| 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) |
| Joe Keller |
Posted - 13 Jun 2013 : 16:54:23
New crop circles in Italy: "Here we go again"
A crop formation was reported at Modena (Finale Emilia) in Italy on June 9, 2013. Near a paved highway, it is thought to have appeared during the previous night of June 8-9. The New Moon occurred June 8 at 16h GMT.
This was one of several crop circles that already this spring have been reported in Italy. Maybe the circlemakers cannot wait for sufficiently tall crops to appear in England.
The five disks inside the large circle, signify the first five Full Moons Feb '13 through Jun '13, which occur between Luna's most southerly and most northerly ecliptic latitudes. Luna's maximum northerly ecliptic latitude, geocentric, of date, for the month, occurs at Feb 10, 06:48 GMT whereas Luna's minimum illuminated fraction (i.e. New Moon) occurs at almost exactly the same time, at 07:20 GMT. Thus the first Full Moon occurring after, rather than before, the maximum southerly latitude, is the Full Moon of 21h GMT Feb 25. The rightmost disk of the crop formation (as the formation is shown in most of the drawings and aerial photos online) is the disk just inside the large circle at the end where there are no disks outside the circle. This disk signifies the Full Moon of Feb 25.
If a New Moon could occur 5 1/2 draconic months = 5.5*27.2122 = 149.67d after the Feb 10 New Moon, it would occur at the most southerly latitude for the month. Instead, five synodic months = 5*29.5306 = 147.65d. That is, the time period between the New Moons of Feb and July, symbolized by the string of five Full Moons within the large circle, is two days too short. Maybe it would have been more obvious to put six disks inside the large circle, but six synodic months = 6*29.5306 = 177.18d slightly exceeds 6.5 draconic months = 6.5*27.2122 = 176.88d.
The April 25 approx. 20:08 GMT Full Moon in the center, occurs at a small (southern) latitude, approx. -1.01deg & longitude approx. 215.87, and the May 25 approx. 04:11 Full Moon to its left, is next nearest the ecliptic, at a slightly larger (northern) latitude, +1.56deg & longitude approx. 243.99. Within the large circle, the sizes of the disks signify the closeness of the Full Moons to the ecliptic, with their diameter inversely proportional to the latitude. Using Luna's orbital inclination 5.145deg, the longitude of the imaginary Full Moon which would have been at zero latitude, is approx.
215.87 + (243.99-215.87)*arcsin(1.01/5.145)
/(arcsin(1.01/5.145)+arcsin(1.56/5.145)) = 226.86
The longitude of the southernmost point of Luna's orbit then, would be 226.86 - 90 = 136.86, and the Sun is at that longitude Aug 9 06:54 GMT. At this time, Mars is at long 107.815, lat +0.783, and Jupiter is at long 99.701, lat -0.153.
This difference in longitude, 8.114deg, is shown on the previous crop formation reported June 6 at Barbiano Lugo. The diameters of the three circles given by online sources seem to be erroneous. Despite the oblique view, one can measure the circles' diameters assuming that the farm vehicle tram tracks are equally spaced. I use the ninth photo from the top at www.fainzashiatsu.it; this is the only aerial photo on that page which appears on my browser. I find that the small circle is about 6/15 of one tram space, the midsize circle about 10/15, and the big circle about 4 + 5/10 + 6/15 = 4.90 tram spaces. The ratio of these diameters is
1:1.67:12.25
which, considering the crudity of the measurement, is as close as can be expected to
1:1.88:11.86
which is the ratio of the sidereal orbital periods
Earth:Mars:Jupiter
and it is these periods by which these planets seem to be identified in the crop formation. With my protractor on the circle diagram on that page, measuring by eye from the centers of the circles, I find that the angle Mars-Earth-Jupiter is about 9deg.
In the Modena crop formation, the outermost disk, of the three outside the large circle on the left, would signify the Full Moon of September 2013. That is the last Full Moon before the equinox. |
| Jim |
Posted - 06 Jun 2013 : 13:56:09
Dr Joe, This acceleration mystery at ~53AU has been kicked around a few years ago. I wonder if disk of the galaxy might be the cause. At some point the gravity effect of the sun will be reduced below the effect the disk has and that point might be at 53AU. |
| Joe Keller |
Posted - 03 Jun 2013 : 16:51:35
quote:
Originally posted by Larry Burford
Joe,
...an anomaly at 53 AU...
Would you briefly summarize your thinking...
LB
I'd like to add to my previous reply. In order to rationalize the presence of an anomaly at 52.6AU rather than the 43AU that results from the most straightforward calculation
1/2 * k * T = G * m * M / r
I had to introduce a factor sqrt(3/2) on the right side of the equation, something I never was able to justify convincingly. I wanted to rationalize the larger, 53AU distance, because:
1. The Kuiper belt "dropoff", i.e. rather sudden and almost total nonexistence of Kuiper belt objects with longer semimajor axes, occurs there; and
2. The graph of the Pioneer 10 anomaly, from an article by JD Anderson et al, shows unexplained anomalies there.
Also, I tried to rationalize the CMB dipole asymmetry as due to the gravitational influence of a large distant outer planet such as my Barbarossa, but such an explanation would entail much larger higher-order harmonics than actually are observed. Now I think that the likeliest explanation for the dipole, lies in something else I remarked on years ago, the nearly perfect "orthogonal triple" formed by
1. Dayton Miller's ether drift vector as determined by him from his Mount Wilson observations;
2. The CMB dipole; and
3. The line to the galactic center, i.e. the main radio source there.
This suggests that the dipole is due to some kind of gravitomagnetic force involving the gravitational pull of the galactic center and Sol's true motion around that center. |
| Jim |
Posted - 23 May 2013 : 20:54:48
Dr Joe, So then the issue is does the electron obey thermal laws? In my world the electron is not real and does not obey any laws(why should it?). It is a sc-fi idea that is deeply embedded in physical theory and the cause of much confusion in all of science. But, that's just me on a rant so getting back to the point-does electric items have any respect for thermal laws? I don't think so. |
| Joe Keller |
Posted - 23 May 2013 : 14:22:37
quote:
Originally posted by Jim
Dr Joe, It is correct for molecules and usually written: 3kT=mv^2. ...
Hi Jim,
Yes, you are correct and now I see what you meant. Before, I thought you meant that my equation was mathematically impossible because the units didn't balance, so I was going to explain, that the units do balance because an erg is the same as a dyn-cm.
My equation isn't from a textbook. It's my hypothesis, that the statistical energy in one degree of freedom, equals the electron's gravitational potential energy at the special distance.
- Joe Keller |
| Jim |
Posted - 22 May 2013 : 18:47:43
Dr Joe, It is correct for molecules and usually written: 3kT=mv^2. The electron(whatever it is)is not an ideal gas and not a molecule. I'd say this 43AU radius is not any special place in the universe. Even so what effect would you expect to find at that distance? |
| Joe Keller |
Posted - 22 May 2013 : 16:09:03
First crop circle of 2013: bell curve & Delta Pavonis
The first crop circle of 2013, anywhere in the world, appeared in NE Tennessee, USA, and is shown on the Earthfiles website, in an aerial photo by Siri Karta. The circle was reported Monday, May 13, and therefore may well have appeared Sunday, May 12 (being difficult to report on a weekend, or less likely to be discovered then).
The New Moon was May 10. The curving line within the righthand (as shown on Earthfiles) circle, signifies that Luna was about 2 days = 24deg past New Moon when the circle was made, i.e. that the circle was made May 12. The gap in the circle itself, signifies that at the future time indicated by the circle, Luna will be about 70deg past Full Moon. (As usual, there is no cartographic-quality information available about the circle. There is only an amateur aerial photo taken from unknown distance and angle. It tells us something about the world's governments, that while they make accurate topographic maps and astronomical databases available to the public, there never has been a geographic-quality photo or map of any crop formation released to the public by any government.)
The lefthand circle also has a gap, symmetrically placed and at least roughly equal in length, to the gap in the righthand circle. To me, this signifies that Earth is to be the same angle past the vernal equinox, that Luna is past full. This occurs May 30.146 GMT, when both these angles are equal at 68.896deg (according to the JPL Horizons ephemeris, using longitudes for the equinox and ecliptic of date).
This time I used a quicker and more transparent method of correcting for the angle of view. I made the Earthfiles photo of the crop circle, into the background of my browser, then plotted the inner and outer ends of the arcs, and of the intersections of the arcs with the connecting bar, on translucent Keuffel & Esser graph paper. I was holding this graph paper orthogonal to what I estimated by eye as the axes of the apparent ellipse shape of the crop circle on which I plotted. Then I measured the major and minor axes of each apparent crop circle ellipse, and corrected the points on the graph paper, multiplying their ordinates by the appropriate axis ratio factor. I supposed that what appeared to be nearly diameters, really were diameters, and found the subtended angles by applying the 2*arcsin(x/2) formula to the angle and then to its supposed supplement, averaging these two results whose errors should largely cancel. This gave two independent results, an inner and an outer, for each crop circle, affording estimates of the mean and sigma for each circle's arc gap:
Lefthand circle : 65.25deg +/- 2.86deg
Righthand circle: 64.32deg +/- 0.85deg
Later I found a less oblique aerial photo by John Mayers, featured by cropcircleconnector.com and elsewhere. By basically the same method I found:
Lefthand circle : 67.90deg +/- 4.45deg
Righthand circle: 75.95deg +/- 5.80deg
From all eight independent determinations together I find 68.35deg +/- 5.78deg SEM, agreeing with the theoretical 68.90deg.
For the end of the curved line which I allege shows Luna's position past New Moon at the time of the formation's appearance, the same method gives about 23.07deg (only the short leg of the inner triangle gives a useful result here). This is Luna's elongation from the Sun at 02:30 GMT May 12, or 21:30 May 11 Eastern Standard Time. (From the second photo, I find about 22.00deg, corresponding to 19:09 May 11 EST).
If the probability distribution for some catastrophe is, as I've guessed based on my interpretation of previous crop circles, normal with mean Feb 17 and sigma = 54 days, then the "tail" beyond May 30 is, to the accuracy of rounding to the nearest day, exactly half the area (~ 2.95%) of the "tail" beyond May 12 (~ 5.99%) or beyond May 13 (~ 5.77%). That is, the date signified by the circle, May 30, is the median expected date of catastrophe given that there has been no such catastrophe up to the date of the circle's appearance, May 12 or May 13.
On the Earthfiles map, I measure the geographic position of the formation, as 53% of the way along a line from Johnson City to Kingsport, Tennessee. I interpolate the Wikipedia geographic coordinates of these towns, to find the crop formation's coordinates as 36deg26'N geographic (= 36.249deg geocentric), 82deg28'W. So, this map implies coordinates reasonably close to those reported by Roger Sugden on cropcircleconnector.com. He gives coordinates
36deg24'24.08" N 82deg27'35.30" W el. 1520 ft.
which I'll use.
Using Wikipedia's coordinates for Stonehenge, and using geocentric latitudes, I find that the geocentric angle between Stonehenge, and this crop formation, is 0.99821 radian, an error of 7 miles (0.10 degree on the globe) from exactly one radian. Note: the exact geocentric angle can be found with elementary geometry, whereas the geodesic arclength on a spheroid would have required advanced calculus.
Likewise, though finding exact angles between geodesics on the surface of a spheroid, requires either advanced calculus, or spherical trigonometry on an auxiliary sphere, elementary geometry can find exact angles in plane triangles whose vertices are points on a spheroid. Assuming that Earth is a perfect spheroid with flattening 296/297, and using the above coordinates for the crop formation, I find that the Nov 1, 1977 North Geomagnetic Pole (not the same thing as the "Magnetic" a.k.a. "Dip" Pole)(position computed by a downloadable program from www.ngdc.noaa.gov) was the right vertex of a plane right triangle with Stonehenge and the crop formation at the other vertices. The evident ~ 0.1 deg error in my assumed position for the Tennessee crop formation, corresponds to roughly 4 yrs error in the 1977 date. So, the elapsed time is 35.5 +/- ~ 4 yr, i.e. round trip light time to a star 5.45 +/- ~ 0.6 pc distant.
The Bright Star Catalog (online, VizieR) has nine entries in this distance range. None is type GV, but one (Delta Pavonis, the farthest of the nine) is, according to the BSC, G6-8IV, and six are type KV (three K0, and one each of K1, K3, K4). Two of these KV stars, 36 Ophiuchi AB, form a binary system; another, 70 Oph, has a type K companion slightly too dim to be in the BSC.
From the current Wikipedia article:
"[Delta Pavonis] is a subgiant of spectral type G8 IV...
"It has been identified by Maggie Turnbull and Jill Tarter of the SETI Institute as the 'Best SETI target' among the list of the 100 nearest G-type stars. Properties in its favor include a high metallicity, minimal level of magnetic activity, low rotation rate, and kinematic membership in the thin disk population of the Milky Way. The lack of detected radial velocity variation suggests that there are no gas giant planets orbiting near the star's habitable zone, which may otherwise destabilize a hypothetical Earth-like planet in that orbital zone. As of 1999, no radio source of technological origin has been detected coming from this star. Delta Pavonis is the nearest solar analog that is not a member of a binary or multiple star system. This is a type of star that is a close photometric match to the Sun."
If there were a third major henge collinear with Avebury and Stonehenge, with Stonehenge at the midpoint, this third major henge would be in Hampshire near the river Avon, near Fordingbridge. A distance between the hypothetical Fordingbridge henge, and Stonehenge, equal to 1.054 times the distance between Stonehenge and Avebury, would make the Gray, Tennessee crop formation exactly one geocentric radian distant. This way, the right angle at the North Geomagnetic Pole would be for about Jul 1, 1974, i.e. 466.4 months +/ 1 month prior to the crop formation, implying a parallax of
1/(466.4/12/2/3.261633) = 0.16784" +/- 0.00036"
whereas the parallax of Delta Pavonis is given by the BSC as 0.170" +/- 0.017" and by Hipparcos as 0.16373" +/- 0.00065" (an Hipparcos revision gives the error as 0.00017"); so the agreement of theory and observation is good. Better yet, extraterrestrials likely would not use our standardized parallax corrected to one AU Earth-sun distance and without aberration. They would use the actual apparent angular displacement toward or away from the Sun; a significant part of this is aberration due to Earth's variable speed toward or away from the Sun. From the Bright Star Catalog, I find the J2000, epoch 2013.5 coordinates of Delta Pavonis as RA 20:08:44.7, Decl -66:11:10, which the NASA Lambda utility converts to 328.25199deg J2013.6 ecliptic longitude (J2013.6 is close enough to the ecliptic-of-date coordinates given by JPL for the Sun). According to the JPL ephemeris, the Sun's longitude is 90deg east of Delta Pavonis', at May 19 2013 01:34 GMT, and 90deg west, at Nov 20 2013 10:15 GMT. Earth's radial speeds then are +0.339202 & -0.345495 km/s, resp., causing aberrations of 0.233380" & 0.237709" away from and toward the Sun, resp. So, the observed parallax, including aberration, is
0.16373 + 0.237709 - 0.233380 - 0.000025 = 0.168034"
where the tiny last term is due to the sum of radii being not 2.0, but rather 1.999695 AU. The difference between theory and observation is 0.000194", just what would be expected from the errors in Hipparcos parallax and Geomagnetic Pole position.
One of the type K stars, Sigma Draconis, has been revised to G9V. As a prospective home for the evolution of life, seems to have at least two strikes against it:
"[Sigma Draconis] is considered a slightly metal-poor star...
"...large orbital eccentricity about the Milky Way galaxy of 0.30 (compared to 0.06 for the Sun.)"
The K4V star is Gliese 570, which has a cool brown dwarf companion and a pair of red dwarf companions. The K3V star is Gliese 783, which has a red dwarf companion and is approaching us at 130 km/s.
Delta Pavonis is a south circumpolar star. Ancient Greek mythology refers to Apollo and other deities as "Hyperboreans", translated as "beings from beyond the source of the north wind". There is also the myth of Santa Claus (Christianized Wotan) at the North Pole. In a sense the South Pole, which is more or less near the position of the constellation Pavo (during Earth's precession cycle, seldom very visible from northern latitudes) is "beyond" the North Pole: the meridian from any point on Earth, to the North Pole, always eventually passes through the South Pole too. "Beyond the north wind" might have been the way that the position of Pavo was remembered by people unaware that Earth is a sphere. |
| Joe Keller |
Posted - 22 May 2013 : 15:38:56
quote:
Originally posted by Jim
...how to get it to balance-or what I am doing wrong?
I've used this equation many times over the years and am sure it is mathematically valid. I just now checked again that the units do balance.
Maybe you could show your work to a high school physics teacher or someone with equivalent qualifications? It must be a matter of finding a simple error in your application.
- Joe Keller |
| Larry Burford |
Posted - 21 May 2013 : 21:07:52
Joe,
Can any of the data you have be interpreted in such a way as to suggest that there might be other **approximately**[1] Sol-centered-spherical EM anomalies within the solar system?
Specifically, between the orbits of Jupiter and Saturn. Other places are possible but for theoretical reasons this one ought to be the most 'detectable'.
The magnitude of the anomalies between Jupiter and Saturn could be significantly different (probably smaller) from the magnitude of the anomalies at the outer edge of the Sol system.
There ought to be some other differences, as well.
LB
[1] Sol is not at the center of the heliopause, and Earth is not at the center of the magnetopause. And neither of these boundaries is spherical, except in a loose approximation. Both are dynamical systems: particles that move within one or more media while influencing at least one of the media.
These hypothetical new boundaries we are discussing ought to be subject to similar physical restraints, if they are physically real.
|
| Jim |
Posted - 21 May 2013 : 19:33:08
Dr Joe, I have tried to use your equation you just posted above. Can you tell me how to get it to balance-or what I am doing wrong? It looks like something is missing on one side of it.to me. |
| Joe Keller |
Posted - 20 May 2013 : 23:12:56
quote:
Originally posted by Larry Burford
Joe,
...observational evidence for an anomaly at 53 AU from Sol...
LB
Thanks for inviting me to discuss this. I haven't yet had time to review my old posts on it, but here is a summary of my somewhat revised thinking now:
Years ago I saw an online article by another physicist, whose name I don't recall, in which he suggested that the so-called "Cosmic" Microwave Background (CMB) really is a Sun-caused phenomenon, because "Big Bang" dreams aside, the Sun is the only object that we really know of, which is big enough and symmetrical enough to cause the CMB. I elaborated on his idea, by speculating that the Sun is the center of a spherical surface many AU in radius, a surface at which some physical interaction, causing the CMB, occurs between the Sun and the rest of the universe, a surface analogous to, but not the same as, the heliopause.
I guessed that this surface would bound the solar system; if so, it would be related to the size of the Edgeworth-Kuiper Belt. Then I considered the equation:
G*M*m/r = 1/2 * k * T
where G = 6.670/10^8 dyn-cm^2/gm^2 is the Gravitational constant, k = 1.3805/10^16 erg/deg is Boltzmann's constant, M = 1.9918*10^33 gm is the solar system's mass (Sun + 4 gas giants + Earth + Venus), m = 9.1090/10^28 gm is the electron mass, and T = 2.7255 K is the apparent blackbody temperature of the CMB. 1 AU = 1.49605 * 10^13 cm.
The equation signifies, that an electron at this radius r from the Sun, would have, if heated to the CMB temperature, a gravitational potential energy that is equipartitioned with its mean energy in any other degree of freedom. The solution is r = 43.00 AU. This happens to be within an AU of the observed median semimajor axis of classical Edgeworth-Kuiper Belt objects. So, we have a radius of obvious physical importance in our solar system (the Kuiper belt radius) which also just happens to define the CMB temperature, via an electron's gravitational potential energy at this radius from the Sun.
The Sun could be at the center of a big ball of "ether". The Kuiper belt formed on the equator of this ball. The CMB is emitted by electrons that are continually falling from (or to) infinity onto the ball.
That's about as far as I went before. To go further, we could consider how the refraction of light at the surface of this ether ball moving through a larger external ether at some velocity (in an ether theory of light transmission, like that of Stokes & Maxwell) would be affected by Earth's position in its orbit. This would be a secondary, nonrelativistic term in the equation for the aberration of starlight. |
| 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
|
| 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. |
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