Just by way of a little note to myself; got a memory like a sieve. Speed of gravity 2.919E 25 metres per second, take the cube root of that and invert it to get the reciprocal. That's the Planck mass. Stick that value into the equation for the Schwarzschild radius with the following alterations.

Predicting "2012" from intragalactic redshift periodicity and Barbarossa's orbit

In my previous post, I noted the periodicity in Blitz's 12-CO line catalog of intragalactic HII region RVs. This periodicity was obviously significant for the largest and most precisely measured regions (those six with >= 100 arcminute diameter and < 1 km/s uncertainty).

Last night I expanded my program to include all 194+47=241 definite regions in Blitz's "A" and "B" catalogs. I weighted the regions, not by diameter squared = area, but rather by diameter to the first power = portion of galactic equator subtended. Then, as described in my previous post, I corrected for any possible second harmonic effect of galactic longitude, by multiplying the weights by a second weight factor chosen so that every second-harmonic "bin" (e.g., galactic longitude 15-30 together with 195-210) has the same total weight.

With the second weight factor, the periodogram peak is 2.3459 km/s. Without the second weight factor (using only the diameter^1 weight factor) the peak is 2.3498 km/s. The diameter^1 weight factor makes the data much lumpier in longitude; I think that the second weight factor is needed to correct for this lumpiness. With the second weight factor, the best fitting sinusoid differs only 16deg from a pure cosine, vs. 22deg without it. Using only a pure cosine to fit (this is justified by a symmetry argument), and also using both weight factors, so that both region size and longitude are considered (uncertainty is considered, too, by the method detailed in my previous post) I find

2.3472 km/s

as my best estimate based on all Blitz's data. This corresponds to Barbarossa's scalar speed, relative to the total solar system center of mass (see my previous post) at 2013.19 AD.

Using only every odd datum in the preceding, gives 2.3431 km/s and only every even datum, 2.3426 km/s. This gives an error estimate: if the value 2.3472 represents the average of results of two half data sets both giving values near 2.3472, then I can find the standard deviation of the (four) such half data set results I know about, and thus the error of the full data set result: it corresponds to 0.86 yr of Barbarossa's travel.

The declination of Arcturus at 4327.5 BC, was +55.2307deg. To make this calculation today, I used:

the "rigorous" precession formula from the 1990 Astronomical Almanac, p. B18 the mean of the J2000.5 and J1999.5 coords. of Arcturus from the respective Almanacs Wikipedia's proper motion values, -1.09345 & -1.99940 "/yr in RA & Decl Wikipedia's RV, +5 km/s

I used the usual first-order proper motion extrapolation, correcting the change in RA according to the secant of the midrange J2000.0 declination. My first order correction for RV, which I've never used before, added only 0.0050deg, which I've included in the result. Porter, Astronomical Journal 12:28, 1892, gives PM -0.80 & -1.98 "/yr in RA & Decl; Porter's PM values would have lessened the result by only 0.0034deg. The consensus of published astronomical opinion seems to be that Ptolemy's catalog confirms Arcturus' proper motion as very roughly constant for 2000 yr, and that Brahe's catalog gives much more accurate confirmation going back 400 yr.

This declination, would have been the geographic latitude of a place where Arcturus reached the zenith, according to a plumb line, at the start of the Egyptian calendar one "Barbarossa period" (6339.5 tropical yr) before the end of the Mayan Long Count. (The start of the Egyptian calendar, was at a summer solstice when Arcturus rose heliacally at Giza; but this was changed slightly, when the Upper Egypt calendar, which began a few days later when Arcturus rose heliacally at Elephantine Island the same year, replaced that of Lower Egypt.)

In a 2009 post, accurizing an observation by Bert Janssen, I explain that, considering Earth's oblateness, and assuming a few miles shift in Earth's pole suggested by Petrie (the Great Pyramid aligns 5 arcminutes off present true north, and is about a mile from the 30th parallel today, despite evidence that a relatively awkward building site was chosen because for some unknown reason, fractions of a mile were important in its placement), the 3-space angle, pole-Giza(Menkaure)-Stonehenge equals the angle pole-Earthcenter-Stonehenge with only 100 meters error. Menkaure's slope, well preserved by its granite siding, also equals (the complement of) this angle, with only 4 arcmin error.

So, Menkaure's pyramid memorializes the geocentric latitude of Stonehenge, not the geographic latitude. Likewise the Bent Pyramid apparently memorializes the geocentric latitude of any place where at 4327.5 BC, Arcturus reached the zenith defined by a plumb line. The conversion to geocentric latitude gives 55.0494deg = 55deg 3'. According to an online discussion by John Legon, Petrie's and Dorner's measured values for the mean angle of the "lower part" of the "lower slope" of the Bent Pyramid, are 55deg 1' and 55deg 5', resp., in excellent agreement with this theory.

The builders knew all along, they couldn't maintain that slope all the way to the vertex, so they fulfilled their mission, by making it the lower slope, or at least the lower part of the lower slope, as it is today (in the mean). What about the upper slope?

The "Sothic cycles" of Prof. Eduard Meyer, are the time intervals between heliacal risings of Sirius on a given date in the official (leapyear-less) 365-day Egyptian calendar. In my earlier posts, I explained that the Egyptian calendar, and "Sothic" date of Amenhotep I, are based rather on "Arcturian" cycles. The date of Amenhotep I is two Arcturian cycles after the beginning of the calendar: the average length of these cycles, I found as (4329-1533)/2 = 1398 yr. The Barbarossa period, 6340 yr, nearly equals 4.5 Arcturian cycles = 4.5*1398 = 6291 yr. Perhaps knowing some of this, Joseph Scaliger chose "Julian Day 1" to be about 6295 yr prior to the beginning of the Gregorian calendar. Also, Hindu texts say there are 6333 Gandharvas, asociated with cyclical divisions of the sky.

The Egyptians would have been likelier to memorialize 1/3 Barbarossa cycle, than to memorialize, say, 1/2 or 1/4, because 1/3 Barbarossa cycle is 1.5 Arcturian cycles, not 2.25 or 1.125. A third of a Barbarossa period, is 6339/3 = 2113 yr, that is, 4329 BC + 2113 = 2216 BC. Maybe the Bent and Red pyramids' slopes (upper slope for the Bent) were chosen in anticipation of a timeline milestone almost 400 yr in their future.

At this milestone (i.e., 1/3 Barbarossa cycle = approx. 1.5 Arcturian cycle) the geocentric latitude, where Arcturus is at the plumbline zenith (i.e., geographic latitude = Arcturus' declination in coordinates of the ecliptic of date), would be 43deg 45', with precise enough accounting for proper motion, radial velocity, and precession, similar to my previous calculation. The most often seen estimates of the slopes of the Red (a.k.a. Northern Dahshur), and (upper) Bent (a.k.a. Southern Dahshur), Pyramids, are both 43deg 22'. However, Dr. Ahmed Fakhry, "The Pyramids" (U. of Chicago Press, 1961), p. 95, gives 43deg 40' for the Red Pyramid. Dr. I. E. S. Edwards (Keeper of Egyptian Antiquities at the British Museum 1955-1974), "The Pyramids of Egypt", p. 89, says the Red Pyramid is "the earliest tomb known to have been completed as a true pyramid", and that its slope is 43deg 36' 11".

The orbit I fit to the four images of Barbarossa, has eccentricity 0.6106. As I remarked in my earlier post, Aitken's text gives 0.61 & 0.615 as mean eccentricities for wide binaries, according to Henry (quoted in Aitken) & Aitken, resp. This eccentricity is close to the "golden ratio", or rather the reciprocal of the golden ratio, 1/1.6180... = 0.6180... . At this eccentricity, the major axis is to the minor axis, as the minor axis is to the interfocal segment. Furthermore, Kapur (cited by Kulshrestha & Sag, Geometriae Dedicata 30:183+, 1989) is said to have proved that a sequence of ellipses for which each ellipse, has interfocal distance equal to the minor axis of its predecessor, and minor axis equal to the major axis of its predecessor, converges to e = 0.6180... (apparently Kulshrestha's abstract gives a slightly wrong value for the golden ratio).

My calculation of Barbarossa's orbit last year (see my earlier post), shows that Barbarossa's aphelion, is 0.4deg or less, from the celestial coordinates of the galactic center. This is more evidence that the sky survey points are real, and that the orbit is real. Also, Barbarossa's orbital pole, at J2000.0 ecliptic coords (200.84, +77.07), is near 45 deg (precisely, 48.24deg) from the galactic north pole at J2000.0 ecliptic coords (180.02320,+29.81153) (Wikipedia value, converted using NASA lambda online utility). These orientations involve a zero rate of change, from galactic tidal forces, of energy and angular momentum.

Height of Mt. Meru: another Vedic record of Barbarossa's period

Above, I mention that apparently, sometimes 27 Gandharvas signified Luna's 27 day (solar day?) sidereal period, but oftener, one speaks of 6333 Gandharvas, perhaps signifying Barbarossa's 6333 year (tropical year?) sidereal period, close to the 6339.5 tropical yr, inferred from the "Sothic" dates of the Egyptian calendar together with the Mayan Long Count, and also close to the 6340 +/- 7 yr calculated from the sky surveys.

Converting this Vedic record of Barbarossa's sidereal period, to sidereal months (instead of tropical years) gives

6333*365.24219/27.322 = 84660 sidereal months = Barbarossa period

Using Joseph Scaliger's obscurely derived 6295 yr, gives

6295/6333*84660 = 84152 sidereal months = Barbarossa period

There is a Vedic record of this figure also. Mt. Meru (roughly the Vedic equivalent of Mt. Olympus) is said to be 84000 yojana high (the yojana was a unit of length equal to several miles).

"Mount Meru...being described as 84,000 Yojanas high, and having the Sun along with all its planets and stars in the Solar System revolve around it as one unit."

Mathematician John Playfair dated Hindu astrology tables to 4300 BC

Koenraad Elst is a contemporary Flemish Belgian philologist. According to Elst's website, "[Elst's] research on the ideological development of Hindu revivalism earned him his Ph.D. in Leuven in 1998." One of Elst's main positions, is skepticism of the "Aryan Invasion Theory" of Indian history.

Elst's essay, "Aryan Invasion Debate", subpart "Astronomical data and the Aryan question", 2. Ancient Hindu astronomy, 2.1. Astronomical tables, first paragraph:

"One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC. His proposal was dismissed as absurd by some, but it was not refuted by any scientist."

I never heard of the above, until today. Is it not remarkable that by reinterpreting "Sothic" dates, I had fixed the start of the Egyptian calendar at 4328 (or maybe 4329) BC?

From sec. 3.3:

"...it is encouraging to note that the astronomical evidence is entirely free of contradictions..."

Elst lists many other Indian astronomical dates; the oldest of these, ~4000 BC, were derived in various ways by various men, perhaps the earliest of whom were Hermann Jacobi, who correlated the constellations to ancient meteorological seasons (Elst, sec. 3.1), and B. G. Tilak, who interpreted a RgVeda allegory to place the equinoctial point in the constellation Orion. Tilak (Elst, sec. 4.2; or sec. 2.4.2 in another online source) relied on Rg-Veda 10:61:5-8; but strangely, Ralph T. H. Griffith's authoritative translation, "The Hymns of the RgVeda" (Motilal; Delhi, new revised edition 1973), relegates these verses to a Latin-only version on p. 653 of Appendix 1; verse 10:61:9 begins, "The fire, burning the people, does not approach quickly...".

For a shorter discussion similar to Elst's, see MN Dutt, transl., "Rg-Veda Samhita" (#22 in the Parimal Sanskrit Series; 1906, reprinted 1986) vol. 1, Introduction, pp. xvi-xviii.

"The next is the Orion-Period, 'which, roughly speaking, extended from 4000 to 5000 BC... . This is the most important period in the history of the Aryan Civilization. ...This was pre-eminently the period of Hymns.' "

Reworking Playfair's "Remarks on the Astronomy of the Brahmins"

Playfair's lengthy remarks originally were published in 1790 in the Transactions of the Royal Society of Edinburgh, vol. 2 (the remarks are said to have been received in 1789). They also are available in an online "Google" book of Playfair's works, and as a chapter in Dharampal's book, "Indian Science & Technology in the 18th Century". Let's rework Playfair's remarks with the help of modern ephemerides.

In sec. 33, Playfair says that the Hindu astronomers gave the maximum "equation of the sun's center" (i.e. maximum difference between actual and mean solar longitude) as 2deg 10' 32". Assuming an observer at the Earth-Luna barycenter, and finding the angle to third order in the eccentricity, I find that it corresponds to e = 0.018985. From the eccentricity formula in the 1965 Astronomical Almanac (which counts centuries from 1900) I find that the date would be 4800 BC. Interpolating quadratically from the eccentricities given by Dziobek, "Mathematical Theories of Planetary Motions" (1892) in Table VI, p. 294, I find that the needed eccentricity occurs at 4900 BC, in good agreement with the 4800BC date implied by the 1965 Astronomical Almanac's eccentricity polynomial.

In sec. 17, the sun's "apogee" is said to be given as 77deg "from the beginning of the zodiac". In sec. 22, Aldebaran is said to be given as 53deg 20' "from the beginning of the zodiac". Suppose that the text has been corrupted: "apogee" should read "vernal equinox". Including proper motion, Aldebaran's longitude, in coords of the equinox & ecliptic of date, at 4800BC, was 335.931, implying that the so-called "apogee" (really, vernal eqinox at the epoch of the original almanac) was at longitude 335.931-53.333+77 = 359.60. It would coincide with the vernal equinox 0.40/360*26000 yr later, i.e. 4770BC.

Besides this 4800BC date, which I find two ways above, there is another way, besides the several discovered by Playfair and Bailly, to get the Kali Yuga date (3102BC) from the almanac. Sec. 10 says that the sidereal year, given by the almanac, is abnormally long: 365d 6h 12' 36". (Correcting for the shorter days in 3000BC, the 36" becomes 09".) This exceeds the modern value of the sidereal year, 365.25636d, by 1/176,000, but is too short to be the anomalistic year, which by interpolating to 3200BC in Dziobek's table, I find to exceed the sidereal year by 1/121,000. This year seems really to be a special kind of "sidereal" year: the time between moments when the RA of the Sun, in the equinox and ecliptic of date, equals the RA of Arcturus. It is a kind of sidereal year relative to Arcturus. I discovered this by using the NASA lambda online utility, to find the RA, in coordinates of the equinox and ecliptic of date, of Arcturus at various ancient dates, corrected for proper motion. Then I used the JPL Horizons online ephemeris, to find the Sun's RA-to-RA time for those dates, then corrected for a year's change in Arcturus' RA, getting 3036BC, in good agreement with the 3102BC date determined for the Kali Yuga according to planetary conjunctions.

Reworking Playfair's "Remarks on the Astronomy of the Brahmins" (part 2)

In sec. 15, Playfair says, that the Hindu tables say that the Sun's apogee advances 1" in 9 yr, relative to the stars. In the last paragraph of my previous post, I mention that at 3000BC, the Arcturian year (a kind of sidereal year that does not depend on defining an ecliptic) advanced, relative to the true sidereal year, 2/3 as fast as the Sun's apogee. The Sun's apogee at ~3000BC, according to Dziobek, advanced 11"/yr (a value that changes little over the centuries). So, the anomalistic year (year to Sun's apogee or perigee) advanced (11/3) " / yr relative to the Arcturian year; maybe this was corrupted to 1/(3^2) " / yr. Alternatively, and more likely, maybe 11" / yr was corrupted to 11" /century = 1/9 " /yr.

In sec. 34, Playfair says that the Hindu tables give the obliquity of the ecliptic as exactly 24deg; this might involve rounding error. Anyway, I find from the polynomial formula in the 1992 Astronomical Almanac, p. B18, that the obliquity of the ecliptic at 3150 BC was exactly 24deg.

In Sec. 8, Playfair says the Hindus give the general precession as exactly 54"/yr. According to the 1965 Astronomical Almanac, p. 490, the general precession at ~3000BC was 50" - 1" = 49"/yr; but above, I found that the Arcturian year advanced, then, 7"/yr. So, 56"/yr would have been the general precession then, relative to the Arcturian year rather than the true sidereal year. Also, because at 3000BC the pole was tipped toward a longitude ~45deg from Arcturus' longitude, the maximum speed of advance, of the Arcturian year relative to the true sidereal year, would have been 10"/yr. The figure, 54" = 49" + (10/2)", is a midrange value useful for that half of the precession cycle when the Declination of Arcturus is most northerly.

Now the arc, 77deg (see sec. 17) between the mysterious "beginning of the zodiac", and the misnamed "apogee" (really, the vernal equinox at 4800BC) can be explained:

Hi Joe, I wonder if I can pick your brains on this hawking radiation problem. We've got Power = (16pi G^2 M^2 / c^4) (pi^2k^4 / 60 hbar^3 c^2) (hbar c^3 / 8pi G M k)^4

That gives us Power = hbar c^6 / 15360 pi G^2 M^2

Well, the power is just how bright it is, and it's very bright as the mass fall to the Planck mass. Now I think the Planck mass is going to be closer to 3.07E-9 than as normally given. It doesn't matter too much though as at the moment I'm only after ball park figures.

Let's say that the speed of gravity is roughly c^3 Then we need to change the terms of the first bracketed expression, which is the surface area of the Schwartzchild radius for light. For gravity it will be a much smaller radius. So change that c^4 to c^12

That cancels out and we are just left with a c^2 in the denominator of the second bracketed term. So multiply hbar by the reciprocal of c^2 Now I reckon that that gives us the reciprocal of the speed of gravity squared. P = hbar * 1.112E-17 /15360 pi G^2 M^2 which gives us a rough answer of about 5E-19Js^1

I think I better add, that in the three bracketed equation for power, there's another term, epsilon which is taken as unity. I think that needs to be looked at. As does something called the trans planckian problem but I do like the power coming out somewhere near the basic charge value.

Reworking Playfair's "Remarks on the Astronomy of the Brahmins" (part 3)

As Playfair noted, the "equation of the Sun", i.e. the maximum difference between the Sun's apparent and mean longitudes, is a well-defined quantity that can be accurately determined with primitive tools, so it is a good way to date the Hindu astronomical tables. In part 1, I used two modern estimates of trends in Earth's eccentricity, to get 4800BC and 4900BC as the date of the tables.

The best modern estimate I can find, that is in a form usable by me, is in Laskar, Astronomy & Astrophysics 157:59-70 (1986), Tables 2 & 3, pp. 61-62. Laskar gives two different fourth degree polynomials, whose coefficients differ only slightly. The coefficients shrink steadily so those of t^4 are about 1/30 as big as those of t; his t is in units of 10,000 yr, so at 6000 yr, the t^4 term is only 1/150 as big as the t term. I also improved my calculation slightly, by using precise numerical integration, for the apparent-mean Sun inequality, instead of third order approximation.

Using the average of the two coefficients offered by Laskar, I get 4929BC as the date corresponding to the Hindu "equation of the Sun", 2deg10'32". Using the two formulas separately, I get 5083BC & 4796BC (mean 4940BC). So, the four authoritative formulas I've used for Earth's eccentricity thousands of years ago, all indicate that the Hindu "equation of the Sun" discussed by Playfair, was current sometime between 4800BC and 5100BC.

The analogous equations of Mars, Jupiter, and Saturn, which I gleaned either from Playfair or directly from Bailly's book (to which I have access on microfilm), are subject to various interpretations, because they involve three bodies. My various calculations, mostly using Laskar's formulas, indicate that these Hindu values are either no older than ~2000BC, or are inaccurate.

The Hindus said that Luna's orbit is inclined 4deg30' to the ecliptic (Playfair, sec. 15). Very modern authority, Simon et al, Astronomy & Astrophysics 282:663+ (1994) says (3.4.a.2) that Luna's mean inclination changes linearly, so slowly that the difference between the modern and Hindu value (using ecliptic of date for each) is 2 billion years! However, Simon gives 5.1566898deg for 2000.0AD. Brown, Monthly Notices of the Royal Astronomical Society 74:552+ (1914), pp. 552 & 561, on the other hand, gives 5.128164 +/- 0.000008deg, based on data from 1847-1901. Linear extrapolation based on the midrange of Brown's data, implies 900BC; but this is only a guess.

Playfair (sec. 40) says the Hindus gave the regression of Jupiter's aphelion as 15deg in 200,000 yr. Modern authorities say that Jupiter's aphelion progresses, and much faster. Jupiter's node also progresses, but at a rate roughly 100x the above figure. If the node is meant, rather than aphelion, and progression is meant, rather than regression, and years were mistranscribed as centuries, I find that the value, 2700"/century, is correct for 9000BC +/- 1000. This is according to the third degree polynomial in Clemence, Astronomical Journal 52:89+ (1946), p. 92. Clemence segregates some terms into a sinusoid of frequency equal to the "great inequality" of Jupiter and Saturn (disparity from exact 5:2 resonance). This phase of this sinusoid is unknown for such a distant epoch, but would affect the result +/- 1000 yr. Also, the range is outside that for which cubic polynomials generally are accurate for these phenomena.

Sense & Synchronicity: Mt. Meru Comes to Microsoft

Let's recall: Mt. Meru, in Hindu legend, is said to be 84,000 yojanas high (the yojana is the ancient Hindu counterpart of a mile, equal to several of our miles, apparently varying over the centuries). (Some less accurate sources round this to 80,000 or even to 100,000.) Mt. Meru also is said to be the home of the Gods, analogous to Mt. Olympus (recall that U. S. Air Force reservist Sid Padrick, said that friendly humanlike beings told him they lived on a somewhat distant unobserved planet in our solar system, even hinting at Barbarossa's longitude by mentioning that it was in conjunction). Furthermore, according to Wikipedia, it was said that the entire known solar system (Sun plus planets) revolves around Mt. Meru as a unit.

My "Barbarossa period", though originally discovered by me as Barbarossa's sidereal orbital period, 6340 +/- 7 yr, calculated from four sky survey appearances, I more precisely define as 6339.5 tropical yr, from the summer solstice 4328BC (start of Egyptian calendar according to Arcturian date of Amenhotep I) to the winter solstice 2012AD (end of Mayan Long Count). In my Oct. 18 post, I noted that the Barbarossa period equals 84,000+ sidereal months. For a precise calculation, I use the tropical year instead of the sidereal (because the calendars define the period in tropical years, not sidereal, and there is evidence that Egyptian and Hindu astronomers eschewed the true sidereal year, preferring phenomena such as heliacal rising, or the right ascension of one bright star); adjust the tropical year to its mid-interval length according to Newcomb's linear formula for precession (in, inter alia, the 1965 Astronomical Almanac); for consistency, use the tropical month instead of the sidereal; and adjust the tropical month to mid-interval length according to the linear formula in Wikipedia. The Barbarossa period is:

84,748.2 tropical months (the secular trends only barely affect the last decimal place)

So, "The solar system revolves around Planet X - Barbarossa in 84,748 tropical months, and there is advanced life on Barbarossa" has been remembered as, "The solar system revolves around Mt. Meru which is 84,000 yojanas high, and Mt. Meru is the home of the Gods."

There is yet another way that the parameters of Barbarossa have been remembered as "84,000". Barbarossa's latus rectum is 84,147.3 times Luna's semimajor axis (the secular trend in Luna's semimajor axis isn't quite big enough to change the last digit). The latus rectum, is arguably the most important measure of the size of Barbarossa's orbit: it is the numerator of the formula giving radius as a function of the true anomaly, theta; and at the critical phase, in Dec. 21, 2012AD, Barbarossa is at theta = 91.022deg, only a degree past the latus rectum, and at distance 85,073.8 Lunar semimajor axes.

So, "Catastrophe occurred when Barbarossa was near, its latus rectum which is 84,147 times Luna's semimajor axis" also became "Mt. Meru which is 84,000 yojanas high".

None of the foregoing involves synchronicity; it only involves the garbling of information over millenia, and perhaps the intentional encoding of information in myths which were likelier to be remembered. On the other hand, synchronicity, as I understand it, is a significant coincidence that not only is unexplained, but cannot be explained by, or to, the limited minds of human beings. Here is a fictitious example:

"I counted the flowers on my houseplants, then got my mail, and there was a bill for the same number of dollars; this happened every day for a year."

If it happened one day, it could be chance, but to happen every day, were this fictitious example to be true, would indicate some kind of organizing process (or organizing being) in the world, far beyond human understanding.

Near Microsoft headquarters in Redmond, Washington, is a boulder. A large building was constructed near this boulder this summer; according to my research, the zoning permit was granted April 8, 2010, and construction began quickly the same day. I and some others have photos of the building after its exterior was completed, and of a sign in front of it; these photos were taken Oct. 11.

The sign says:

"PROPOSED LAND USE ACTION Project No: L090463/L090464 Title: Redmond Medical Office Bldg. Description: 84,715 sq.ft. medical office bldg. & emergency care clinic Applicant: ***** Co.; contact: D**** D**** Contact: D**** L**** City of Redmond (425) 556-2471 WWW.REDMOND.GOV/LANDUSEAPPS"

This superficially appears to be a routine bureaucratic notice, but there is synchronicity:

The summer solstice, 2010AD, is 84,714.7 tropical months after the summer solstice, 4328BC. As above, this figure is corrected (to midrange value) for the (barely significant) linear secular trends in the tropical year and month. It also is corrected for the (1.8 day) effect of eccentricity, on the time of the solstice at the different positions on Earth's orbit; I considered the change in perihelion and eccentricity too.

From numerical analysis, I thought the 1-sigma error in my calculated orbital parameters for Barbarossa, was 1/1000. However, the calendar data suggest it is only 1/10,000, and various resonances between the planets and protoplanets (discussed in my earlier posts) suggest 1/20,000, i.e. +/- 4 Lunar semimajor axes. Be this as it may, my orbit for Barbarossa gives a Sun-Barbarossa distance of 84,715 Lunar semimajor axes, at the summer solstice, 2009 AD (2009AD, not 2010AD).

The "Project No." also involves synchronicity. In an earlier post, I showed that the original height of the pyramid of Khafre, relative to the base of the pyramid of Khufu, is to the Lunar proxigee (closest approach of Luna to Earth, including perturbations away from the Keplerian ellipse), as one day is, to the period of Barbarossa. Wood's 1986 value of the proxigee is 356,375km. Vyse gives 1011 cm as the height of Khafre's base above Khufu's. This implies a height for Khafre, above its own base, of

well within Petrie's 5664 +/- 13 inch estimate. (Using the height above Khufu's base, and using the proxigee, allowed the smallest height for Khafre.) Maybe some ancients preferred to measure in Lunar proxigees rather than Lunar semimajor axes. Barbarossa's Latus Rectum, in proxigees, is

L = 90,528

only 7/10,000 more than the "L090463" or "L090464" figures in the bureaucratic notice.

Hi Joe, how does this relate to the Metonic month? There is that famous bronze age "witch's hat" that shows the 19 year cycle of the moon.

(Edited) It was thought for a long time that the various henges of Europe were about the sun but now it's thought they were about the moon. These people were on the cusp of changing from hunter gatherers to farmers. The nineteen year event was to show the people that the moon was still the "boss" as it were.

Another quick thought about this, is on the famous shepherd speech in Oedipus Rex, about Arcturus. To the modern ear, he just seems to e twittering on about nothing but to the Greek audience?

Hi Joe, how does this relate to the Metonic month?

...speech in Oedipus Rex, about Arcturus.

Hi Bob! Thanks!

Playfair says that the ancient Hindus mention the Metonic cycle, but do not mention the supposedly more useful Saros cycle. Playfair also says (sec. 12) that the Hindus mention that the Lunar perigee (apse) revolved in 3232 days = 8.8487 Julian yr; 3232 d. also is the modern value given in Lang, Astrophysical Data (1992), though the most modern and exact sources give a period of 8.8504 Julian yr = 3232.61 days. Ptolemy equated 3277 synodic months to 3512 anomalistic months; this is equivalent to saying that the apse revolves in 8.8487 Julian yr, so Ptolemy was in exact agreement with the ancient Hindus, on the period of Luna's perigee advance.

Sophocles' mention of Arcturus as a commonly used calendar marker, supports the idea that the Egyptians and Hindus used it in various ways to mark dates.

The Lunar proxigee (absolute closest approach) is less, than the Keplerian perigee with mean elements. Practically all the difference, 5974 km, is due to the Sun. The primary effect, is due to the angle between perigee and the Sun, i.e., the phase of perigee. The secondary effect, is due to the season of the year, because of Earth's eccentricity.

Neglecting the effect of Earth's eccentricity, that is, minimizing the perigee with respect to Lunar phase, but averaging it over season of the year, should give a perigee minus proxigee difference, (1 - Earth ecc.)^3 times as big, i.e. only 5679.8 km, thus 356,669.3 km for the proxigee.

If the Egyptians used this proxigee in planning the height of Khafre's pyramid (so Khafre's height above Khufu's base would be to Luna's "proxigee", as one day is to the Barbarossa period) then the calculation of Part 1 becomes

-1011cm + 356,669.3km / (6339.5*365.24258) (4328BC trop yr) * (1-1.5ms/d/cent*63.4cent)(4328BC day) = 5666.5 inches, now 2.5 in. more than, instead of 2.5 in less than, Petrie's 5664 +/- 13 (ch. 8, end of sec. 67, in Birdsall's online edition of Petrie's book). In units of this yearly averaged proxigee, Barbarossa's latus rectum is

L = 90453

six times closer, to the 90463.5 indicated by synchronicity (see Part 1), implying an error of only 1/9000 in my calculated latus rectum for Barbarossa.

Hi Joe a little update on that Hawking radiation problem, I used the wrong value for the Planck mass, not that anyone is too sure of what it is!

We have, Power = hbar * c^6 / 15360 * pi * G^2 * M^2 for the e.m. side of things

We have, Power = hbar* c^-2 / 15360 * pi * G^2 * M^2 for the gravity side of things

c = 2.99792458E 8 G = 6.67428E-11 hbar = 1.05457148E-34 M = 4.3413642 (which is the Planck mass micro lack hole)

Putting some numbers in 1.1173369E-51 / 15360 * pi * G^2 * M^2 = 2.8980456E-19

That's about 1.72135 times the charge on the electron. Why? I do think I've made some sort of basic mistake here. I really think this should be exactly 1.6021764187E-19

The trouble is, that it has to mean altering that denominator and it is constructed from the sacred cow of 8 * pi * G I think the denominator is going to be 0.5 hbar and the numerator is going to have 2 * 1/137 in it. Though having said that, it's bad enough saying that something, gravity, can go faster than light, without questioning the derivation of the Planck mass.

Sloat, The charge is a unit of energy and the number you want(~1.6-E19) is just a number. How can you make energy from a number? You never explain or account for units-what happens to all the units used in your calculations? If you just use numbers that look good and dump the units the numbers belong to don't you have nothing at all? It seems to me all you have is numbers with no meaning. 1.602x10E-19Joules is the basic charge found everywhere but without knowing what a Joule is or dumping the Joule from the charge unit the number has no meaning at all.

Ephemeris for Barbarossa: 2007, 2008, 2009, 2011 observing seasons

This ephemeris, is so those who have taken photos, can check them more efficiently than with my earlier, probably less accurate ephemerides. Linear interpolation suffices for Feb. & Mar. The intervals in each year, are 30 days, always at 12h GMT (12h UT). The ephemeris is accurate for Jan. and Apr., with quadratic extrapolation.

This is the most exact ephemeris I now can make for Barbarossa. It's based on my orbit (found in spring 2009) through the four sky survey points. Earth parallax was corrected using a first-order correction for Earth's eccentricity.