Half Maximum on a clear night). I compared these 9 pixels to the surrounding 16 pixels with Student's "t" test for unequal variance (Dixon & Massey, Intro. to Statistical Analysis, 2nd ed., Sec. 9-3, bottom half of p. 121 continuing onto p. 122; Table A-5, p. 384. Snedecor, Statistical Methods, 5th ed., Table 2.7.1, p. 46). The t value was 2.6, 23 degrees of freedom; p<1%, 1-tailed.

I used the brightest pixel as the definitive position. I divided the 24 micron pixel size by the focal length, to get the angular pixel size of 1.7", then counted pixels from a nearby reference star on the sky survey. Mainly because the photo is somewhat rotated, over a long oblique distance the error from this sometimes was almost 20%, so for Frey I used a reference star only (30,16) pixels away, i.e, error < 10". For Frey, I used a correction factor to lessen even this small error, by testing true vs. pixel, EW & NS distance, over a long distance in roughly that direction on the photo; for Barbarossa (see below) I skipped this last step because its reference star was only (5,12) pixels away.

The Barbarossa that I found on this photo, is ~1' NW of its predicted position, retrograde along the orbital path. (The 1997 sky survey Barbarossa also was ~1' retrograde of predicted, based on only the 1954 & 1986 positions, according to Kepler's 2nd law.) The predicted c.o.m. position according to my newest program (posted above) is

11:26:24.0, -9:14:32

Frey's position and the 50:1 mass ratio let me predict Barbarossa itself at

11:26:23.6, -9:14:27

The best Barbarossa candidate is found at

11:26:19.8, -9:13:48 pixel coord. (291, 210)

This is 68" retrograde along a 35deg slope (Barbarossa's orbital slope is 30deg). The same t test procedure as for Frey, gives t=5.4, 23 d.o.f.; p<0.05%, 1-tailed, for the significance of the detection.

A catalog star near Barbarossa, had R2 mag +19.33, and was unusually faint (yet B2 mag 20.16, much brighter than I estimate for Barbarossa or Frey, however) on the 1983 Blue sky survey, for a star this bright on the 1987 Red sky survey. On a clear filter CCD photo, such a star might not appear much brighter than Barbarossa or Frey. Its t test, using the procedure above, was 6.5 with 23 d.o.f.

The Barbarossa on this photo is inconsistent with those detected on Riley's March 29, 2007 photo; the philanthropist's Feb. 16, 2009; or the U. of Iowa Feb. 23, 2009. All three of these older detections are consistent with each other, and about 1' S of my latest predictions for their dates.

Update March 26:

The large plutino, Orcus, has been called the "anti-Pluto" because of its similar size and similar, but roughly diametrically opposed, orbit. There might be an "anti-Barbarossa" or second Barbarossa, as I discuss above.

All three recent Frey detections - the philanthropist's 2/16/09 & 3/6 photos, and Genebriera's 2/23 photo - show a light distribution sloped several arcsec NE-SW. I hope to find the statistical axes of these three distributions (corrected for the slight rotation of the photos) to show that they must be the same object. My latest estimate of the Barbarossa::Frey mass ratio, is 0.9791::0.0209. So Frey would have ~0.0002 solar mass, about the same as Saturn's 0.0003.

Saturn's rings (typically chunks of water ice) are said to be not only much brighter, but also fundamentally different qualitatively from the rings of the other giant planets. Frey, like Saturn, might have just the right mass to have such rings.
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Joe Keller

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Posted - 26 Mar 2009 :  15:21:24  Show Profile  Reply with Quote
(email just sent today, March 26, 2009)

To: Prof. Mike Brown, Cal Tech

Dear Prof. Brown:
I challenge you to a public debate! I've discovered Lowell's "Planet X", which I have named Barbarossa. Would you be willing to take the other side, that there is no such planet?

Dr. Neil Tyson already has turned down my offer of debate. I hardly can ask Dr. Phil Plait because I've been censored from his messageboard.

Joseph C. Keller
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Joe Keller

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Posted - 27 Mar 2009 :  18:57:54  Show Profile  Reply with Quote
Preliminary report:

Paleotsunamis haven't been completely cataloged, but western Australia was hit by two, in approx. 6220 & 6250 BP (these were the biggest to hit W. Australia in the last 10Kyr, until one or more bigger ones did hit it c. 1500 AD). One of these might have been the one that hit New South Wales also, ~6500 BP, sweeping maybe 10km inland in a delta region.

An ice core from 19840ft in the Peruvian Andes, showed that the fourth biggest dust increase in the last 10Kyr, occurred 6300 BP (the graph implies accuracy only to the nearest century). Though this dust increase was only the fourth biggest, it lasted 400yr, vs. 100-200 yr for the three that had higher maxima. This same ice core purports to show, by 18-Oxygen levels, that the maximum temperature in the last 10Kyr occurred 6400-6500 BP, though the rise and fall were gradual. The article says that the modern El Nino pattern began c. 5000 BP. By the "magnetic susceptibility" test, the fastest qualitative change in loess formation in China in Holocene times apparently was ~6020 BP as I convert the 14-C date.

Sea level at the South China coast has fluctuated, but the largest rate of change in Holocene times, was the decline between ~6350 - ~6050 BP (investigator's dates, not mine). The oldest beach sediment found at the Syrian coast is 6430 +/- 130 BP.

A big forest fire occurred in Italy 6150 +/- 190 BP (I used a chart of Blaauw's to convert the author's 14-C dates). Also there was massive sedimentation at about this time and also the time of onset of the Younger Drayas; those were the two main times.

All this seems to be evidence that the Younger Dryas event (12680 BP according to the German limnology) had a little brother event at 6340 BP. This indicates another such event soon, maybe in 2012.
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Joe Keller

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Posted - 28 Mar 2009 :  17:28:31  Show Profile  Reply with Quote
Complete Report on Geological Cycle Ending 2012

I predict for 2012, an Earth change which recurs every 6341.5yr (this seems to be Barbarossa's anomalistic period; Barbarossa's sidereal period, from the four sky surveys, is 6340.0yr). It will be the biggest Earth change in recorded history. The acute phase will last ~1000yr.

Last time it happened, it revolutionized society. The proto-Indo-European language started in the 5th millenium BC, indicating a population bottleneck. The great agricultural civilizations started, or restarted, in the 4th millenium BC. They were obsessed with astronomy.

The penultimate time it happened, coincides with Plato's (Critias-Solon-Egyptian) date (~11500 BP) for the destruction of Atlantis (a history which mingles the relatively recent story of the Thera eruption and tsunami and Hellenic conquest of Minoan civilization, with the older story of a large continent beyond the Atlantic and a destroyed ocean-crossing civilization in that general direction); and better with the medium Edgar Cayce's date ("10500 BC" = 12511 BP in 2012) for the final destruction of Atlantis, which followed a partial destruction 7500yr earlier, according to Cayce's "psychic reading". The Earth change caused the well-documented "Younger Dryas" (named for a tundra wildflower then growing in Scandinavia) said by most experts to begin ~12900BP, but the most precise onset time, a sudden climate change in Germany determined by limnology, from varves, is 12683 BP ( = 6341.5 * 2 )(A Brauer et al, Nature Geoscience 1:520+, 2008). (I express time "BP" = Julian years before 2012, which will be our "present" soon enough.) Published archaeology studies say that all the big animals in N. America, larger than the bison, became extinct during the ensuing 1300yr "YD" period, which resembled a relapse of the Ice Age. Their extinction is said to have happened in < 200yr, possibly instantly. The reason for their extinction is unknown; they throve during the previous Ice Age and were well adapted to those conditions. Furthermore southwestern N. America then had a temperate wet climate. Yet the "Clovis point" culture, technologically if not racially similar to a W. European culture at that time, became extinct in N. America during the YD period, though perhaps evolving into the "Folsom" culture. Lacking firearms or railroads, the Clovis people hardly could have hunted the big game to extinction in < 200yr; the Amerindians did not exterminate the bison, moose or bear despite millenia of sometimes wasteful hunting. There is " evidence at Monticchio [lake in Italy] of a Younger Dryas-like oscillation during the penultimate deglaciation" (Brauer A et al, Proc. of the Natl. Acad. of Sciences of the U.S.A. 104:450+, 2007).

Below, I'll present evidence that drastic Earth change also happened 6341.5 BP, though it differed from the Younger Dryas. At the end of this article, I'll average the available dates and see how close I come.

Paleotsunamis haven't been completely cataloged, but western Australia was hit by (?!) two, in 6231+/-53 & 6261+/-55 BP (Scheffers, Earth & Planetary Sci. Letters 270:137+, 2008)(I assume Scheffers follows the usual practice of giving 95%, i.e. +/- 2-sigma intervals). These were the biggest to hit W. Australia in the last 7Kyr, until one or more bigger ones did hit it c. 1500 AD. One of these might have been the one that hit New South Wales also, "~6500 BP" (Bryant & Nott, Natural Hazards 24:231+, 2001; accepted in final form 2000), sweeping maybe 10km inland in a delta region; though some tsunamis could be matched to comet strata, here there is "no information about the cause or origin" (Dominey-Howes, Marine Geology 239:99+, 2001; Sec. 3.1.1). Scheffers lists ten W. Australian paleotsunamis between 0 & 5000BC (his series' start; see Fig. 9) but these are clustered into only eight centuries (Table 1). Dominey-Howes' older list has only two for all of Australia in the same interval. The chance that any of the 50 centuries involved would have a tsunami from each list, is a priori about 8*2/50 = 32%. Only one century has a tsunami from each list; they affected opposite coasts of Australia but their best-estimate dates may differ insignificantly, only 18yr.

[Detailed calculation of tsunami chronology: Scheffers corrects his radiocarbon dates for the two (?) tsunamis in W. Australia, to ***4220 +/-53 BC & ***4250 +/-55 BC (not BP) where I've assumed that in Table 1 he followed the usual practice of listing the +/-2*sigma interval. Scheffers calibrated his dates from 14-C to calendar, including an ave. 395yr reservoir correction.

[Bryant's New S. Wales figure is problematic. Bryant included the mandatory, for marine samples, 13C/12C correction, but did not calibrate, nor make the reservoir correction, which he said was 450yr for his locale. Bryant also cautions, "Because older material can be incorporated into a deposit, the ages may not represent the actual age..." (Sec. 4). He based his date on a histogram of eight samples (Fig. 10); I'll use the youngest of these, whose uncalibrated value is 5700 +/-(100/sqrt(3)) (histogram error). By analogy with Scheffers' calibration & reservoir correction for his similar 14-C dates, this becomes 4190 BC +/-78 (sum of independent, histogram and Scheffers' errors). I must add 55 for the differing reservoir corrections, and 8 for the different dates of the papers, getting now ***4253 BC.

[ The mean of the three dates, weighted by 1/variance, is 4238 BC = 6249 BP. The uncertainty (one sigma) is approx. 38 yr, summing the independent errors within and between terms. This puts 6341.5 BP at 2.4 sigma, and the alternative period, the presumed Barbarossa tropical year 6281yr, at 0.8 sigma. ]

This shows that the Pacific and Indian Oceans had rare simultaneous large tsunamis c. 6300 BP. There is much more evidence than this, of sweeping Earth changes at this time.

An ice core from 19840ft on the highest peak in the Peruvian Andes, showed that the fourth biggest dust increase in the last 10Kyr, occurred 6317 BP (the graph implies accuracy only to the nearest century)(LG Thompson et al, Science 269:46+, 1995). Though this dust increase was only the fourth biggest, it lasted 400yr, vs. 100-200 yr for the three that had higher maxima. Though the biggest eruptions were at other times, volcanic eruptions were abnormally frequent worldwide then. By the "magnetic susceptibility" parameter, the fastest qualitative change in loess in China in Holocene times occurred 6029 BP as I convert the 14-C date using Blaauw's chart (see below) and correct for the date of the article (Y He et al, Quaternary Res. 61:52+, 2004, rec'd 2002; Fig. 3).

By far the most frequent depositor of tephra on Kamchatka during the Holocene has been Mt. Avachinsky. Avachinsky's biggest eruption during the Holocene was ~6286 BP, ~4 cu. km (Quaternary Research 59:36+, 2003).

The American analog of Avachinsky, is Glacier Peak, Washington state. Though the 6th millenium BC Mt. Mazama eruption was much bigger (est. 50 cu. km.), Glacier Peak has erupted often during the Holocene; its biggest eruption, or rather series of eruptions, during the Holocene, was the "Dusty Creek Assemblage" "5100-5500 BP"; even bigger eruptions occurred "11250 BP" & earlier (Beget, Quaternary Research 21:304+, 1984; Table 1). These anachronistic 14-C dates must be corrected as 14-C dates now are; Beget gives "6900 BP" for Mt. Mazama though the dating I find in recent journals, is 7600 +/- 100 BP. The correction from 14-C to calendar date, at least back to 4500 BP is, to within about +/-30yr error, the same as multiplication by 9/8 (Blaauw et al, J. Quaternary Sci. 19:177+, 2004; "wiggle match" chart). So the Dusty Creek Assemblage occurred 5815-6215 BP, by extending Blaauw's correction. This roughly matches both the start and end of the Andean ice core dust dates 5917-6317 BP (see above). (With Blaauw's correction, though extrapolation of it might not be accurate, the earlier big eruption of Glacier Peak becomes 12684 BP, only a year different from Brauer's starting date for the Younger Dryas. However, the volume of even this Glacier Peak eruption, apparently was less than Mt. Mazama, and Mazama was only twice, Krakatoa's 1883 eruption of 21 cu km. So it seems that volcanic eruptions either worked as a team to change climate, or eruptions were symptoms not causes.)

This same Andean ice core purports to show, by 18-Oxygen levels, that the maximum temperature in the last 10Kyr occurred 6417-6517 BP, though the rise and fall were small and gradual. (The article says that the modern El Nino pattern began c. 5017 BP.) Cave calcite from NE Iowa confirms the temperature change by showing that near this time, 18-Oxygen & 13-Carbon simultaneously underwent their fastest rate of change (Dorale et al, Science 258:1626+, 1992), changing rapidly for 300 & 100 yr, resp.; the Uranium-Thorium date is 500yr younger, but this could be due to an absence of correction, for the 234-U to 238-U ratio.

Sea level at the South China coast has fluctuated, but the fastest rate of change there in Holocene times, was the decline between ~6360 - ~6060 BP (investigator's dates, read from his chart)(He, op. cit., Fig. 4). The oldest beach stratum found at the Syrian coast is 6432 +/-58 BP (Sanlaville et al, J. of Coastal Research 13:385+, 1997, Table 1; I assume the investigator reports 2*sigma range, which I convert as always to 1*sigma). The ocean highstand at Australia, an especially inactive continent, was 6284 BP (Eisenhauer, Earth & Planetary Sci. Letters 114:529+, 1993). On p. 545 Eisenhauer says, "...the apparent sea-level rise at Barbados [West Indies] after about 6000 BP is probably...due to spatial changegs in the Earth's geoid...".

From 12Kyr to 6Kyr ago the Ice Age glaciers receded and the sea rose quickly. This stopped 6Kyr ago. Since then, Australia and (more or less) Asia slowly have risen relative to the ocean, and America slowly sunk. Something is being adjusted.

A big forest fire occurred in Italy 6148 +/-100 BP (again I used Blaauw's 9/8 rule to convert the investigator's 14-C dates). There were two episodes of massive sedimentation at the site: one at about this time, and one at 13247 +/-95 BP, near the onset of the Younger Dryas (Giraudi & Frezzotti, Quaternary International 25:81+, 1995).

Last but not least, anomalous geologic activity apparently occurred at Cape Liptrap, on the passive Australian coast, 6275 +/-54BP (my calibration, following Blaauw, of the investigator's 14-C date)(Sarah M. Flanagan, "Low Lying, Late Quaternary, Marine Terraces of Cape Liptrap, Australia", Smith College undergraduate research, 2003 or later, online at; Conclusions). Though possibly contradicted by a subsequent refereed publication (Gardner T et al, Quaternary Sci. Reviews 28:39+, 2009), Flanagan found that part of the terrace was buckled upward by 1m. Gardner dated the same terrace (another part of it?) 5988 +/-53 BP (Gardner's calibration; Table 1) and said this terrace "has not been displaced" (Gardner, sec. 4.3). Maybe Flanagan not only didn't calibrate, but didn't apply the "reservoir correction", typically 420 yr for Australian beaches. On the other hand, maybe Flanagan not only found buckling Gardner missed, but also found that the buckling occurred on the older part of the terrace only.

All this seems to be evidence that the Younger Dryas event (12683 BP according to German limnology) had a little brother event at ~6341.5 (6281 ?) BP. This indicates another such event soon: in 2012.

Hellenic astronomers knew how to measure the precession of the equinoxes. Alexander the Great established contact with India; the Romans continued the contact by sea (there still is a colony of Indian boatbuilders in Arabia). According to the figure given on Wikipedia, 12th cent. AD Indian astronomers knew the equinox precession accurately enough to predict a solstice to the day, a millenium in the future. Likely either, a somewhat more accurate measurement by Hellenic astronomers survived in Indian literature though lost to Europe, or Indian astronomers improved on the Hellenic measurement by lengthening the interval of observation.

Aided by Hellenic or Indian knowledge, Mayan astronomers could have set their "long count" to end on a solstice. The start date of the long count is an obvious reference to the Old Kingdom of Egypt.

More problematic, is how the makers of the Mayan calendar, would know Barbarossa's orbital period. Maybe not the orbital period, but the two latest disaster dates, were among Atlantean knowledge now lost. Alternatively maybe Barbarossa brightened at about the time of the latest disaster (4330 BC if the 6341.5yr period applies to Dec. 2012; 4270 BC if Scaliger's 6281yr tropical Barbarossa period applies instead) and astronomers with Keplerian knowledge estimated the period from the angular speed and acceleration.

(Addendum the following day, March 29, 2009)

My dates and uncertainties herein differ slightly from the authors', because I:

1. When necessary, "calibrated" 14-C yrs to calendar yrs, slightly extrapolating the linear relationship from Blaauw's chart.

2. Added a few years for the difference between the authors' Present and 2012 Present.

3. Sometimes read dates from graphs, judging the uncertainty myself; or used the uncertainty that seemed to be implied by the graph, sometimes in conjunction with other data.

4. Converted the usual +/-2sigma (95% confidence) range to +/-1sigma.

5. When I had to do the calibration, I multiplied the uncertainty by the same factor as in #1, and added to it (Pythagorean addition) the approximate 1sigma uncertainty on Blaauw's graph, i.e. +/-30yr.

The results of this careful work, are these eleven dates:

1. Bicoastal non-cometary Australian paleo-megatsunami: 6249+/-38 BP
2. 400 yrs of dust begins, Peruvian Andes ice core: 6317+/-29
3. Mt. Avachinsky's biggest eruption in Holocene: 6286+/-34
4. Glacier Peak's 400yr Dusty Creek tephra begins: 6215+-/44
5. Fastest change, magnetic suscept., Chinese loess: 6029+/-44
6. Slow worldwide cooling begins, Andean ice core: 6417+/-29
7. Fastest change, S. China sea level (dropped 300yr): 6360+/-29
8. Oldest Syrian beach deposit: 6432+/-58
9. Australian sea level's slow drop starts: 6284+/-29
10. ? Anomalous buckling, Cape Liptrap, Australia: 6275+/-54
11. Italy: fire & main Holocene sediment: 6148+/-100

The simple arithmetic average of these dates is 6274 BP (counting from 2012) with standard error of the mean, +/- 35 (as always, 1 sigma). Weighted by the reciprocal of sigma squared (textbook method) the weighted mean is 6299 with standard error +/- 32.

These eleven dates are normally distributed (I used the formulas in Snedecor, Statistical Methods, 5th ed., secs. 8.5 & 8.6, pp. 199-203; interpolation in Table 2.7.1, p. 46). The kurtosis is equivalent to t(infinity) = 0.633, p=53%, 2-tailed; i.e. 53% of normally distributed sets of 11 numbers will have more kurtosis than these. The skewness is equivalent to t(infinity) = -1.103, p=28%, 2-tailed; i.e. 28% of normally distributed sets of 11, are more skew. Discarding the Chinese loess date, doesn't help, because then the skewness becomes about equally big but positive.

So, these 11 dates are about as normally distributed as I can expect by random chance. Likely all of them report one and the same phenomenon. They are not a mixture, of dates reporting the primary event, and dates reporting subsequent processes.

Edited by - Joe Keller on 03 Jan 2010 11:27:53
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Joe Keller

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Posted - 31 Mar 2009 :  19:57:43  Show Profile  Reply with Quote
(email sent March 31, 2009)

Dear Sir:

It seems you didn't even read the first sentence of my email. I didn't ask to visit Mr. Gore. I asked to visit one or two scientists who advise him.

Joseph C. Keller, M. D.

Date: Tue, 31 Mar 2009 14:03:24 -0500
Subject: Re: New Climate Change Information: Request Interview with Experts

Dear Joseph,
Thank you for your kind request. Unfortunately, Mr. Gore's schedule is extremely overbooked and we're unable to offer any availability. With Mr. Gore's travel and work schedule booked fully throughout the year, it's very difficult to decline invitations such as yours, but it's an unfortunate inevitability of the growing influence of the climate crisis message and the demand on Mr. Gore's time. We do apologize, but thanks for your interest.

Bill Huskey
Office of The Honorable Al Gore and Mrs. Tipper Gore
2100 West End Avenue
Suite 620
Nashville, TN 37203

On 3/20/09 2:01 PM, "Joseph Keller" <> wrote:

To: Vice President Albert Gore (ret.), Scheduling Requests,

cc: editor, "Atlantis Rising"; also posted to messageboard, <> (Dr. Tom Van Flandern, founder); & interested members of Lowell family

Re: Scheduling Request

Dear sirs:

I wish to schedule one or two of Mr. Gore's scientific advisors to come to my house to visit with me about global warming. ...
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Joe Keller

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Posted - 31 Mar 2009 :  20:07:50  Show Profile  Reply with Quote
How to Look for Frey

The three known detections of Frey this year, all show the same elongation, of a ringed planet. The best way to confirm the existence of the Barbarossa/Frey system, for anyone who has access to a big telescope, is to extrapolate Frey's geocentric coordinates quadratically:

Frey detection, midpoint 05:16 UT Feb. 16, 2009:
RA 11:26:59.0 Decl -9:18:47.5

Frey detection, midpoint 01:26 UT Feb. 23, 2009:
RA 11:26:53.7 Decl -9:18:43

Frey detection, midpoint 05:23 UT March 6, 2009:
RA 11:26:44.7 Decl -9:18:30

The biggest apparent motion is Earth parallax, next biggest is Frey's binary orbit around Barbarossa, least but still considerable is Barbarossa's solar orbit. Extrapolation encompasses all these, and will be useful during the few remaining weeks Frey may, in the northern hemisphere, be seen on the meridian during astronomical darkness.

On the philanthropist's March 6 photo, the Frey image at the expected extrapolated position, was significant at t=2.62, p<1% 1-tailed. Yesterday by the same method (brightest 3x3 1.7" pixel bloc vs. surrounding 16 pixels) I found that on the philanthropist's Feb. 16 photo, Frey's image is significant at t=2.61. The 2/16 photo was a 200+ minute Red filter exposure, the 3/6 photo 25 min Clear. The philanthropist told me that the astronomer told him that the two exposures were equivalent for his camera [assuming yellow light?]. Wratten 25 sometimes is used for astronomical Red; it requires 3 f stops in sunlight; 25 * 2^3 = 200. I think Frey is a reddish object, but if the CCD camera's red sensitivity is poor, the two exposures indeed might be almost equivalent.
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Posted - 02 Apr 2009 :  19:22:44  Show Profile  Reply with Quote
Preliminary report:

Beware "errors" (disinformation, sabotage) in the April 2, 1998 Nature article. The diagrams show that the Nabta stones mark an object rising and setting 9deg N of the EW line. This is what Barbarossa would do soon after 2012AD - 6340 (one orbital period) = 4329 BC. It agrees precisely with Barbarossa's rising and setting ~200 yr after that date, when it would be at its most southern ecliptic latitude.
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Joe Keller

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Posted - 03 Apr 2009 :  15:16:03  Show Profile  Reply with Quote
Full report: Nabta stones recorded Barbarossa outburst

Abstract. Despite suspiciously numerous publication or editorial errors in the 2 April 1998 Nature article by Malville et al, it appears that the Nabta megaliths (three collinear central megaliths, and outer Alignment V) recorded the rising and setting azimuths of Barbarossa approx. one Barbarossa orbit ago. Barbarossa might have periodic gravitationally powered infall brightening, resembling white dwarf nova cataclysmic binary variables of SU UMa type, but with longer period. Alternatively, Barbarossa might have brightened via an unknown force related to its effect on Earth at that time.

1. Gravitational infall brightening. How much gravitational infall would be needed to make Barbarossa as bright as a 100W bulb one km away? Let's assume Barbarossa is the size of Earth with 6000x Earth's mass. Earth's escape velocity is 11km/sec, so Barbarossa's would be 850km/sec. One kg per sec infall would give .5*(850*1000)^2 = 3.6*10^11 watts. If that's converted to visible light at the same efficiency as a 100W bulb, then we have 3.6 billion 100W bulbs at 200 AU distance, as bright as

3.6*10^9/(214*1.496*10^8)^2 = 3.5/10^12 100W bulbs @ 1km

If the mass of Luna gradually fell in, it could give Barbarossa that 100W bulb @ 1 km brightness, for

7.4*10^22 * 3.5/10^12 sec = 8000yr

If the mass of Barbarossa fell in (i.e. Barbarossa formed this way, and it's ongoing) that brightness could last 4 billion yr (really somewhat less at first, because at first the central mass would be less) which is the time since the beginning of the solar system. Maybe the infall is episodic, lasting, say, 400 yr per 6000yr orbit. Then when it's bright, it would be 15 100W bulbs @ 1 km, and at 1690 lumen per bulb, that's 0.002 lumen/m^2 (0.002 lux). Overhead full moonlight is ~1 lux. So during 400yr cataclysmic outbursts Barbarossa would be 6.7 mags dimmer than the overhead full moon, i.e. mag -12.6+6.7= -6.

More conservatively, if Barbarossa is only 0.01 solar mass (3000 Earth mass) and the infall occurs during 1000yr of the 6000yr orbit, the power would be (1/2)^2/2.5 as much, i.e. mag -3.5; if the present infall is 1% that, it's still mag +1.5, which is impressive enough for a nova, especially if chaotically fluctuating or flashing.

Alternatively, an unknown intermittent physical interaction between Barbarossa and the known solar system might cause geological change on Earth and brighten Barbarossa. Barbarossa's orbital energy is however ~1/400^2 its gravitational self-energy, thus insufficient to illuminate it for much of the previous 4 billion yr.

2. The Mayan God Bolon. The Mayan name "Bolon" resembles Latin "bolus" and Indo-European words of similar meaning like English "ball". The region of Barbarossa's light emission (not Barbarossa itself) might have been big enough ( >1 arcminute) to be discerned as a ball, hence the name. Associations of Mayan Gods or incarnations whose names include the word "Bolon", apparently include war, creation, "innumerable generations", lightening, and nine branches or colleagues (moons?).

3. Barbarossa's solar orbit and rising azimuth. My computer program, based on the four sky survey positions for Barbarossa & Frey, predicts the Dec. 21, 2012 winter solstice position (to this accuracy, the same as the 12h UT position) of the Barbarossa/Frey center of mass, as

RA 11:27:46.95 Decl -9:22:53.1

These are "barycentric" (i.e. known solar system barycenter excluding Barbarossa; at Barbarossa's distance, same as heliocentric +/- 1", so I'll say "heliocentric" when I mean "barycentric" to avoid confusion with the Sun-Barbarossa barycenter) J2000.0 coordinates. The geocentric position at that time is ~1/4 deg E of this, and generally is within 1/4 deg, mainly E or W, of the heliocentric position. Barbarossa itself is always within ~1 arcminute of the c.o.m.

Suppose Barbarossa brightens at this (Dec. 21, 2012) point of its solar orbit. The heliocentric Declination of this point, in the celestial coordinates of the equinox of date, one period (=6340.0 yr) before Dec. 21, 2012, is ("rigorous" formula, Astronomical Almanac 2005, p. B18) +12.09633 deg.

To arcminute accuracy, the azimuth effect of Earth's oblateness is negligible for low Declinations, because it is higher-order. To see this: stretch the z-axis by a factor 1+1/297, find the "stretch azimuth" for the "stretch Declination" using the perfectly spherical Earth, then shrink the z-axis by the same factor. The lowest-order error occurs because tan(theta) is not exactly proportional to theta, so the error is < 1/297 * 0.33*theta^3.

So, using the half-angle oblique spherical triangle formulas in the CRC Math Tables, the azimuth of rising (neglecting atmospheric refraction), for the Barbarossa/Frey center of mass, is 13.11 deg N of E. The spherical triangle is formed by Earth's N pole, the Nabta site 22deg30'29.7"N 30deg43'31.2"E (Malville et al, Nature 392:488+, 1998), and the sub-Barbarossa point 90deg from the Nabta site.

About 290 yr after 2012, Barbarossa reaches its most negative ecliptic latitude. Making first order corrections, the Declination, for equinox of date, of that point of the orbit, when previously attained (Earth's summer solstice aligned with Barbarossa then), would have been +12.10 - 1.13 (i.e. ecliptic latitude change) - 1.78 (i.e. net motion along southward-tending ecliptic) = +9.19. The corresponding azimuth of rising is 9.96 deg N of E.

4. Summary of evidence for Barbarossa's effect on Earth's climate. Not only the Mayan calendar, but also the dates of various geological changes associated with the Younger Dryas (two Barbarossa periods ago, c. 12600yr BP) and with the climate reversal of one Barbarossa period ago, c. 6300yr BP (which entailed the onset of the El Nino ocean current), suggest that Barbarossa will again interact with Earth beginning c. 2012 AD. The climatological harmonic frequencies I've found in the literature, are the same as the frequencies arising from the interaction of Earth's precession and Barbarossa's period (see my earlier posts to Dr. Van Flandern's messageboard at

According to Poisson's theorem (proved by Tisserand, it was the culmination of conjectures by Laplace and Lagrange) orbital period is approximately conserved when the other orbital elements are randomly perturbed. Meteor swarms with Barbarossa's period (e.g. Barbarossa's "Trojan asteroids" at the leading and trailing Lagrange points) would tend to maintain that same period even when perturbed into very elliptical sungrazing orbits. One especially big swarm might enter the inner Solar System every 6340yr (Barbarossa's sidereal period). This matches evidence of meteor strikes at the beginning of the younger Dryas (carbon layer of forest fires, nanodiamonds, iridium; see last night's "NOVA" episode on PBS) and also the ambiguous evidence of meteor strikes c. 6300 BP: Australian tsunamis, 400yr of increased atmospheric dust, increased activity by some frequently erupting volcanoes, and global tectonic readjustment evidenced by receding shores at Australia and perhaps Asia, with continued rising sea level, relative to the landmass, at Barbados.

Alternatively, the meteor strikes might be a minor or coincidental component. The main process might be a fundamental new physical force. Unlike the Sun's other big satellites, Barbarossa lies outside the "Kuiper Belt dropoff" at ~52.6 AU; at this distance, Pioneer 10's radio signal underwent a still-unexplained alteration. Apparent millisecond pulsar radial accelerations cluster near +H*c, the Hubble parameter times the speed of light. My most accurate estimate so far, says that Barbarossa's radial acceleration relative to the Sun, will equal -2*H*c, just a week before Dec. 21, 2012. (Barbarossa passed the outgoing latus rectum of its orbit in 2003).

5. Likely sequence of events at Nabta c. 6340 BP ("Present" defined as 2012). I gather that Nabta's construction has been dated at 6500-6000 calendar yr BP, by artifacts similar to those so dated at other sites. Some hearth charcoal (see Malville, Nature letter, 1998; p. 488) had 14-C date 5500 +/- 80 BP (where I've converted the presumed 2sigma given by Malville, to 1sigma format). By a slight extrapolation of Blaauw's chart (see previous posts) I convert this to (5500*9/8+(2012-1998)) +/- sqrt((80*9/8)^2+30^2) = 6202 +/- 95 (1sigma) BP relative to 2012.

If Barbarossa brightened (from its present Red mag +19) at 6340 BP, there would be some human response lag. Some geological phenomena persisted 400 yr, so Barbarossa might have remained visible at least until its greatest negative ecliptic latitude, 6340-290=6050 BP; as mentioned above, the azimuth of rising then was 9.96 N of E.

6. Publication and editorial errors in Nature article. There are so many crucial errors in the Nature letter as published, that sabotage or disinformation must be suspected. Nabta's longitude is given as W, not E.

The prominent horizontal & vertical distance scales on Fig. 1, imply a vert::horiz scale ratio of 5.86::1, according to which the slope of Alignments I, II, & III, as drawn, is 64deg N of E, not the ~26deg N of E ( = summer solstice sunrise azimuth) stated in the text and by other articles, investigators and groups. Assuming that the horiz & vert scales really are the same, then the slope as drawn is 19.51deg N of E (by ruler from the page of an original copy of the journal). The slope of Alignment V as drawn on Fig. 1, is -6.97deg (i.e. 6.97deg S of E). If the original map submitted by Malville was accurate, then the likeliest explanation is that it was compressed only slightly, vertically, in publication in Nature (changing ~26deg to 19.51deg), and that the printed scale is erroneous.

The text on p. 489 (last line) gives the azimuth of Alignment V as "126", i.e. 36 S of E, by inference but not by name. If the printed scale is believed, then the line drawn is indeed at azimuth 35.62 S of E; but if the printed scale is believed, then Alignments I-III aren't 26 N of E, they're instead 26 E of N.

7. The true azimuths of Nabta. Several other articles, mostly subsequent, have been published, mostly by Malville's group but also by at least one other group. I've been unable to see anything but abstracts of these, because they are in journals not on the shelf here nor even available online through the rather extensive services to which Iowa State Univ. subscribes. Many of these journal articles or other publications are not indexed by "Web of Science" (online Science Citation Index). So, I must find the true azimuths entirely from Malville's 1998 Letter to Nature.

Malville states that the azimuths of Alignments I-III are 24.3, 25 & 28; presumably this is N of E, because Malville (p. 490) gives the refraction-corrected summer solstice sunrise as 63.2 E of N = 26.8 N of E. The mean of Alignments I-III is 25.77 +/-1.13 Std Error of Mean, but the slope in Fig. 1 is 19.51. So, the slope of Alignment V, -6.97 on Fig. 1, probably really is -arctan(tan(6.97)*tan(25.77)/tan(19.51)) = -9.46 (i.e. 9.46 S of E).

Neglecting refraction, the summer solstice sunrise is 25.57 N of E by my calculation from spherical trigonometry (I used Earth obliquity 23.50, which is thought to be the mean of the main Milankovitch cycle according to Wittmann as cited in the "Axis Tilt" article in Wikipedia; Wittmann's sinusoid gives 23.48 for 6340 BP, but the IAU polynomial cited gives the probably inaccurate 24.13). So, Alignments I-III match the true solstice sunrise even better than they match Malville's estimated apparent solstice sunrise.

I find no definite error in Fig. 3b. On the page I measure 24deg N of E, not the text's 28deg (90 minus 62; see p. 490), but lacking any axis, on this small diagram, the difference could arise from my ruler error. This is a fourth azimuth at the summer solstice sunrise ( = winter solstice sunset). On Fig. 3b, I measure the three collinear stones just N of the center, as azimuth 8.40 N of E. Correcting this for possible vertical scale compression, gives arctan(tan(8.40)*tan(28)/tan(24)) = 10.00 N of E. I found copies of Fig. 3b on two websites; the monitor frame aided accurate measurement, and I got 7.58 and 9.84. Averaging all three of these measurements and then applying the vertical scale correction, gives 10.25deg +/-0.79 SEM.

This is confirmation, independent of Alignment V, of Barbarossa's rising azimuth (range during relevant time period, 13.11 to 9.96deg N of E, neglecting refraction). The setting azimuth is the same angle but N of W, i. e. S of E, and is given by Alignment V, 9.46deg S of E.
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Joe Keller

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Posted - 04 Apr 2009 :  19:26:11  Show Profile  Reply with Quote
Mauna Loa = Olympus Mons = Great Red Spot?

This week, Richard Hoagland remarked on the "Coast to Coast" radio show, that Hawaii is the same latitude as Jupiter's Great Red Spot. The 1981 National Geographic atlas shows the highest point of Mauna Loa (on the "big island", it's the main volcano, slightly shorter than Mauna Kea but with almost all the map's lava flows) at 19.48 N. This would be geographic latitude; it converts to geocentric lat 19.36 N (see formula below).

A USGS website gives the planetocentric latitude of Mars' Olympus Mons as 18.4 N (planetographic, 18.6 N). (Since 2002, Mars latitudes generally are given as planetocentric.)

Rodriguez et al, Planetary and Space Sci 48:331+, 2000, Table 2, give the 1993-1999 average planetographic latitude of Jupiter's Great Red Spot's center, as 22.27 S. The tangent of the planetographic latitude is (equatorial radius / polar radius )^2 times the tangent of the planetocentric latitude. This conversion formula, as published on a NASA website with their values of Jupiter's equatorial & polar radii, gives the center of the Great Red Spot's average planetocentric latitude as 19.85 S.

Arcsin(1/3) = 19.47. There might be a dynamical reason for this latitude.
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Joe Keller

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Posted - 05 Apr 2009 :  22:22:35  Show Profile  Reply with Quote
Barbarossa's Declination One Period Ago, and Egyptian Temple Azimuth

Review. Above I mentioned that based on the four sky survey positions, Barbarossa's Declination, one period prior to Dec. 21, 2012, in heliocentric celestial coordinates of the equinox of date, would have been +12.10. Its Declination about 290yr later, at its most negative ecliptic latitude, would have been about +9.19. At the Nabta megaliths, this would give (without correction for atmospheric refraction) azimuths of 13.11 or 9.96deg (N of E for rising, and N of W for setting). Nabta's layout has azimuths NS, EW (off by only 1'), and about 26 N of E (the summer solstice sunrise then and now; it's uncertain whether this better fits the refraction-corrected or uncorrected value). The mysterious km-long "Alignment V" is, if my interpretation of the grossly erroneous Fig. 1 in the April 2, 1998, Nature article is correct, at 9.46 S of E, which would correspond to the setting of a star at Declination +8.73. The Nature article's Fig. 3b shows collinear stones at Nabta's central site with azimuth about 10.24 N of E, corresponding to the rising of a star at Declination +9.45.

Other Egyptian temples. "We have then a [histogram] peak at [azimuths corresponding to risings or settings, at that temple's latitude, of stars at Declinations + or -] ~ 11 1/4. In Paper 3 [Shaltout, Belmonte & Fekri, Journal for the History of Astronomy 38:141+, 2007; unavailable on the internet, except for a fee from a French company ; it seems to be on Dr. Shaltout's website but I can't access the paper, nor, usually, the site] we had a long discussion about this peak. It mostly corresponds to temples facing an interval of declination between -10 1/2 and -12deg. These are the declinations of the sun at dates in the vicinity of Feb. 20th and Oct. 22nd and would mark the beginning of the actual sowing and harvest seasons [reference given], hence the name 'seasonal'."

- Belmonte, Shaltout, Fekri & Miranda, "On the orientation of ancient Egyptian temples: (4)", Sec. 1.2, p. 4 (available online).

These azimuths seem hardly needed to mark planting (Oct., in the earliest times typically pressing the grain into the mud after the Nile flood) and harvest (Feb.) sunrise. Surely the variety and even the species of grain (wheat vs. barley) grown would vary, as would agricultural practice. Not only harvest, but also optimum planting time would vary. Winter wheat in the "upper Midwest" U.S. region now is planted later than formerly, to avoid an insect ("Hessian fly date"). Climate change in 3000 yr would alter the times of Nile floods, and winter temperatures. One degree of arc difference in sunrise azimuth, corresponds roughly to only three days in February, in Egypt. Furthermore, planting after the Nile flood, and harvesting when the grain is ripe, need no calendar.

On the other hand (Shaltout & Belmonte, "On the orientation of ancient Egyptian temples: (1) Upper Egypt & Lower Nubia", J. for the History of Astronomy 36:273+, 2005; Table 1) there is a borderline significant trend, for Shaltout & Belmonte's 10.5 to 12 deg Declination orientation (or my 9 to 12) to be found oftener in later temples. Of 133 temples with Declinations tabulated, 40 are Ptolemaic or Roman era, 8 are Middle or Old Kingdom or archaic, at least when begun, and 85 are New Kingdom. Of 12 temples (in this preliminary group; eventually they studied three times as many) aligned at Declination 7.0 to 14.0 (+ or -), 6 were Ptolemaic/Roman and 6 New Kingdom. The exact probability that none of the 8 pre-New Kingdom, would have the alignment, is 46%. The exact probability that, given all are New Kingdom or Ptolemaic/Roman, at least half would be the latter, is only 11%. Furthermore all three temples facing the north Declination (+7 to +14, not -7 to -14) are Ptolemaic/Roman (exact probability 2.6%)(the Declinations of these three average +12.1 +/-0.6 SEM). A survival of 6000 BP should be strongest in the oldest temples, not the newest. Maybe as the freeborn culture of the Old & Middle Kingdoms gave way to the slave economy of the New Kingdom and Ptolemaic/Roman era, religious motivation became needed in agriculture.

Maybe Nabta was inspired by Barbarossa's brightening, then (the one Mayan association of "Bolon" which I discovered in my Google search but didn't mention above, because I didn't then know its relevance, is with seeds) the two crisscrossing direction lines (Barbarossa's rising and setting were at the northern ends of the lines) became associated with planting because the sun rises/sets at the southern ends of the lines, in February. So, Egyptian temples mostly face the southern Declination, not the northern; especially the southern sunrise, because that's more dramatic.

Maybe in the Ptolemaic/Roman era, Alexandrian scholars effected a renaissance of the oldest Egyptian knowledge, and began to make the temples face north again, correcting the sign of Barbarossa's Declination. This might have been the same time that the calendar knowledge was exported to Central America.
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