| T O P I C R E V I E W |
| Samizdat |
Posted - 05 Dec 2005 : 16:29:49
Has any of you read, or have you preliminary thoughts on the new book by Michael Strauss, "Requiem for Relativity: the Collapse of Special Relativity?"
http://www.relativitycollapse.net/
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| 20 L A T E S T R E P L I E S (Newest First) |
| Larry Burford |
Posted - 18 May 2013 : 21:24:06
Joe,
A while back, if memory serves me well, you mentioned something about having observational evidence for an anomalie at 53 AU from Sol that causes light to behave a little differently than we would expect based on present theories.
Would you briefly summarize your thinking on this, and are you interested in discussing it?
LB
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| Joe Keller |
Posted - 29 Mar 2013 : 14:38:28
Cambodian temples indicate 2012
Wikipedia gives the coordinates of Angkor Wat as 13deg24'45" = 13.4125 N, 103deg52'00" = 103.8667 E. Mercury's maximum Declination Jul 22 2012 07:26 GMT, near the end of retrogression, is +13.242038deg. As usual, I find that the latitude correction for the pole shift indicated by Giza, is
-340"*cos(29.9792)*sin(103.8667-31.1344)
= -0.0781deg
Also, just as the Borobudur result was accurized by using parametric latitude, the Angkor Wat result might be accurized by using geocentric latitude. Using the Zhongolovich 1952 ellipsoid, this correction is
arctan((296.7/297.7)^2*tan(13.4125))
- 13.4125 = -0.08674deg
Thus the geocentric latitude of Angkor Wat, corrected for the Giza pole shift, is +13.2476, only 20.2" greater than Mercury's maximum Declination in Jul 2012 near the abovementioned stationarity.
Under the category "Buddhist Temples in Cambodia", Wikipedia lists, among others, eight Cambodian temples for which coordinates are given and which are within a few arcminutes latitude (all of them north of it) and longitude (most of them east) of Angkor Wat:
Preah Palilay ("PP")
Preah Khan ("PK")
Krol Ko ("KK")
Ta Som ("TS")
Bayon ("B")
Angkor Wat ("AW")
Neak Pean ("NP")
Ta Prohm ("TP")
When I plot these on graph paper, I find with the long edge of a Keuffel & Esser "Doric" A88231 French curve, that PP, PK, KK & TS all can be fitted on one curve. Generally the extra degree of freedom of a given French curve accommodates only three arbitrary points, vs. two for a given circle. |
| Joe Keller |
Posted - 25 Mar 2013 : 19:37:33
Javanese temples also indicate 2012
The largest Buddhist temple in the world is Borobudur in Java. It is collinear with two other Buddhist temples, Pawon and Mendut.
Coordinates from Wikipedia articles:
Borobudur 7deg36'29"S 110deg12'14"E
(= 7.60806 S 110.20389 E)
Pawon 7.6061596 S 110.2195215 E
Mendut 7.604873 S 110.230034 E (from "Wikigogo", corroborated by others)
Most likely these all are accurate either to the nearest 0.0001deg or to 1" = 0.0003deg. The great circles between any one temple and any adjacent temple, always make a 7.0deg angle with the parallel of latitude (where 0.5" error in the latitude of a temple typically corresponds to 0.6deg error in the result; so a true angle of 7.6deg is not excluded).
Petrie's determination of the ancient pole was 340" +/- 10" W of N at Giza. For a spherical Earth this shift decreases the latitudes of all three temples by 289.2". Their corrected latitudes are:
Borobudur 7.68839 S
Pawon 7.68649 S
Mendut 7.68521 S
In Mesoamerica (see above article) pyramid sites tend to be at geographic latitudes equal to minimum Declinations of stars (Arcturus) or planets (Jupiter, Venus). For Saturn, let's consider not the point where the time derivative of the apparent Declination of date is zero, but rather the point where the time derivative of the Declination is largest, that is, where the second time derivative is zero. This point is near opposition, rather than stationarity. For Saturn in 2012 AD, opposition defined as maximum Sun-Earth-Saturn angle, is Apr 15, 18:27 GMT; opposition defined as opposite ecliptic longitudes for the Sun & Saturn, or as minimum Saturn-Earth distance, differs by only a few minutes from this. However, the largest (positive) time derivative of Saturn's apparent Declination according to the equinox and ecliptic of date, is five days earlier, Apr 10, 16:58 GMT; at this time, Saturn's Declination is -7.663614. This is only 77.7" N of the temple of Mendut, or 89.2" N of the temple of Borobudur. If the corrected geographic latitude of Borobudur is converted to parametric (a.k.a. reduced) latitude, assuming flattening of 1/297.5 in its meridian as per Zhongolovich 1952, the result is 7.662854, which differs from the relevant Declination of Saturn by only 2.7".
The interspacing of the temples corroborates this information. The above largest time derivative of Saturn's Declination, is (from a centered 12 hr interval) +0.027830 deg / Julian day; the above distance between the temples Borobudur & Mendut is A+B = 0.02611 deg (let's denote the Borobudur-Pawon distance by A, and the Pawon-Mendut distance by B). Also, B/(A+B) = 0.40213; the tangent of the angle which Saturn's path makes at that time, to the parallel of Declination, is (from a centered 12 hr interval) d(Decl)/d(RA)/cos(Decl) = -0.3924702.
The book, "Barabudur" (Gomez & Woodward, ed., 1981) contains a map of the three temples on p. xv, by Janet Opdyke. On Opdyke's map, by my ruler measurements and retaining barely significant digits, A+B = 0.0258 deg in units of geographic latitude. Also, B/(A+B) = 0.394, in perfect agreement with theory. The slope from Borobudur to Pawon (from the centers of the topmost temple levels that are shown on the map) is 8.6deg; from Pawon to Mendut 7.6deg; and from Borobudur to Mendut 8.2deg. The theoretical slope, 7.66deg (to echo Borobudur's parametric latitude) thus lies halfway between the slope, 7.0deg found from online GPS coordinates, and the slope 8.2deg found from Opdyke's map.
Some non-quantitative information. It's well known that in Egypt, temples often were rebuilt on the same foundation, repeatedly for many centuries. Other examples are the large Roman temple built upon the much older megalithic foundation at Baalbek, and the Christian church atop the pyramid of Cholula. Building on the same site, could happen because the site was thought to be sacred, or thought to need exorcism, or because it was cheaper to reuse the foundation, or because there was a town there but all the other land nearby was being used for something else already. That Borobudur is dated to the 9th cent. AD, but the greatest Mesoamerican pyramids seem to have been started a millennium earlier, does not preclude a common date for the original site selection of them all.
The simplest "precessional alarm clock" is a monument at the Declination (i. e. latitude) which some bright star or planet will have at the date for which the "alarm" is set.
A star like Arcturus changes position slowly due to precession and proper motion, but also there is a small short-term periodic change, mainly due to "aberration of starlight" from Earth's yearly orbital motion. It is most convenient to define the Declination as an extremum (i. e. a top or bottom of the yearly wiggle). Thus the pyramid of Cholula was placed (if corrected for the pole shift indicated by Giza's layout) at the minimum of Arcturus' Declination which occurs in March 2013.
Planets have large periodic changes in Declination due not only to their own orbital motion but also to Earth's. It is most convenient to define the Declination as that at stationarity (either before or after retrogression) or, for superior planets, at opposition. Since we must calculate their Declination anyway, the definitions of stationarity and opposition which require the least additional work, are as zeros of the first and second derivatives of Declination, resp.: that is, stationarity can be defined as when the Declination reverses direction, and opposition as when the Declination is changing at the largest rate. Thus El Castillo seems to correspond to the stationarity of Jupiter in Jan 2013; Mundo Perdido to the stationarity of Venus June 2012; and Borobudur to the opposition of Saturn April 2012. Borobudur's choice of the April 2012 opposition suggests that by the next opposition in April 2013, we will have "overslept". |
| Joe Keller |
Posted - 16 Mar 2013 : 18:49:27
A simple, compelling excerpt from my Teotihuacan analysis
"...The geographic latitude of El Castillo was chosen equal to the minimum Declination of Jupiter near its post-retrogression stationarity Jan 2013. The minimum Declination of Jupiter near its stationarity, geocentric, apparent (excluding refraction, which would be tiny so near the zenith as at El Castillo) using coordinates of date, including nutation and aberration, is +20.764257deg at 20:15 GMT Jan 23, 2013, according to the JPL Horizons ephemeris (and Luna's is similar, +20.633134; Luna's lower limb would be 1772.486"/2 less: 20.386955). Wikipedia's geographic latitude for El Castillo is +20.6828, to which 0.07106 is added for the effect of the 5'40" W of N ancient pole as seen from Giza. The difference between the Declination minimum and the corrected latitude, is only 37.4" (if Jupiter's minimum Declination is as observed from El Castillo instead of Earth's center, the error is a little less, 36.2"). The corrected latitude of the Pyramid of the Magician, is 20.36080 + 0.07019 = 20.43100, 158.6" greater than Luna's lower limb as above.
"The pyramid Mundo Perdido is to Venus, as the pyramid El Castillo is to Jupiter. The geographic latitude of Mundo Perdido was chosen equal to the minimum Declination of Venus near its post-retrogression stationarity Jul 2012. The minimum Declination of Venus near its stationarity, geocentric, apparent (excluding refraction, which would be tiny so near the zenith as at Mundo Perdido) using coordinates of date, including nutation and aberration, is +17.384489deg at about 00:04:30 GMT Jul 06, 2012, according to the JPL Horizons ephemeris. Wikipedia's geographic latitude for Mundo Perdido is +17.22005, to which 0.07030 is added for the effect of the 5'40" W of N ancient pole as seen from Giza. The difference between the Declination minimum and the corrected latitude, is 338.9". If Venus' Declination is observed from Mundo Perdido instead of Earth's center, the error is a little less, 327.0". If the Mundo Perdido site were surveyed originally at the start of the Younger Dryas 12,680 yr ago (2013AD - 12,680) and Giza only at the start of the Mayan Long Count 5125 yr ago, extrapolating the pole shift correction, changes the +338.9" error, to -34.2".
"Venus' Declination at minimum geocentric apparent Right Ascension of date, which occurred Jun 27 2012 04:21 GMT near stationarity, was greater, +17.834013deg. At El Mirador, the latitudes usually given online for the La Danta & El Tigre pyramids are 17.75156 & 17.75606, resp. Correction for pole shift vs. Giza, as above, gives 17.82166 & 17.82614. So, the errors are only 44.5" & 28.3", resp., about the same as the error regarding Jupiter at El Castillo.
...
"If the North Pole position is changed to its former position suggested by Petrie's survey of Giza (i.e. 340" W of N as seen from the Great Pyramid, per Petrie's value 5'40" +/- 10"; but no closer nor farther from Giza) then Arcturus' minimum Declination on Mar 25, 2013, would differ only 0.30" (not much more than coordinate rounding error) from the former geographic latitude of the Cholula pyramid. ..." |
| Joe Keller |
Posted - 24 Feb 2013 : 19:05:17
The preceding is the single most important post I've ever made to this messageboard. It contains my most precise calculations and leads to the most compelling conclusions. The presently available coordinates for the Teotihuacan/Cholula pyramids limit the precision of the "precessional alarm clock" to +/- 1 yr, but more precise coordinates could much improve this. |
| Joe Keller |
Posted - 22 Feb 2013 : 17:29:49
Cholula/Teotihuacan: an accurate, robust "precessional alarm clock" (phrase due to J. M. Jenkins)
Summary. If the line between the Pyramid of the Moon and the Pyramid of the Sun at Teotihuacan represents the N-S line at the time of construction, then not only do the present latitudes of the pyramids of Teotihuacan and Cholula roughly equal the present Declinations of Algieba and Arcturus: the original difference in latitude between the Pyramid of the Moon and the Pyramid of Cholula, precisely equaled the present difference in apparent Declination of date, between Algieba and Arcturus. Furthermore, let us consider the point P, where the present ecliptic intersects Arcturus' present parallel of Declination. The present difference in Right Ascension between Arcturus and P, equals 1.6126 times the angle between the Avenue of Teotihuacan (which Millon and Dow say is oriented 15deg25' E of N) and the line between the Pyramids of the Moon and Cholula. The present difference in Right Ascension between Arcturus and Algieba, equals 1.6124 times the angle between the Pyramid of Moon - Pyramid of Sun line, and the Pyramid of Moon - Pyramid of Cholula line. This ratio is determined by the difference in Right Ascension between Algieba and Antares: 1.6123 radian. If Teotihuacan's "other" orientation, 16deg30' +/- 30' E of N (inferred from streets, etc., aligned S of E) is used instead of the Avenue, it corresponds to the RA difference between Arcturus and Avior, with ratio 1.60307. Assuming the pole shift 5'40" W of N at Giza, indicated by Petrie's survey, the pyramids El Castillo and Mundo Perdido are positioned at latitudes corresponding to the Declination minima of Jupiter and Venus, resp., at their latest stationarity; with the pyramid of Cholula corresponding to the minimum Declination of Arcturus as it varies mainly due to stellar aberration.
I use the Wikipedia coordinates of the Pyramids of Cholula & of the Moon. These are copied correctly from the cited reference, a Google service called "Geohack" at toolserver.org, on which they seem to be given to the nearest 0.0001deg, roughly the accuracy of GPS (which is affected by atmospheric phenomena). Millon gives as central coordinates for his map, the coordinates of the Pyramid of the Sun, but both his longitude and his latitude end in 30", suggesting that the difference between Millon's and Wikipedia could be mostly the rounding error of the former.
Let us suppose that the Pyramid of Cholula originally were at a geographic latitude equal to the time-local minimum of Arcturus' apparent Declination of date, which for this year occurs at March 25.162, 2013AD (based on Hipparcos catalog data and including correction for Proper Motion, parallax, precession, nutation and aberration). Then if the line between the Pyramids of Moon & Sun represents geographic north at the time of construction, it would need to be oriented (according to spherical trigonometry) 2.0987deg W of N, for Algieba's apparent Declination of date, on March 25.162, to equal the original geographic latitude of the Pyramid of the Moon. On Millon's map I measure this orientation as 2.1064deg and estimate the one-sigma error resulting from my contributing ruler measurements as roughly 0.034, so even if ruler measurement is the only error, the discrepancy between measured and theoretical orientation is only 0.2 sigma.
If the Pyramid of the Moon - Pyramid of the Sun line really is at 2.0987deg W of N as required above, then the angle PyrSun-PyrMoon-PyrCholula is 1/1.61241 times the difference in Right Ascensions of date, of Arcturus & Algieba. Though this happens to be near the Golden Ratio = 1.618034..., it is much nearer the Right Ascension difference of Algieba & Antares measured in radians, 1.612326. Dividing the Right Ascension differences, by a factor such that the Antares-Algieba RA difference becomes 1.0 radian, keeps all the angles less than 90 degrees, even with the inclusion of Antares in the set, and also allows the inclusion of Antares, by means of this hint, without building a monument for it. Thus the layout expresses not only the Declination difference but also the Right Ascension difference between Arcturus & Algieba. The consistent time interval is still several years, because in both coordinates, the two stars change at nearly the same rate: in their change in apparent Declination they differ from each other only by a fraction of an arcsecond per year, and their change in Right Ascension differs only Arcturus-Algieba = 42-49-1+0 = -8"/yr, including precession and Proper Motion; -8"/59deg = -1/27000. The change in Right Ascension Antares-Algieba = 55-49-0+0 = +6"/yr; +6"/92deg = +1/55000. The pyramid coordinate rounding error is roughly 0.00005/0.5deg = 1/10000, but if the pyramid coordinates were exact, then the difference in the ratios 1.612326 for Antares-Algieba, and 1.61241 for Arcturus-Algieba, a part in 19200, would disappear in 1/19200 / (1/27000 + 1/55000) = 0.9 yr.
Let us also consider the point P where Arcturus' present parallel of Declination intersects the present ecliptic. The angle between the Avenue of Teotihuacan, and the line PyrMoon-PyrCholula, is 1/1.61263 times the difference in Right Ascensions of date, of Arcturus and P. The Right Ascension of date, of P, does not change with precession, but Arcturus' large Proper Motion in Declination affects it indirectly by +9"/yr due to the small angle, between the ecliptic and the Declination parallel. The difference in Right Ascension, of Arcturus and P, changes 42-1-9 = +32"/yr; +32"/87deg = +1/9800. The rounding error in the orientation of the Avenue of Teotihuacan, might be 2.5' --> 1/1300 or 0.5' --> 1/6500. Millon adopted Dow's 1964 astronomical measurement of 15deg25', but gave honorable mention to another researcher's measurement, 15deg28'. A value of 15deg25.6' would produce the abovementioned monument-free standard ratio, RA Antares minus Algieba expressed in radians.
The Right Ascension of Avior, a.k.a. epsilon Carinae (reaches more than 10deg altitude at Teotihuacan now, and was farther north in the past)(not to be confused with the famous eta Carinae) changes little with precession, only 18.5"/yr, because it is near the south ecliptic pole. (This is even less than Canopus, which changes 20"/yr.) The angle between 16deg30' E of N (the "other" Teotihuacan angle, based on the 16deg30' +/- 30' S of E figure quoted by Dow in American Antiquity, 1967, for an EW street that had been measured precisely) and the line PyrMoon-PyrCholula, is 1/1.60307 times the difference in Right Ascensions of date, of Arcturus and Avior, at the same date, Mar 25.162, used above. If the correct "other" Teotihuacan angle were 16deg11' instead of 16deg30', the ratio would be the same as the Antares-Algieba standard. As with P, Avior's difference in RA with Arcturus changes rapidly with precession, 42-1-18.5 = 22.5"/yr. Millon's 1972 book accompanying his map, says that S of E orientations at Teotihuacan generally range from 16.5 to 17deg. However, the most prominent long EW structure at Teotihuacan, is the EW wall shown on Millon's large photogrammetric paper map, forming the northern boundary of the Citadel (the large courtyard of the Pyramid of Quetzalcoatl). My own measurement Feb. 27 on Iowa State University's copy of Millon's map, shows that this wall's orientation (along its northern, outside edge) is 90deg + 55' +/- 1' clockwise from the Avenue, i.e. 16deg20' +/- 1' S of E.
The needed "other" Teotihuacan angle is seen even more accurately in the angle which, according to spherical trigonometry, the great circle from the El Castillo (at Kukulkan) to Mundo Perdido (at Tikal) pyramids, again using 0.0001deg precision Wikipedia coordinates, crosses the parallel of latitude of the Pyramid of the Moon: the complement of 16deg12'. Accounting for pole shift, this would have been equal to an ancient angle at Teotihuacan that would be 16deg13' now. The other natural point on the Castillo-Perdido great circle, is its intersection with the PyrMoon-PyrCholula great circle: at this intersection, the Castillo-Perdido great circle's angle with due north, is 15deg27', near the 15deg25.6' needed by my theory for Teotihuacan's main avenue angle (pole shift considerations change the 15deg27', to 15deg28'). So, the pyramids El Castillo and Mundo Perdido were placed on the unique great circle that would corroborate the famous "15.5" and "16.5" degree angles at Teotihuacan.
The geographic latitude of El Castillo was chosen equal to the minimum Declination of Jupiter near its post-retrogression stationarity Jan 2013. The minimum Declination of Jupiter near its stationarity, geocentric, apparent (excluding refraction, which would be tiny so near the zenith as at El Castillo) using coordinates of date, including nutation and aberration, is +20.764257deg at 20:15 GMT Jan 23, 2013, according to the JPL Horizons ephemeris (and Luna's is similar, +20.633134; Luna's lower limb would be 1772.486"/2 less: 20.386955). Wikipedia's geographic latitude for El Castillo is +20.6828, to which 0.07106 is added for the effect of the 5'40" W of N ancient pole as seen from Giza. The difference between the Declination minimum and the corrected latitude, is only 37.4" (if Jupiter's minimum Declination is as observed from El Castillo instead of Earth's center, the error is a little less, 36.2"). The corrected latitude of the Pyramid of the Magician, is 20.36080 + 0.07019 = 20.43100, 158.6" greater than Luna's lower limb as above.
The pyramid Mundo Perdido is to Venus, as the pyramid El Castillo is to Jupiter. The geographic latitude of Mundo Perdido was chosen equal to the minimum Declination of Venus near its post-retrogression stationarity Jul 2012. The minimum Declination of Venus near its stationarity, geocentric, apparent (excluding refraction, which would be tiny so near the zenith as at Mundo Perdido) using coordinates of date, including nutation and aberration, is +17.384489deg at about 00:04:30 GMT Jul 06, 2012, according to the JPL Horizons ephemeris. Wikipedia's geographic latitude for Mundo Perdido is +17.22005, to which 0.07030 is added for the effect of the 5'40" W of N ancient pole as seen from Giza. The difference between the Declination minimum and the corrected latitude, is 338.9". If Venus' Declination is observed from Mundo Perdido instead of Earth's center, the error is a little less, 327.0". If the Mundo Perdido site were surveyed originally at the start of the Younger Dryas 12,680 yr ago (2013AD - 12,680) and Giza only at the start of the Mayan Long Count 5125 yr ago, extrapolating the pole shift correction, changes the +338.9" error, to -34.2".
Venus' Declination at minimum geocentric apparent Right Ascension of date, which occurred Jun 27 2012 04:21 GMT near stationarity, was greater, +17.834013deg. At El Mirador, the latitudes usually given online for the La Danta & El Tigre pyramids are 17.75156 & 17.75606, resp. Correction for pole shift vs. Giza, as above, gives 17.82166 & 17.82614. So, the errors are only 44.5" & 28.3", resp., about the same as the error regarding Jupiter at El Castillo.
From my measurements on Millon's map, the distance between the Pyramids of the Moon and Sun is equivalent to 25.02" geographic latitude, where the last digit is doubtful due to ruler error. Perhaps this distance was chosen for additional redundancy in the code. The difference in RA between Arcturus and the point P is 87.146deg. The geometric mean of these two angles is 46.7'; 16deg11' - 15deg25' = 46' is just the increment needed, to make the "other" Teotihuacan angle, 16+ deg E of N, perfectly correspond to Avior in this theory. Another interpretation of the PyrMoon-PyrSun distance, is that according to a formula of Newcomb for the historical rate of precession, the 25.019" corresponds to exactly half the mean precession rate since 130 BC +/- 80 (or maybe more) yr, where the uncertainty is from my estimated ruler error: this matches the dates of the earliest known major construction at these pyramid sites.
The Tycho-2 catalog reveals several times as many stars of Vmag < 8.00, as does the Skiff spectral type catalog. I've not yet had time to assess the Tycho stars, but can see from their number that the correlation of early K giant stars (Arcturus, Algieba, Botein and others) whose reduced Declinations are geographic latitudes of tetrahedral corners, as discussed in my previous investigations, might or might not be statistically significant.
Let us consider the Right Ascension of Luna. At 01:15 GMT Mar 25 = Mar 25.052, according to the JPL ephemeris, the J2000 RA of Luna becomes equal to the J2000 RA of Algieba according to the Bright Star catalog (corrected for proper motion only). Luna's RA changes 31"/minute, so aberration, or the use of J2013.23 instead of J2000 meridians, hardly affect the result. (The time derivative of the nutation displacement of Earth's pole, which I got online from celnav.de, is suspiciously large though perhaps consistent with the amplitude of the 0.5 yr nutation term. If I omit the nutation altogether, i.e. use the mean pole corrected for precession and secular obliquity change only, I find that the minimum Declination of Arcturus is Mar 21.706. I calculated nutation by interpolating 60 day intervals; if I use much smaller intervals, the date of Arcturus' minimum Declination can change by several weeks.)
If the North Pole position is changed to its former position suggested by Petrie's survey of Giza (i.e. 340" W of N as seen from the Great Pyramid, per Petrie's value 5'40" +/- 10"; but no closer nor farther from Giza) then Arcturus' minimum Declination on Mar 25, 2013, would differ only 0.30" (not much more than coordinate rounding error) from the former geographic latitude of the Cholula pyramid. However, if the Pole position were the same when Teotihuacan/Cholula was surveyed, as when Giza was, then the 2.1deg W of N orientation of the PyrMoon-PyrSun line, did not indicate the Pole. Instead, this angle gives more evidence for the c. 130 BC construction date. The time midpoint between 130 BC and 2013 AD is 942 AD; denote the mean celestial pole then, according to the online NASA Lambda utility, by B. Denote the mean celestial pole at 2013 AD by C. Denote the position of Algieba at 2013 AD, according to the online Hipparcos catalog, by A. Spherical trigonometry gives the angle BAC = 1.612326 (see above for this number's importance) * 2.137244deg. Including the effect of Petrie's 5'40", the angle between the PyrMoon-PyrSun line and the original Earth pole would have been 2.0987 + 200.99"/3600 = 2.1545deg. The difference from 2.1372, 1.0', is only 0.5 sigma times my paper map measurement error (see above) and implies only 0.7 sigma deviation from the measured PyrMoon-PyrSun angle (vs. 1.0 sigma & opposite sign, without the 201" correction). These coincidences suggest that the builders of Giza in 2500 BC, knew that the small upcoming pole shift would be perpendicular to their chosen meridian. The result for Arcturus suggests that the pole shift the Giza builders foresaw, mostly occurred between 130 BC and the present.
These are the reasons Algieba was chosen:
1. It is one of the 50 brightest stars in the sky, and the brightest star in the mane, or sickle, of Leo.
2. Algieba's Right Ascension (J2000 10h20m) interpolates with almost equal steps that of Antares (16h29m), Arcturus (14h16m), the Sun, or rather its antipode, at Mar 25.162 (0h16m = 12h16m - 180deg) & Avior (8h23m), all of which together span only about 8h RA, so are simultaneously visible in the Teotihuacan night sky in late March.
3. Suggestively, Arcturus, Algieba and Avior have the same color; all are, or have primaries that are, early K giants, i.e. K0 to K3, type III (possibly K7 for Avior) while Antares is M1.5 Ib. Algieba has a bright, late G secondary. Avior & Antares have moderately dim, early B secondaries, so the subjective colors of these stars might be less red than the primary's spectral type would suggest. Similar color is another clue that the stars all belong to the same monument scheme.
4. Algieba's Declination is very near that of Arcturus.
5. When Arcturus' Declination is minimum March 25.16, 2013, Luna is roughly south of Algieba. |
| Joe Keller |
Posted - 15 Feb 2013 : 17:54:55
The near-miss asteroid: disinformation?
Or, conspiracy theory du jour
Months ago I interpreted crop circles as saying that something would be happening with a bell curve probability peaking Feb 17 (and a standard deviation of roughly two months). Then we are told that there will be an asteroid near-miss Feb 15, and an explosion in Russia that day is attributed to a small fellow traveler [update Feb 16: only briefly was there such an attribution; mainstream astronomers quickly publicized that the Russia impact was due to a meteor of much different orbit, therefore unrelated to the near-miss asteroid] of that near miss. The "asteroid" might be a small interplanetary probe launched by the U.S. to distract amateur astonomers and provide, for a few more crucial days, a false alternative explanation for what really is happening. |
| Joe Keller |
Posted - 07 Feb 2013 : 16:28:22
How unusual is it that Algieba1 is off by 2.80"?
Executive summary: re Tortuguero Monument 6, Arcturus is "Bolon". His nine "companions" are the "reduced Declination tetrahedral corner stars" (two lie in the southern hemisphere; the dimmest are Vmag +9.00) Algieba, Botein, HD208202, HD65735, HD178555, HD139486, HD20682AB, HD73854, & BD+19 4022.
Another approximating star, to the "reduced" tetrahedral corners (whose reduced latitude, equals the geographic latitude of the actual corners)(see Appendix) at March 25.0, that I've found in the Bright Star Catalog, is HD208202 (a.k.a. HIP108119) whose Vmag is +6.36. Using the Hipparcos data again, I find that it is 13.94" too far north, to lie at Declination equal to the geographic latitude of the "reduced" tetrahedral corners when Arcturus' Declination is minimum. Curiously, HD208202 also is a double whose brightest component is an orange giant, spectral type K0 III (for Algieba the brightest component is K1 III; Arcturus is classed as K1.5 III). Earth's most flattened meridian, according to the 1952 ground-based Soviet determination, is 06W at 1/295.2. A spheroid this flattened, would have its "reduced" regular tetrahedral corners 10.43" farther north in geographic latitude, than for a spheroid flattened only 1/298.0; thus HD208202 would be only 3.51" too far north.
This many online Bright Star Catalog (9110 rows of data) stars would be expected in a band 2.80+13.94=16.74" wide at 19.775deg Declination:
9110/(4*pi)*2*pi*cos(19.775)*16.74/3600*pi/180 = 0.35
My computer program finds regular tetrahedra inscribed in a triaxial ellipsoid flattened 1/298.0 & 1/295.2, with a vertex at the South Pole. If a "reduced" vertex lies on the least flattened meridian, it must have geographic latitude 6.093" greater than if the other meridians were flattened the same so that the ellipsoid were a spheroid, and the other two vertices at that latitude, must have latitude 3.05" less. If a vertex lies on the most flattened meridian, it must have geographic latitude 6.476" less, and the other two vertices 3.24" greater.
So for Earth's actual triaxial ellipsoid, the most southerly possible inscribed "reduced" regular tetrahedron vertex (with one vertex at the South Pole) is at geographic latitude 3.05-2.80=0.25" south of the Declination of the brightest component of Algieba, and the most northerly possible such vertex 3.51-3.24=0.27" south of the Declination of HD208202. (These Declinations are at March 25.0 when Arcturus' Declination is minimum; all Declinations include aberration and nutation.) By linear interpolation I find that a change in spheroid flattening from 1/298.0 to 1/298.05 causes 0.18" decrease in the vertex latitude, and a change from 1/298.0 & 1/295.2 to 1/298.0 & 1/295.15 causes 3.05*0.05/2.8 = 0.054" decrease in the latitude of the most southern vertices of a tilted tetrahedron with south pole vertex. Rounding error thus could explain much of the discrepancy observed with the Declinations of Algieba and HD208202.
The only other approximate "tetrahedral" star that I find in the Bright Star catalog (for northern, not southern Declinations) is Delta Arietis (Botein), Vmag +4.35. Amazingly it is K2 III, about the same spectral type as the others. Hipparcos data show that at the relevant time it lies 5.97-3.05 = 2.92" south of the most southern "reduced" vertex for the triaxial ellipsoidal Earth.
Now let's consider the Right Ascensions of these, corrected for mean precession & ecliptic (NASA Lambda utility) but not nutation or aberration:
Arcturus RA J2013.23 14:16:17
Algieba 10:20:42
HD 208202 21:54:55
Delta Arietis (Botein) 03:12:23
HD 65735 08:01:34 (see below)
HD 178555 19:10:35 (southern hemisphere)(see below)
The difference between HD 208202 & Delta Arietis, is 5.291h. Between Algieba & HD208202, 11.570h = 6h + 5.570h. Between Algieba & Delta Arietis, 7.139h = 12h - 4.861h. Between Delta Arietis & Arcturus, 11.065h = 6h + 5.065h. This suggests some involvement with the 5+ hr period I'd identified in earlier posts as astronomically fundamental. For the southern hemisphere star (see below), between Arcturus & HD 178555 is 4.905h. Between Delta Arietis and HD65735, 4.820h. When the four non-giant stars found below are included, along with Arcturus, for ten stars total, the periodogram in RA has its highest peak, 4.91, at 3.02 hr RA period, and also its only near-zero, 0.0200, at 2.911 hr RA period.
There is one near miss among the stars near Declination -19: HD178555 (Vmag +6.13, spectral type K1 III ! ) lies 21.54" too far south in the same sense that HD208202 lies 13.94" too far north. That is, allowing for the southernmost "reduced" corners of any slightly tilted regular tetrahedron inscribed in Earth's triaxial ellipsoid with a vertex at the North Pole, HD178555 is 21.54-10.43-3.24 = 7.87" too far south.
In absolute terms, on March 25.0, HD178555 lies farthest in Declination, from Algieba: 24.34" (30 days earlier: 25.01"). Then the greatest difference in Declination, in absolute terms, is between HD178555 & Botein: 27.51" (30 days earlier: 28.58"). When I measured on Millon's large paper map, the distance between the centers of the top platforms of the Pyramids of the Moon & Sun, I found that the component of this distance, parallel to the "Avenue of the Dead", is 769.3m, where the last digit is doubtful due to my ruler error. Using Zhongolovich's Earth dimensions from the 1987-1988 CRC Handbook of Chemistry & Physics, I find that if this were a N-S distance it would correspond to 24.89" geocentric or 25.02" geographic latitude difference, where all hundredths digits are doubtful due to ruler error; this is consistent with the Algieba - HD178555 absolute Declination difference March 25 - 30 = Feb 23. The complete interpyramid distance (not just the component parallel to the Avenue of the Dead) measures 806.7m; if this were a projection from the Avenue of the Dead (i.e. a side of the right triangle rather than its hypotenuse) the distance along the avenue of the Dead would correspond to 25.019*(806.7/769.3)^2 = 27.51", consistent with the Botein - HD178555 abs. Decl. difference March 25.
Searching the 604,000-row Skiff spectral type catalog online at VizieR, for magnitudes 6.31-9.99 (thus overlapping the Bright Star Catalog 0.2 mag at the bright end) and spectral types "G9III", "K0III", "K1III", "K2III", & "K3III", I find no additional objects at Declinations of date, comparable to the foregoing. I confirmed this by scanning the entire Skiff catalog between Decl +19.7 & +19.85 (554 rows; many rows were essentially duplicates, due to variations in naming or spectral classification) by eye for these spectral types, but did find one more: HD65735, Vmag 6.30 (too bright to fall into my previous search) K1 III. For 2013, this star is 10.43+3.24-11.59 = 2.08" south of the northernmost corners; for 2014, 3.05-1.11 = 1.94" north of the southernmost corners. I also scanned the Skiff catalog between Decl -19.85 & -19.7, limited to Vmag < 6.31, and found no additional stars with these spectral types and appropriate Declinations on the relevant dates. Neither did I find any of type V, IV, II or I, for colors G9-K3 (or any color whatever for types IV & III) and Vmag 6.21-9.99.
I do find HD139486 (southern hemisphere), Vmag 7.65, type B9.5V (in absolute value 6.09-3.05 = 3.04" south of the southernmost reduced corners, Mar 25 2013, and 4.86-10.43+6.48 = 0.91" north of the corner on the most flattened meridian, Mar 28 2014); HD 20682AB, Vm 7.60, A2V (0.31-3.05 = 2.74" north of the southernmost corners in 2013, and 10.43+3.24-11.94 = 1.73" south of the northernmost corners in 2014); HD73854, Vm 9.00, F1V (22.84-10.43-3.24 = 9.17" north of the northernmost corners in 2013, and 7.27-6.09 = 1.18" north of the corner on the least flattened meridian in 2014); and BD+19 4022, Vm 9.00, F5V (10.43+3.24-12.38 = 1.29" south of the northernmost corners in 2013), whose Declinations will be very near the abovementioned "reduced tetrahedral corners" at 2013.23AD and/or 2014.23AD. These four type V stars, plus the five early K type III stars already found, could be the "nine companions" of "Bolon" (=Arcturus) which "descends" to its local minimum apparent Declination in March 2013. (I used the Hipparcos catalog for astrometric data on all stars, or its extention, the Tycho catalog, for the dimmest stars, HD73854 & BD+19 4022.)
In 2014 (to save time in calculating aberration, I assumed that Earth's velocity would be exactly the same, exactly one sidereal year later) at Arcturus' minimum Declination March 28.0, HD178555 would be only 10.43+3.24-13.04 = 0.63" north of the southernmost (southern hemisphere) reduced tetrahedron corner. Delta Arietis would be 6.95-6.09 = 0.86" north of the corner on the least flattened meridian.
Appendix. The "reduced" tetrahedral corners.
For simplicity let's consider a two-dimensional cross-section of a sphere, a great circle. Suppose particles stream (in the plane of the circle) with velocity (X, Y) and elastically (i.e. with perfect recoil) strike the perimeter of this circle with equal probability at all points. A segment of the perimeter, (dx, dy) absorbs a momentum vector proportional to (-dy*X, dx*Y). From the symmetry of the circle, we know that the sum of all these absorbed momentum vectors all over the circle's perimeter, must have direction (X, Y) like the particle stream.
If the circle now is flattened into an ellipse, dy becomes b*dy with b<1. The sum of all the absorbed momentum vectors now has direction (-b*dy*X, dx*Y). The tangent of the orientation angle of the absorbed momentum vector has been multiplied by 1/b.
If a particle stream is directed perpendicular to the surface of Earth's ellipsoid at the corners of an inscribed regular tetrahedron, its orientation angle is the geographic (a.k.a. geodetic) latitude of those corners, by the definition of geographic latitude. Unlike a sphere, an ellipsoid lacks symmetry; it slightly resembles other flattened objects like boards or sails. The absorbed momentum vector is not exactly parallel to the particle stream direction. It is normal to a point on the ellipsoid, the tangent of whose geographic latitude is greater by a factor of 1/b, than the tangent of the orientation angle of the particle stream. That is, its reduced latitude equals the geographic latitude of the actual tetrahedron corners. |
| Jim |
Posted - 22 Jan 2013 : 21:16:23
Dr Joe, The ice age cycle requires about a million quads of energy to go from max. ice to no ice on the north area of our planet. A million quads can be moved over time bit by bit so we can use any reasonable period of time for the process to go from no ice to max ice-lets say 10,000 years or 100 quads per year. We remove 100 quads from the Arctic for 10,000 years and we have a 2,000 meters of ice covering 5% of our planet,s north lands(and sea). The energy can be returned to the north through deep sea vents in the Arctic Ocean over any reasonable number of years-lets say 500 years. We add 2,000 quads per year to the Arctic Ocean for 500 years and we have no ice. These vents and the geothermal activity is currently unknown to science and due to that ignorance no one is looking into these details at this time. |
| Jim |
Posted - 16 Jan 2013 : 23:42:06
The ice age cycle requires a shift in energy flows somewhere. Ice will form when the temperature is below 273 kelvin but only when water is involved. If the radiation law is correct a body at 273 kelvin radiates about 280 watts per square meter or so. The sun never provides that much energy anywhere near the poles and still the ice melts. They say greenhouse gas causes this melting. You hope maybe polar shifts can be the cause. I say the cause is mantle heat. It is the mantle that is causing the climate to change. |
| Joe Keller |
Posted - 16 Jan 2013 : 21:59:57
quote:
Originally posted by Jim
...Why would a shift in the poles cause energy to shift from place to place on the surface of our planet?
I think I'm ready to try to address this. The "heat of fusion" of water ice is about 80cal/gm. The "solar constant", i.e. the power of the Sun at Earth's distance, is 2.0cal/minute/ sq cm. Since the density of ice is only a little less than 1gm/ml, the Sun puts forth enough power to melt through a cm of ice in 40 miutes. This gives an idealized lower bound of 40*10^5 minutes * pi (to account for Earth's rotation) = 24 yrs to melt through a km of ice (Chicago is thought to have been under 2000 ft of ice during the most recent Ice Age). Really, it takes far longer than this, because much of the incoming solar energy is lost back into space, or carried away by winds and currents to the other places where ice is - allegedly - forming.
The same holds true for the reverse process, of latent energy release and ice deposition, but with yet another problem: if the wettest places on Earth have only about 100 inches (2.5m) of rainfall yearly, how could 1km of ice accumulate in less than 400 yrs? Polar regions tend to have relatively little precipitation: 10 inches/yr and 4000 yrs might be more like it.
Jim, is this related to your ideas?
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| Jim |
Posted - 16 Jan 2013 : 14:58:01
Dr Joe, The ice age cycle requires a change in energy flows and at this time no one even has a guess of how much energy is involved making and melting all the ice. Why would a shift in the poles cause energy to shift from place to place on the surface of our planet? |
| Joe Keller |
Posted - 15 Jan 2013 : 22:08:30
The Serpent Mounds: another Platonic solid, another pair of stars
(revised Jan 20, 2013)
The Ontario & Ohio Serpent Mounds are to a regular octahedron and Deneb and Vega, as Teotihuacan & Cholula are to a regular tetrahedron and Algieba and Arcturus. I use the same computer program as for my previous post, and the same Hipparcos catalog, to find the Declinations for current times including effects of nutation, aberration & parallax.
The Declination of Algieba1, gamma1 Leonis (when Arcturus is at its minimum Declination this spring due to aberration) was found in my previous post to differ only 2.80" from the geographic latitude whose reduced latitude equals the geographic latitude of a corner of a regular tetrahedron inscribed in the Earth spheroid with a corner at the South Pole. Analogously I can attempt to inscribe a regular octahedron concentrically in the spheroid so that the edges of the base are parallel and perpendicular to the equator, but if the inscribed base is square then the peaks are inside the spheroid. If I modify the base to a rectangle, and place the peaks on the equator anyway, I find that the octahedron is most regular, in the sense that the variance of the lengths of its twelve edges is the smallest, if the corners of the base are at reduced (i.e. parametric) latitude 45.096305; the geographic latitude, whose reduced latitude equals the geographic latitude of the former point, is 45.289021 (I use Earth flattening 1/297.8 because it was found in 1952, from purely ground-based measurements, that the flattening was 1/298.0 at 96W & 1/295.2 at 06W, and for other longitudes I can interpolate those minimum and maximum values). That is, this is the latitude of the "reduced" corners of the most nearly regular rectangular octahedron that can be inscribed orthogonally in the spheroid. At March 18.2, 2013 (see below) Deneb's apparent Declination is 133.15" north of this latitude. If I choose instead the octahedron whose base is square, the reduced latitude is negligibly different: arctan(297.8/296.8) = 45.096360.
Wikipedia and many other online sources agree that the geographic coordinates of the Serpent Mound of Ohio, are 39deg01'33.09"N, 83deg25'49.60"W; other sources give coordinates differing from these by only fractions of an arcsecond. From a snapshot from Google maps someone put online, I find that such coordinates correspond to points near the midpoint of the serpent curve. Due to the Ohio serpent's orientation, no point on the Ohio serpent is much closer than this, to the Ontario serpent.
Some online sources give coordinates for the Ontario headquarters building of the Hiawatha Tribe, or for (presumably the headquarters of) Serpent Mounds Park in Ontario, but I found only one source giving coordinates for the Serpent Mound of Ontario itself: www.megalithic.co.uk gives 44deg15'N, 78deg10'W; when I checked the 1:50,000 topographical map in the Iowa State Univ. map room the morning of Jan 16, I found that the megalithic.co.uk coordinates are those of the nearest large town, Keene. ISU's 1978 topographical map shows that the park is only 1km wide at its widest. It occupies a peninsula into Rice Lake. The online coordinates for the park, are about right. My ruler measurement to the marked historical site on the map, gives 44deg 12' 30" N, 78deg 09' 16" W, probably accurate to the nearest arcsecond. I discovered Feb 06, on a website called waymarking.com, that someone else has determined the coordinates as 44deg12.406' = 44deg12'24.36" N, 78deg09.295' = 78deg09'17.70" W. This is about 5.30" closer than mine, to the Ohio serpent mound.
On a spheroid flattened 1/297.8, the Lambert approximation which I copied from Wikipedia, gives geodesic distance 6.486895 deg between these points ("degrees" here signifies length the same as a degree measured along the equator of the spheroid) where I have subtracted 13.24" because of the compression that might occur if this part of Earth's crust were rotated to a NS orientation (see Appendix). The geodesic distance between points on the same meridian of the spheroid, and with geographic latitudes equal to the "octahedron corner" and the apparent Declination of Vega, most nearly equals the Ohio-Ontario distance, at Mar 18.2 2013, when it is only 27.17" less than the adjusted Ohio-Ontario geodesic distance.
If originally the Ontario & Ohio serpent mounds had lain on the same line of longitude, then by spherical trigonometry the pole could have been as far north as 63.17deg. If the Ontario serpent mound had been then at a latitude equal to today's current Declination of Deneb, then the pole would have been at about 63N, 4W, not far from one of Hapgood's positions (not the most recent Ice Age position, but an earlier Ice Age), 72N, 10E.
Appendix. Suppose a unit sphere flattens to an oblate spheroid with axis ratio 1-3*f, f = 1/297.8/3, while maintaining constant volume. The "b" axis of the spheroid is now approx. 1-2*f, and the "a" axis is 1+f to maintain volume. The length of a meridian decreases according to sqrt(((1-2*f)^2+(1+f)^2)/2) = 1-f/2. The north-south height of a typical small sector of Earth's surface, decreases according to a stretch factor approx. 1-f/2, i.e. a stretch of -f/2, a negative stretch, which could be called a compression. The width of the sector increases according to a stretch factor 1+f, a stretch of +f. By spherical trigonometry, the azimuth from the Ohio to the Ontario serpent mound, is th=35.52117deg (near the null compression orientation, arctan(1/sqrt(2)) ) E of N, so the stretch along this line is small, f*(sin(th)^2 - cos(th)^2 / 2 ) = 0.00635*f. When the pole shifted, the stretch increased by (0.00635-(-1/2))*f*6.490495deg (distance measured in "equatorial degrees") = 13.24". |
| Jim |
Posted - 13 Jan 2013 : 21:47:43
Dr Joe, It seems to me all your sources use the same flawed model we have been kicking around here for several years. We have a model with two barycenters that are assumed to be fixed points. These barycenters don't even exist in the real system they attempt to predict, but that is irrelevant because for most users the fact the model is very near to an accurate indicator of how the real system behaves is amazing. you are doing very fine detailed work and the model is never nearly finely tuned enough to give true positions of any of the objects you are looking at. |
| Joe Keller |
Posted - 09 Jan 2013 : 18:42:47
Teotihuacan & Cholula: Platonic solids, Arcturus, spring 2013
I recalculated the apparent Declinations of Algieba and Arcturus as precisely as possible. I found that throughout early 2013, the difference in their Declinations is only about 1 arcmin more than the difference in latitude of the respective pyramids, of the Moon at Teotihuacan, and Cholula. For details see "Appendix. Method" at bottom.
Again I considered the hypothetical effect of a likely pole shift. In light of my result for the Serpent Mounds (see my next post) I assume that originally the Pyramid of the Moon was at a vertex of a regular tetrahedron inscribed in Earth's spheroid with one corner at the South Pole. For Earth's spheroid, I adopt flattening 1/298.0 for the reasons given in the Appendix. Analytic geometry gives a quadratic equation for sin(parametric, a.k.a. reduced, latitude); this results in geographic latitude 19.713773, 51.02" greater than the 19.6996 given by Wikipedia for the Pyramid of the Moon today. Now suppose that originally the Pyramid of the Moon was not at this latitude, but rather at the "reduced tetrahedral corner", i.e. the geographic latitude whose corresponding reduced latitude equals the geographic latitude of the inscribed tetrahedron: this greater geographic latitude is 19.775010, 271.48" north of the present geographic latitude of the Pyramid of the Moon.
Because Teotihuacan and Cholula are less than a degree apart, I can use plane trigonometry approximations to find that a pole direction shift, theta, to the west of north, increases the latitude difference between the pyramids of the Moon & Cholula, by a factor cos(38.53490-theta)/cos(38.53490). The larger the pole shift, the farther south Cholula was, assuming we know the latitude of the Pyramid of the Moon as discussed above. During early 2013, Arcturus moves a few arcseconds south and then north again, as its aberration changes. There is a minimum allowable geographic latitude for Cholula, which just equals Arcturus' minimum Declination (of date) achieved about March 25.0. At this time, Algieba (comparison of the epoch 2000.0 position computed in the online Hipparcos catalog, to the Bright Star Catalog, confirms that it is gamma1 Leonis, the brightest component) has apparent Declination only 2.80" S of the assumed original geographic latitude of the Pyramid of the Moon, the tetrahedral latitude for the spheroid. The needed latitude for the pyramid of Cholula, is consistent with a pole shift 2.1012deg W of N.
Months ago, my measurements on the large paper copy of Millon's map at the Iowa State Univ. library, found that from the centers of the top platforms of those pyramids, the alignment is 2.1064 deg W of N. My measurements were, I think, often off by 0.1mm but rarely by 0.3mm; thus the measurement errors roughly are distributed equally over the interval [-0.2mm,+0.2mm]. I had to add several measurements, including the measurements by which I determined the centers; I calculate a sigma error, from the ruler measurements alone, of 0.0336deg. So, the difference between the interpyramid azimuth I measured on Millon's map with a ruler, and what is needed to achieve perfect equality of Arcturus' apparent minimum Declination March 25 with the original geographic latitude of Cholula, is only 0.15 sigma according to my estimated ruler measurement error.
Using the NASA Lambda utility to convert J2000 to J2026 coordinates for Arcturus & Algieba (gamma1 Leonis) I find that at present, the Declinations of these stars are decreasing 18.60" & 18.33"/yr, resp., due to precession and proper motion. So on a timescale of months or a few years, their Declination difference mainly changes due to aberration or nutation. One year's change in the Declination of Arcturus, is about 1/4 of the latitude difference discrepancy which the pole shift west of north is correcting; that is, it corresponds to about 0.5deg, far larger than my map measurement sigma error of 0.03 deg.
Summary. Let's assume that true geographic north then were indicated by the alignment of the pyramids of Moon and Sun at Teotihuacan (2.1deg W of N today). Let's assume also that the original reduced latitude of the Pyramid of the Moon, equaled the geographic latitude of the corners of a regular tetrahedron inscribed in the Earth spheroid (assuming flattening 1/298.0) with one corner at the South Pole. Then Arcturus would have been at the zenith over Cholula at its minimum apparent Declination this spring, and Algieba (gamma1 Leonis, the brighter companion, is the star recorded by the Hipparcos satellite) then would have been only 2.8" south of the zenith over the Pyramid of the Moon.
Sociological comment. Such elaborate warning as these calendars and pyramids provide, implies that the event will be not only catastrophic, but will occur without warning otherwise. Expect a sudden hammerblow, like a giant lightening strike from space, that comes with little warning (only strange unexplained sounds?) because it comes at the speed of light.
The date, Dec 21, 2012, was determined by the need to end the Mayan calendar on a recognized important day so that the calendar could not be dismissed as arbitrary. The pyramids of Teotihuacan and Cholula, playing on the Declination of Arcturus, indicate the spring of 2013 and definitely exclude the springs of 2012 or 2014. The crop circles (see my above posts) seem to be indicating a bell curve for the predicted time, Feb 17 +/- half maximum 64 days = sigma 54.3 d. Algieba's opposition is Feb 18.
Appendix. Method. This time, I started with original stellar coordinates (Arcturus; and gamma1 Leonis, the brighter member of the Algieba double) from the Hipparcos catalog, in J2000 coordinates but of epoch 1991.25AD; using Julian days, I applied the exact Hipparcos proper motions to these coordinates for all times.
I accounted for precession, mean obliquity and the motion of the ecliptic plane, simply by getting the J2000 coordinates of the mean pole from the NASA Lambda online coordinate conversion utility; these are given in increments of 0.01 Julian yr, so I interpolated quadratically over the range Dec 31, 2012 - Apr 30, 2013, from values at 2013.00, 2013.16 & 2013.32AD. I found nutation, based on a formula by Meeus, from the online utility at www.celnav.de, and interpolated this quadratically too, adding it to the mean pole.
I found Earth's heliocentric position and velocity, by quadric (4th degree) interpolation, on 30 day intervals starting Dec 31, of Earth's JPL Horizons J2000 heliocentric apparent celestial coordinates, and converting to xyz coordinates. For aberration, I divided Earth's velocity by the speed of light, and added that vector to the star's position. For parallax, I multiplied Earth's position vector by the Hipparcos parallax in radians, and subtracted that vector from the star's position. Then I renormalized the star's xyz position vector and reconverted to celestial coordiates.
These calculations required a computer program. I wrote a BASIC program with double precision.
The 1987-88 CRC Handbook of Chemistry & Physics notes that the latest determination it gives of Earth's oblateness, is based on space probe data. The second latest determination given, Zhongolovich 1952, isn't: he approximated Earth as a triaxial ellipsoid with flattening 1/298.0 in the meridian 96W and 1/295.2 in the meridian 6W. Because ancient people would have relied, as Zhongolovich did, on ground-based data (Zhongolovich used data along the Struve arc, which ran mostly through Russia) and because space probe data introduce errors from unknown physical effects, such as the Explorer I rocket or Pioneer probe accelerations, I should use the best, last ground-based determination not contaminated by space probe data, but as applied to the meridians of Teotihuacan or Cholula, 98.8 or 98.3 W.
There is a long tradition of thinking about regular polyhedra: Plato, Kepler, and most recently science journalist Richard Hoagland, who has publicized the occurrence of planetary features (Hawaii, Olympus Mons) near arcsin(1/3), the latitude of three of the corners of a regular tetrahedron inscribed in a sphere with a corner at the South Pole. |
| Jim |
Posted - 02 Jan 2013 : 23:41:19
Dr Joe, I wonder how much of the unknown force you reference above is nothing more than error within the generator. As you know I have been asking about this for many years and I'm very happy to read your latest comments on all the facts you have obtained from the generator. You have a real talent for using this generator at JPL and I for one hope you keep working on it. happy new year. |
| Joe Keller |
Posted - 02 Jan 2013 : 22:15:06
Resonance of Miranda, Umbriel, Titania, Oberon: same frequency as Chandler wobble
The period of Earth's Chandler wobble, nowadays usually is said to be 433 days, or to vary between 416 and 433 days. Some claim to explain this by a complicated interaction of ocean currents and whatnot, but then again, maybe the Chandler wobble is caused by the same force that causes four of the five moons of Uranus (all except Ariel) to resonate with a 431 day period.
For my investigation, I got the JPL ephemeris times of zero and increasing, J2000 Uranocentric ecliptic latitudes for the five major Uranian moons, arbitrarily using the increasing zeroes occurring Jan 15-18, 2013. Then I used the JPL orbital periods, and the near-circularity of these orbits, to find the angles from this point for any time. I considered angles modulo 180.
Four of the five major moons (Miranda, Umbriel, Titania, Oberon) achieve true anomalies (the same as mean anomaly, for circular orbits) (modulo 180 deg) with standard deviation about 5 deg, every 431 days for at least several cycles forward and backward. Furthermore the common ecliptic latitude is near zero at these times. That is, they align every 431 days, with the nodes of Uranus' equator, on the plane of Uranus' orbit.
The nearest to my origin and therefore my most accurately calculated resonance, is at Nov 13.446 GMT, 2012. The standard deviation of the ecliptic latitudes (modulo 180) is 5.42deg at minimum, and the mean latitude then is +1.76deg.
The most massive Uranian moons are the ones whose orbital planes are closest to the equator of Uranus. That is, Miranda's inclination is 4.22deg, Ariel 0.31deg, Umbriel 0.36deg, and Titania & Oberon 0.10deg. At my January reference dates, Titania & Oberon have ecliptic longitudes 167.63 & 167.73, resp. I can estimate the invariable plane of the solar system (excluding the Sun's rotational angular momentum) as an average of the orbits of Jupiter, Saturn, and Neptune, weighted by their orbital angular momenta. The angle of each plane above the ecliptic, in the direction of longitude 167.68deg, is proportional to sin(167.68 - ascending node) and the result is +1.46deg (Neptune by itself is +1.65deg). Including the Sun's rotational angular momentum, multiplies the result by (1-0.034) and adds a term 0.034*7.25*cos(167.68-166) giving +1.66deg.
So, these four Uranian moons align, with a standard deviation, modulo 180deg, of about 5deg, every 431 days (same period as Chandler wobble) typically only 0.3deg from the plane of the solar system's "ecliptic", i.e. the invariable plane (excluding the Sun) or 0.1deg (including the Sun). This is more evidence that there are forces at work in the solar system, that we do not yet understand. |
| Joe Keller |
Posted - 02 Jan 2013 : 12:29:53
August 15 crop circle at Wappenbury: indicates Feb 17, 2013
From the photos and diagrams on cropcircleconnector.com, I count
6*6 + 6*6 + 3*6 + 8*12 + 7 = 193 circles
Aug 15, 2012 + 193d = Feb 24, 2013
but perhaps the innermost tiny 7 circles signify sidereal lunar months. Then we have
Aug 15, 2012 + (193-7)d = Feb 17, 2013
while 193/7 = 27.571, roughly equals the length of the sidereal month, average 27.322d, and almost exactly equals the average length of the anomalistic month, 27.555d. |
| Joe Keller |
Posted - 01 Jan 2013 : 15:03:11
Measuring the asteroids' longitudes in the plane of Jupiter's orbit instead of Earth's (i.e. Jupiter ecliptic coords., using the 1992 World Almanac orbital elements for Jupiter corrected from 1990 to J2000 coords.) I find, as expected, similar results. The minimum standard deviation of the longitudes is 3.37deg, and occurs at Jan 4.7 instead of Jan 4.4. |
| Joe Keller |
Posted - 29 Dec 2012 : 15:41:49
To the asteroid-based dates Jan 4.4 & Jan 22.9, I can add another asteroid-based date, Dec 10.6. This is the time when the sum of the three break angles is minimum, in the broken line described in my Dec 26 post, the total length of whose four segments is minimum Jan 22.9. A meta-analysis of these three estimates, gives mean Jan 2.3, standard deviation 21.7 days. |
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