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Joe Keller
USA
747 Posts |
 Posted - 18 Dec 2009 : 18:18:52
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The Asteroid Resonance - Part 2
In the previous post, I show that my sample of 25 of the most massive (according either to gravitational observations, or to their large dimensions) asteroids, exhibits a breakpoint at somewhere between 5.13h and 5.18h sidereal rotation period. Asteroids just below, but not exceeding, this rotation period, are in orbital resonance with the 6334.329 Julian yr resonance. (This resonance is the empirical 5124.58 yr resonance, on which the Mayan Long Count apparently was based, times sec(36); cos(36) is half the "golden ratio" and also the abscissa of major resonances and antiresonances of Jacobi polynomial families, with powers of 2).
The three asteroids (Davida, Camilla, Psyche) in best orbital resonance, happen to have consecutive rotation periods among the 25. The chance of this is p = (25-2) / (25*24*23/6) = 1.0 %.
Others have said that Earth's rotation period originally was near 5h. For now, let's pretend that Earth's axis is perpendicular to the ecliptic. If angular momentum were transferred from Luna's orbit back to Earth's rotation, Luna's orbit would become synchronous (assuming a circular orbit then) at 4.86h; then R/r = 2.29, i.e. Luna is slightly inside the Roche limit (for a fluid body; this would be outside the Roche limit for some plausible rigid moons).
If the angular momentum return, from Luna to Earth, stopped when Luna reached the fluid-body Roche limit R/r = 2.88 (using the traditional value 2.44 for the equal-density case, and correcting for densities) then Earth's sidereal rotation period would be 4.98h. If early Luna had density only 1 gram/ml (Earth::Luna density ratio = 5.5), then the fluid-body Roche limit would be R/r = 4.31, and Earth's rotation period there, 5.24h. So, a moderately less dense early Luna, originating at the fluid-body Roche limit, could imply an original Earth rotation period between 5.13h and 5.18h, i.e. the critical period suggested by the asteroid data.
Really, Earth's axis is tilted 23.44deg to the ecliptic; consideration of the vector components of the infinitesimal rotation, implies an Earth rotation period of 5.05h, not 4.98h, when Luna was at the fluid-body Roche limit. At this accuracy, assumption of other suggested values of the fluid-body Roche limit (2.423 generally is thought most accurate) hardly matters, nor does assumption of an average tilt of 24deg instead of 23.44, nor does averaging the cosines of the total Earth-Luna inclination 23.44 +/- 5.1deg, nor does modification of the Roche limit by inclusion of the Sun's tidal force.
Early Luna must have been less dense; suppose it were basalt rubble which eventually compressed to solid basalt today. The density ratio of "solid" to "broken" basalt is (www.simetric.co.uk) 3.011/1.954 = 1.155^3. So, the Roche limit would have been 16% greater, the angular momentum retained by Luna 8% greater, and that of Earth ~ 1.6% less. That is, Earth's rotation period would have been 5.05*(1.016) = 5.13h. If early Luna were a broken basalt rubble at the fluid-body Roche limit, Earth's rotation period would have been exactly the critical rotation period (rotation period of 511 Davida; also, half the mass-weighted harmonic mean rotation period of Jupiter, Saturn & Neptune) at which asteroids show orbital resonance with my "third period", 6334.329 yr. (This "third period" has a deep mathematical relationship to the Mayan Long Count, and also approximates the Barbarossa period; see earlier posts.) |
Edited by - Joe Keller on 21 Dec 2009 13:17:38 |
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Joe Keller
USA
747 Posts |
Posted - 18 Dec 2009 : 21:37:53
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Baalbek
Wikipedia's Baalbek article has a simple groundplan of the Baalbek temple site. Called "Nordisk familjebok.png", this map is oriented with East at the bottom and North to the right.
In the upper left corner, is a dotted line presumably corresponding to the oldest part of the structure. This line is oriented, according to my protractor measurements from the screen and from the printout, 15 +/- 1 deg north of east.
At the winter solstice in 2012, Barbarossa's heliocentric ecliptic latitude will be -11.803. At the last Barbarossa event, approx. 6340 yr before 2012AD, Earth's axis was tilted almost exactly toward Barbarossa's ecliptic longitude, with obliquity (polynomial formula, 1990 Astronomical Almanac) 24.134 deg. This implies that Barbarossa's declination then was +12.331.
My quick estimate, is that an object with this declination, viewed from 34.007N (the latitude of the Baalbek temple) would rise 15.1 deg N of E. So, the Baalbek temple seems also to incorporate, in its oldest known strata, the "unexplained azimuth" (i.e., azimuth toward the rising of Barbarossa c. 4328BC as seen from a given temple's latitude) recently noted by Shaltout et al in Egyptian temples (see my earlier posts on that subject). |
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Joe Keller
USA
747 Posts |
Posted - 19 Dec 2009 : 17:54:34
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Unpublished Wall Street Journal letter
Here is the letter I mailed (no response received) to the Wall Street Journal (a Murdock publication headquartered in New York) postmarked Nov. 27, 2009.
"Re: Global Warming with the Lid Off [title of WSJ editorial]
Regarding your Nov. 24th editorial on 'hiding the truth about climate science': it proves the need to be scientifically self-reliant, now! Don't wait for a journal editor to tell you the Mayan Long Count, 5125 years, is a common multiple of the orbital periods of Jupiter, Saturn, and Uranus. Likewise, Joseph Scaliger set Julian Day Zero, 6295 years before the start of the Gregorian Calendar, because he knew an astronomical cycle.
"Brauer dates the Younger Dryas climate change (related to the nanodiamond 'Black Layer' and Clovis human extinction) at 12,683 years before 2012AD. Half that time ago, another partial human extinction removed most cranial diversity in North America and most linguistic diversity in western Eurasia (leaving mainly proto-Indoeuropean); there were simultaneous bicoastal Australian megastsunamis and frequent North Pacific volcanoes. Accurate interpretation of 'Sothic Dates' puts Year One of the Egyptian calendar at 4328BC. Real researchers are needed.
"Sincerely,
Joseph C. Keller, M. D., B. A. cumlaude (Mathematics) Harvard, 1977" |
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Joe Keller
USA
747 Posts |
Posted - 22 Dec 2009 : 14:15:24
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The Asteroid Resonance - Part 3 (Review)
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
- Shakespeare, Hamlet, Act 1, Scene 5
The asteroids. From two lists of the most massive asteroids as determined by gravitational interactions (one list on Wikipedia, and one by Dr. Hilton on the USNO website) and also Wikipedia's list of asteroids of largest dimension, I compiled a list of 25 especially massive asteroids. All these had rotation periods and sufficiently precise orbital periods given on Wikipedia. (I always excluded Trojan asteroids.) The IRAS survey gives 72 more asteroids of estimated average diameter > 150km; 15 of these had, on Wikipedia, rotation periods and sufficiently precise orbital periods, so were added, to make 40 total on my list of sufficiently studied, massive asteroids. (My internet searches failed to find adequate data on any asteroids when such data were lacking from Wikipedia.)
The rotations. Assuming no change in Luna's density, and conservation of angular momentum, Earth's rotation period would have been 5.05h, when Luna was at its presumed formation distance at the fluid-body Roche limit. Early Luna would have been less dense; assuming the density ratio early Luna::present Luna = "broken basalt"::basalt, Earth's rotation period at Luna's formation would have been 5.13h. On my list, two of the 40 asteroids, 511 Davida and 39 Laetitia, have rotation periods 5.13h and 5.138h, resp. (Davida is named for David Todd, who happened to be the first astronomer to predict the position of the trans-Neptunian planet.) Five asteroids have rotation in the range [4.148h, 4.84h]. The other 33 are in the range [5.18h, 29.43h].
The "first", "second", and "third" periods. The "first period" I discovered, is Barbarossa's orbital period according to the four sky survey images: 6340 +/- (conservatively) 9 yr. Many other solar system periods and historical phenomena resonate with this period; using these, the best estimate I can make of its true value, is 6339.364 Julian yr.
The "second period" is approximately the Mayan Long Count. Using modern values, the closest possible common multiple of all important solar system periods or half-periods, is 5124.58 Julian yr.
The "third period" is 5124.58*sec(36) = 6334.329 Julian yr. Cos(36) is half the "golden ratio". Cos(36) also is the abscissa of my recent discovery, the "Jacobi 2 Resonance". At cos(36), families of Jacobi polynomials show major peaks (e.g., the Legendre polynomials) or troughs (e.g., the Chebyshev polynomials) in the strength of the periodicity of their logarithms, for period equal to log(2). Like the "first" and "second" periods, the "third" period resonates exceptionally well with solar system periods.
The resonances of 511 Davida and 39 Laetitia. At the winter solstice, 2012AD, Barbarossa's extrapolated heliocentric ecliptic longitude (J2000.0 coords.) is 176.37deg. According to the online JPL ephemeris (my conversion to ecliptic coords.), at 0h UT Dec. 21, 2012, the heliocentric ecliptic longitudes (J2000.0) of 39 Laetitia and 511 Davida will be 174.39 and 170.71+180=350.71, resp. The closest approach of Laetitia's orbit to Barbarossa, is at longitude 173.74. The closest approach of Davida's, is at about the same longitude, 173.39. So, the same two asteroids which show the pristine 5.13h rotation period, also align with the Barbarossa-Sun axis, with only +0.75 and -2.6 degrees longitude error, at the end of the Mayan Long Count, 12h UT Dec. 21, 2012.
Something is special about the 5.13h rotation. That's why this is posted in the thread, "Requiem for Relativity".
Also, both these asteroids resonate with the "first", "second" and "third" periods:
Remainder on division
"First" period
39 Laetitia 0.024
511 Davida 0.896
"Second" period
39 Laetitia 0.342
511 Davida 0.337 (both are thirds; difference = 0.005)
"Third" period
39 Laetitia 0.931
511 Davida 0.003
(The "first" and "third" periods differ by about the orbital period of a typical main belt asteroid, so those resonances aren't independent.) |
Edited by - Joe Keller on 22 Dec 2009 16:04:46 |
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Joe Keller
USA
747 Posts |
Posted - 22 Dec 2009 : 21:41:38
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The Asteroid Resonance - Part 4
Apparently, something maintains 511 Davida and 39 Laetitia, at one and the same axis of rotation. The most recent determination I've found, of Davida's rotation axis, is that published by Conrad in 2007, the result of one night's observation with the Keck telescope: Davida's axis is ecliptic longitude 297, latitude 21. The most recent determination I've found, of Laetitia's axis, is that published by Kaasalainen in 2002, a restudy of observations from 1949-1988: Laetitia's axis is longitude 323, latitude 35. The angle between Davida's and Laetitia's axes, 27 deg, is small, at significance p = 5%.
An earlier analysis of Laetitia's data, by basically the same Finnish group, was published by Lumme & Bowell in 1991: longitude 327, latitude 36. However, differences between studies often show that the errors in axis determination are bigger than would appear from the standard error bars. That is, there is systematic error much bigger than the measurement error.
A review article (Cunningham, Minor Planet Bulletin, 1985) states that 180 deg ambiguity is one of the common errors. For Laetitia, I combined the five published determinations listed in Cunningham's Table 1, with the two by the Finnish group, adding 180deg to the longitude, when needed to make the measurements believably similar. I then averaged the seven longitudes (range 283-327) and latitudes (range 10-61) to find longitude 307 +/- 6 (Standard Error of the Mean), latitude 38 +/- 6 (SEM) for Laetitia's rotation axis.
For Davida, I combined the two in Cunningham, with the one by Conrad, again adding 180deg to the longitude when needed. I then averaged these three longitudes (range 297-306) and latitudes (range 10-34) to find longitude 302 +/- 3 (SEM), latitude 22 +/- 7 (SEM) for Davida's rotation axis. This comprehensive result indicates that Davida's and Laetitia's axes are only 17 deg apart; p = 2%. The difference in latitudes, between Davida's axis and Laetitia's, amounts to 1.7 sigma, p = 9%, two-tailed. Thus the similarity of the rotation axes is more significant than their dissimilarity.
For greater accuracy, I add the axes vectorially, instead of averaging the longitude and latitude. This gives the same result for Davida, and for Laetitia gives long. 309, lat. 39.
The unweighted vectorial average for all ten published determinations, is (long,lat) = (306,34). Abad, A&A 397:345+, 2003, gives the Hipparcos solar apex motion according to the distance or spectral type of the reference stars. Relative to Type O & B Hipparcos stars (these are thought to be very young stars, whose velocities might approximate that of interstellar gas) the solar apex motion is toward (long,lat) = (271,45) with sigma about 5deg. This is a separation of 29deg, p = 12%, two-tailed.
A novel way to estimate the solar apex motion, is to find pairs of nearby, Type O or B or early A, stars, whose motions relative to the Sun, are the same. I checked the twelve Type V stars with Hipparcos parallax > 30mas and Johnson B-V < 0.020. Using Hipparcos parallax and proper motion, and Wilson/Evans Radial Velocity (VizieR online catalog by Duflot), the Sun's motion directions relative to these stars are almost equal in four pairs, where each pair of stars is separated by ~ 90deg:
1. Sirius and Alioth (1st & 4th nearest of the 12). The Sun's motion relative to these stars, is 18.4km/s toward (RA,Decl)=(132,+43), and 16.1km/s toward (122,+31), resp. The solar apex directions differ only 14deg, and the stars are 105deg apart in the sky.
2. Vega and Regulus (2nd & 3rd nearest). The Sun's motion relative to these, is 19.0km/s toward (RA,Decl)=(256,+1), and 28.7km/s toward (253,-4), resp. These solar apex directions differ only 6deg, and these stars are 109deg apart in the sky.
3. Deneb el Okab (zeta Aquilae) and Algorab (delta Corvi) (5th & 6th nearest). The Sun's motion relative to these, is 27.5km/s toward (RA,Decl)=(289,+39), and 33.4km/s toward (285,+36), resp. These directions differ only 4deg. These stars are 102deg apart in the sky.
4. Alpheratz (alpha Andromedae) and Alnair (alpha Gruis) (8th & 10th nearest). The Sun's motion relative to these, is 32.1km/s toward (RA,Decl)=(269,+53), and 31.1km/s toward (265,+49), resp. These directions differ only 5deg. These stars are 81deg apart in the sky.
Enlarging the investigation, I checked the 42 stars (excluding two with obvious large binary motion: a companion in the Duflot catalog within a few arcminutes, that is almost as luminous, hence massive, and has much different RV) with Hipparcos parallax > 20mas, Johnson B-V < 0.030, and Hipparcos Visual magnitude < 6.7 (excluding 14 stars with V > 9; I want only relatively massive stars). These are spectral color types B and early A, types IV & V plus a few III.
Of all 42*41/2=861 possible pairs, the pair ranking third, in closeness of agreement in their direction of motion, is epsilon Hydri (in the south circumpolar constellation Hydrus) and mu Serpentis (in Serpens Caput). Their speeds (relative to the Sun) differ 20%, but their directions of motion differ only 2.7deg. These stars are 107deg apart in the sky. The vectorial mean Sun velocity relative to these, is 22.6km/s toward ecliptic (long,lat)=(310,33), differing only 3 degrees from my meta-determination (see above) of the shared Davida-Laetitia asteroid rotation axis.
More evidence that Davida's and Laetitia's rotation axes are equal, is that the determinations cluster as if systematic errors sometimes were the same. Cunningham's second listed determination for Davida, is (long,lat) = (306,34); his first & third determinations for Laetitia, are (128,38) & (121,37), presumably correctable to (308,38) & (301,37). His first determination for Davida is (122,10); his fourth determination for Laetitia is (130,10).
Mars' published theoretical Newtonian lunisolar, or rather simply solar, precession period is 170,000 yr. If these asteroids had the same oblateness and rotation period as Mars, they would have about nine times that precession period (it is independent of density and radius) but their shorter rotation periods make it about 45 times. Still, because Davida's and Laetitia's orbital semimajor axes differ considerably, the precessions should randomize in ~ 10^8 yr.; really it's probably less than a tenth that, because of the asteroids' irregular shape. An unknown force keeps them aligned. |
Edited by - Joe Keller on 27 Dec 2009 14:35:45 |
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Joe Keller
USA
747 Posts |
Posted - 28 Dec 2009 : 21:34:08
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The Asteroid Resonance - Part 5
Review. After compiling a list of, approximately, the 40 most massive asteroids for which adequate data are available, I found that two of them, 39 Laetitia ("S" or silicaceous type) and 511 Davida ("C" or carbonaceous type), will be, at the winter solstice 2012AD, 0.75deg from conjunction with, and 2.6deg from opposition to, Barbarossa, resp. In itself, this isn't statistically significant, but their rotation periods are nearly equal: 5.138h and 5.13h, resp., a significant clustering, considering the large range of those periods.
The 5.13h period (review). Straightforward calculation, using conservation of angular momentum and accounting for Earth's axis tilt, shows that, assuming Luna's modern density, Earth's rotation period would have been 5.05h when Luna was at the Roche limit. The actual period would have been greater, because the original Luna would have been less dense, hence the Roche limit larger. The result is rather insensitive to Luna's density; use of an authoritative value of the ratio, solid basalt::broken basalt, increases Earth's theoretical primordial rotation period to only 5.13h. Can it be mere chance that this is the rotation period of the two asteroids (among the 40) which are aligned with Barbarossa at the end of the Mayan Long Count?
The 5.13h period (new information). R Duffard et al, "Transneptunian Objects and Centaurs from Light Curves", A&A manuscript 12601, 5 Nov 2009, on arXiv.org, say (sec. 2.2, p. 3):
"...assuming that all objects have single-peaked light curves...A Maxwellian curve was fitted...for a mean period of 5.13 hours."
When the functional form is known (e.g., it is known that it should be a Maxwellian curve), even a moderate number of data points such as Duffard's (n=72), can give a very accurate estimate of one parameter. Duffard states that it is "obviously not true" that all the objects have single-peaked light curves, but Duffard could be wrong. |
Edited by - Joe Keller on 28 Dec 2009 21:37:00 |
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Joe Keller
USA
747 Posts |
Posted - 29 Dec 2009 : 21:27:40
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The Asteroid Resonance - Part 6
The IAU Minor Planet Center lists 511 Davida's rotation period as 5.1294h, and 39 Laetitia's as 5.138h. The mean of these is 5.134h. So, today I arbitrarily investigated all asteroids on the IAU rotation period list, whose rotation periods are within 0.054h of this mean, i.e., from 5.08h to 5.188h inclusive.
There are 19 such asteroids. As I did for Davida and Laetitia, I found the JPL ephemeris' heliocentric Right Ascension predicted for them for 12h UT, Dec. 21, 2012. The two asteroids with rotation period < 5.11, namely 3165 Mikawa & 7895 Kaseda, both will be more than two hours of RA away from heliocentric conjunction or opposition with Barbarossa, which is about the same as being more than two hours RA from 12h RA and also from 0h RA. The nine asteroids with period > 5.1655, namely 132 Aethra, 1011 Laodamia, 33107 1997 YL16, 87 Sylvia, 3086 Kalbaugh, 7816 Hanoi, 1296 Andree, 53435 1999 VM40, & 4713 Steel, likewise will be more than two hours RA away from conjunction or opposition with Barbarossa. Of the three asteroids with period 5.11h, two (153 Hilda & 6260 Kelsey) will be more than two hours RA from conjunction or opposition with Barbarossa, but one (6379 Vrba) will be, only an hour of RA, ahead of opposition. 2292 Seili has period 5.121h; it will be an hour of RA behind conjunction.
The remaining four asteroids, of the 19, have period from 5.1294h to 5.1655h, inclusive. All four are within three degrees either of heliocentric conjunction or opposition with Barbarossa, at the end of the Mayan Long Count. As discussed previously, 511 Davida is 2.6deg behind opposition, and 39 Laetitia is 0.75deg ahead of conjunction. (These values refer to the distance along the orbit, from the orbital point nearest Barbarossa's position). Remarkably, 1717 Arlon (rotation period 5.1484h, diameter ~ 9km) is 3.1deg behind conjunction, and 947 Monterosa (rotation period 5.1655h, diam. est. 27km) is 1.75deg ahead of conjunction.
Thus the four asteroids whose rotation periods are clustered near or slightly above the critical value, 5.13h, all are within 3.1deg or less, of either heliocentric conjunction, or heliocentric opposition, with Barbarossa, at the winter solstice, 2012AD. This is so significant statistically, that it proves a causal relationship between the end of the Mayan Long Count, and either Barbarossa, or if not Barbarossa, something else, near 176deg ecliptic longitude then.
*********
Update Dec. 30, 2009
Let's expand the table in Part 3 (Dec. 22) to include Monterosa and Arlon. I use Wikipedia's value, 4.562yr, for Monterosa's orbital period. Because Wikipedia's value for Arlon's orbital period is given to implausibly many digits, for Arlon I use instead another online value, 3.2534yr, from the website of WR Johnston, Nov. 2008.
Remainder on division
"First" period (Barbarossa's orbital period, est. 6339.364 Julian yr)
39 Laetitia 0.024
511 Davida 0.896
947 Monterosa 0.602
1717 Arlon 0.535
"Second" period (Mayan Long Count; best resonance, 5124.58yr)
39 Laetitia 0.342
511 Davida 0.337
947 Monterosa 0.319 (all are thirds)
1717 Arlon 0.146
"Third" period (5124.58yr * sec(36); see previous posts)
39 Laetitia 0.931
511 Davida 0.003
947 Monterosa 0.512
1717 Arlon 0.007
Thus there is an tendency for these four asteroids' orbital periods, to be whole, or sometimes half, divisors of the "first" and "third" periods, and to have a third left over, when divided into the Mayan Long Count. |
Edited by - Joe Keller on 30 Dec 2009 21:56:54 |
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Stoat
United Kingdom
863 Posts |
Posted - 31 Dec 2009 : 05:55:14
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Hi Joe, do you mind if I go a little off subject to pick your brains about something we discussed earlier in the thread? You remember that I think that h = c^2 / b^2 is the best bet for the speed of gravity; b being the speed of gravity here. Also, that writing the lorentzian in terms of the refractive index i.e. sqrt(1 - 1 / 1.5009 34) is somewhat similar to the Riemann conjecture, in that we can replace that reciprocal of h by the prime number sequence.
My rough muddle of an idea. At the speed of light there's a phase change, the sign changes from a minus to a plus. In effect it's just the old luxon wall revamped in terms of the speed of gravity. Jump into your space ship and accelerate upto the speed of light; you use a lot of energy to do this but you do have an immense, hidden store of gravitational angular momentum in the core of every particle of your ship. At the speed of light, your relativistic mass doubles. Thereafter your mass starts to fall. You're burning grav energy as fuel after all.
At the speed of gravity your mass has fallen to the square root of two, of twice the ship's mass. A lunatic pilot might e tempted to put his foot down and go faster, But effectively he's in the future of the universe, he'd need to navigate by going everywhere at the same time. Wow!
So back to Rieman, PI(1 / 1 - 1 / p^s
s is a complex number (a +jb) a = 0.5 and b = 14.134725
I get about p^0.5(0.9854 + j 0.1706)and get a value of half e for s.
Frankly I'm pretty naff at maths, so could you check this out for me? Strangely I think we get a devil's stair case. From twice the speed of light to three times the speed of light, your spaceship mass decreases but from three to four it stays the same. That's because four isn't a prime. The question is, does this staircase mirror over to the sublight part of the lorentzian? Would the steps be scaled right down? A fractal space is begining to make a little more sense to me, I suppose the pretty pictures made would be us and the whole shooting match.
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Stoat
United Kingdom
863 Posts |
Posted - 31 Dec 2009 : 06:10:03
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Oops To save you rummaging through your bookshelves, I used; which I think is right
a^(b + j c) = a^b(cos(c In a) + j sin(c In a))
Obviously square the results and take the sq root. |
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Stoat
United Kingdom
863 Posts |
Posted - 31 Dec 2009 : 06:24:26
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oh, while I'm on Joe, another question for you. I was looking at the idea of an f.m particle, which would have a wave, the cosine of the natural log of the lorentzian. This does give anti parallel wave movement but i couldn't see what any information could be transmitted by it.
Then I was looking at the "fractal" y =|x| could I just do the same with that cosine wave and say that the gaps in the half wave can sometimes hide a devil's step in them? |
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Joe Keller
USA
747 Posts |
Posted - 01 Jan 2010 : 17:26:32
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quote:
Originally posted by Stoat
Hi Joe, ...h = c^2 / b^2 is the best bet for the speed of gravity; b being the speed of gravity here. ...
Comment by JK: I like it, that h is dimensionless, which is correct. I also like it that you are looking to mathematical number theory, to find dimensionless numbers. The Riemann zeta function, and prime numbers generally, are central to number theory, so I like that strategy of yours too: looking to prime numbers and the zeta function. I think there's something important here, but I don't have enough time to work on this idea as much as I want to.
I'm inclined to avoid complex numbers here, if possible. Consider that the fine structure constant seems to be 1/137.036, and 137 is prime. Also consider that the (dimensionless) electric-to-gravity ratio,
"X" = q^2 / (G*m^2)
where q & m are the electron charge & mass, resp., and G is the gravitational constant, is about
"X" = 4.1655 * 10^42
I find that (the base of the logarithm doesn't matter, because this is a ratio of logs) log(X)/log(137.036) = 19 + 1 - 1/19 - 1/19^2 -..., with only 0.004% error. |
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Joe Keller
USA
747 Posts |
Posted - 01 Jan 2010 : 18:52:54
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The Asteroid Resonance - Part 7
Theoretical basis of 5.13h rotation period. The "Planck time" is sqrt(hbar*G/c^5). Essentially, the 5.13h rotation, is to the Planck time, as gravity is to electricity.
The usual definition of the electric to gravity ratio, for the electron, is q^2/(G*m^2). I consider a "modified electric to gravity ratio" which counts only the gravitational attraction of the electric field to itself. For a maximally compressed electron, according to the Schroedinger wave theory explanation of the Heisenberg uncertainty principle, the mass-energy of the field is alpha times the mass-energy of the electron, where alpha is the fine structure constant. So, I multiply the electric to gravity ratio by 1/alpha^2.
A refinement, is to realize that when, through compression of the electron and its field, the total electron mass increases from m to m + m*alpha, the electron can be smaller by a factor (1+alpha), because more mass-energy is available to make shorter deBroglie waves. The field now isn't just m*alpha, it's (m + m*alpha) * alpha = m*(alpha + alpha^2). Successive such approximations lead to m*(alpha+alpha^2+alpha^3+...) = m*alpha/(1-alpha).
So, my "modified electric to gravity ratio" is q^2/(G*mprime^2), where mprime = m*alpha/(1-alpha). The "gravitational Planck time", is defined as "Planck time" * "modified electric to gravity ratio", and satisfies the equation:
"gravitational Planck time" * 2*pi / sqrt(2) = 5.1287hr.
The four asteroids showing alignment with Barbarossa at the end of the Mayan Long Count, have rotation periods from 5.1294 to 5.1655hr.
Alignment of a "quasi-Centaur" with Barbarossa. Duffard's 2009 arXiv.org paper (see earlier post) has a table at the end (after the references) of TNO rotation periods. The only TNO whose rotation period, as given there, might be 5.13h, is 2002 PN34 (asteroid #73480), whose rotation period is given as
"4.23 or 5.11) +/- 0.03hr".
This would seem to include the possibility of 5.11+0.02=5.13hr.
At 2012, this TNO (diam. ~ 100km) is indeed only about an hour of ecliptic longitude past opposition to Barbarossa. Online sources give various estimates of its period or semimajor axis, corresponding to periods from 170.5yr to 174.8yr.
The orbit is far from the ecliptic when it crosses Uranus or Neptune, but is near the ecliptic at perihelion < 4AU outside Saturn's orbit, so Saturn is the main perturbative influence. Resonance (6::1) with Saturn would give orbital period 176.75yr. The remainders on division into my "first", "second", and "third" periods (see previous posts) are 0.867, 0.994, and 0.838. |
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Stoat
United Kingdom
863 Posts |
Posted - 02 Jan 2010 : 12:19:48
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Hi Joe, food for thought there. I've been looking at the esu as well. First thought being what's the force if we wanted two electrons touching each other, at twice the Compton wavelength of the electron. Now to get my speed of gravity here, I had to decrease the Compton wavelength to about 2.39E-12 so I stuck in a cos theta, as a temporary little patch. I think it's fair enough, as these two electrons are spinning.
Divide that force by the mass of an electron to get a deceleration of twice the speed of gravity. Integrate twice to get d = ut + bt^2 and take u as being the Fermi velocity for copper. The displacement d again being the Compton wavelength. So a positive time root and a negative time root on just either side of the charge number value. Personally I don't care much for the idea of negative time but as a heuristic device it's okay here.
Something else to note , it's a square law for gravity but the deceleration is pretty horrifying, it's down to sub light in less than a millimeter.
Now I chose the Fermi velocity of copper, for no other reason than it's a common metal. All of the Fermi velocities I've seen, are at about a hundredth of the speed of light. The fine structure constant springs to mind there as well.
Any way the upshot is, for the electron, esu force of about 1.01E-5 newtons,
f_esu /2b*c^2 = f_grav
where b is the speed of gravity.
For the emu we take the esu force, where once again, the radius is twice the Compton wavelength of the electron squared.
f_esu/c^2 = f_emu
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Joe Keller
USA
747 Posts |
Posted - 03 Jan 2010 : 15:56:15
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The Asteroid Resonance - Part 8
The Cassini space probe found that Saturn's innermost ring, D68, has a complicated shape, but usually lies within a few km of 67645km from Saturn's center (Hedman, Burns, Showalter et al, Icarus 2007). (D68's radius has increased slightly since the 67580 +/- 10km found by Voyager; see Showalter, 1996.) Comparison with Titan's orbit, using Kepler's law relating semimajor axis to period, implies an orbital period of 4.895h for ring D68, if its orbit is circular at the distance found by Cassini. (This neglects the gravitational effect of Saturn's bulge, and of ring and moon material). The same article by Hedman et al (sec. 7, p. 18) says that the shortest orbital period of ring material, is 5.25h. So, the accurate minimum period might be 5.13h. (Hedman et al remark that Saturn's true mean rotation period, ~10.5h, also is slightly uncertain, so there might be exact 2::1 resonance.)
Few eclipsing binary stars have orbital periods shorter than 5.13h. The closest to 5.13h, is AV Telescopii, with 5.16h. In Dec. 2012AD, this star will be at a heliocentric angle of 95.35deg from Barbarossa. Sky surveys show that within a few arcminutes of this star, many other stars lie along short arcs (whatever the significance, if any, of that might be). AV Telescopii is Visual mag 14.1-15.1, variable type E/KW a.k.a. E+KW, where "E" signifies "eclipsing binary" and "KW" signifies "yellow main-sequence primary with hotter subdwarf secondary" (www.assa.org.au); the "K" signifies "contact" (specifically, the first phase of mass exchange) not color spectral type K. If the primary is spectral type mid-G V with magnitude alone +15.1, then "spectral parallax" (i.e. distance estimate assuming average absolute magnitude for spectral type) gives 1000pc distance (or nearer if there is intervening dust). The star's mean proper motion corroborates this, suggesting ~400pc distance according to our Sun's apex motion. Though this star might be too distant to influence our solar system, it might show effects related to its 5.13h (or rather, 5.16h) resonance. |
Edited by - Joe Keller on 03 Jan 2010 16:09:53 |
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Joe Keller
USA
747 Posts |
Posted - 05 Jan 2010 : 13:27:01
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Hi *******,
Thanks for checking. I'm unfamiliar with the asteroid resources, so I didn't think I could do a good job checking, by myself.
...
The reason I asked about the axes, is that I had decided to check NASA's claim that there is no planetary alignment on Dec. 21, 2012. It turns out, that it depends what one means by a planetary alignment. At the winter solstice 2012, the asteroids 511 Davida, 39 Laetitia, 947 Monterosa and 1717 Arlon all are within 3 deg or less, of heliocentric conjunction or opposition with an object I discovered in a perfect orbit on four sky surveys, near the positive CMB dipole (discovered Feb. 2007). What is significant, is that the four asteroids, are exactly the four asteroids on the IAU list whose rotation periods lie between 5.1294h & 5.1655h: four consecutive asteroids, when the periods are arranged in order, all lying within one of two 6-degree intervals of approximate alignment.
Furthermore, by averaging all axis determinations in the literature (correcting for 180deg ecliptic longitude ambiguity where necessary) I find that Davida and Laetitia, at least, have the same rotation axis (a condition which, according to Newtonian physics, shouldn't persist more than a few million years).
If Luna's orbit is "played back" to the Roche limit, one finds 5.05h for Earth's primordial rotation period; the most reasonable correction I could make, for a less dense early Luna, makes that 5.13h. An authoritative 2007 article about Saturn's rings, says the shortest orbital period of their particles, is 5.25h, but the radius estimates that the article gives for the innermost ring, D68, correspond to about 4.98h. There's also a simple theoretical expression involving the Planck time and, essentially, the electric to gravity ratio, that gives 5.1287h as the period corresponding to a sort of "gravitational Planck time". So there's reason to believe that this period of rotation has undiscovered physical significance.
The object I discovered on sky surveys in 2007 (all fairly starlike, fairly consistent magnitudes, and seeming to show the "Eberhard effect" suggesting they really are on the plates, not scanning artifacts), which I named Barbarossa (not for the German WWII military operation, but from the prologue to a novel by one of my fellow Harvard grads, that was made into a Hollywood movie) shows a perfect orbit on four sky surveys: eccentricity=0.61, i=12.9, present distance 213AU, a=344AU. A year ago, the U. of Iowa let me use their 14 inch robotic scope to search, but often the images didn't turn out, the procedure was surprisingly time-consuming, and anyway I never was able to re-image the object unequivocally. A few experienced amateurs also have tried to image "Barbarossa" at my extrapolated coordinates, with telescopes as big as 16 or 17 inches, but also without any unequivocal success. Most of the imaging attempts were made before my extrapolation methods were very good. The sky surveys were using photographic plates and 40 inch Schmidt cameras, with hourlong exposures. Since no one knows the nature of the object that I found (it might even be intermittently self-luminous), the stacked brief CCD exposures might or might not be adequate; so, there really hasn't been a good attempt to duplicate the original positive sky survey result.
There are resonances or other mathematical relationships between the orbital period of Barbarossa (6340 +/- (conservatively) 9yr, from the sky surveys; mass ~ 0.01 solar, as estimated from simple outer planet precession resonances which might explain the lack of disruption of Neptune's orbit), the Mayan Long Count, and many physically or observationally important solar system periods. For details, see my posts to Dr. Van Flandern's messageboard, but just one sample:
5125yr Mayan Long Count / 84.01yr Uranus orbital period= 61.005 (an integer)
Recent articles in authoritative archaeology journals suggest not only the Clovis human extinction c. 12900 Before Present (or rather perhaps 12680 BP, according to Brauer's lake varves) but also, according to recent fossil cranial data, widespread human extinction (drastic reduction in cranial diversity) in N. American and Europe, roughly 6000 BP without drastic climate change. The oldest known megalithic observatory, at Nabta in Egypt, dates to ~ 6500 BP. Australia, at least, had more-or-less simultaneous bicoastal megatsunamis then.
My own simple interpretation of Eduard Meyer's Sothic Dates, puts Day One of the original Egyptian calendar, at the summer solstice 4328BC = 6339.5yr before the winter solstice 2012AD, at which time Arcturus rose heliacally on the summer solstice at 30N.
If, when the Giza pyramids were new, one stood sighting Sirius on the meridian at the peak of Menkaure's pyramid, simultaneously Arcturus would have appeared at the peak of one of the large Giza pyramids. If, 6170 yr earlier, one also sighted Sirius on the meridian at the peak of Menkaure's, the other large Giza pyramid, then would have had, at its peak, the very same point in the constellation Crater where Barbarossa will be in Dec. 2012 (all this is with ~ 1deg error, consistent with the precession uncertainty implied by Ptolemy's data). Thus the Giza pyramids encode their date of construction, and also the critical position of Barbarossa and the approximate period of Barbarossa's orbit.
The Giza pyramids and the Mayan calendar were part of a philanthropic effort to preserve warning information for millenia so that "this time around, it can be different". If Khufu was an egomaniac, why did he apparently not bother to have more than a few small cheap statues made of himself? This time it CAN be different: the truth can be discovered, survival strategies can be improvised. But only if the government-funded astronomers stop acting like they work at a Dickensian "Circumlocution Office".
Sincerely,
Joseph C. Keller, M. D.
*********
addendum on messageboard only:
A month ago I went to the office of the Dean of Arts and Sciences at Drake Univ. and offered to speak for 15 or 30 minutes, on this subject, to their faculty club. After the Dean himself finished scowling at me from a distance for a minute or so, while refusing to see me, the Associate Dean took me to his office where he tried smilingly to shoo me out the door without even finding out anything about my qualifications. I left seemingly on good terms, after spending a few minutes telling him my qualifications and giving him some sample results from my work, but I never received any answer about speaking to their faculty, or any other response. |
Edited by - Joe Keller on 05 Jan 2010 14:02:26 |
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Jim
1607 Posts |
Posted - 06 Jan 2010 : 14:20:55
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| Hi Dr Joe, You seem to have your mind made up weather or not the model is true and correct. So, can I ask what kind of events are you expecting to occur in 2012? |
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Joe Keller
USA
747 Posts |
Posted - 07 Jan 2010 : 13:22:49
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quote:
Originally posted by Jim
Hi Dr Joe, You seem to have your mind made up weather or not the model is true and correct. So, can I ask what kind of events are you expecting to occur in 2012?
Hi Jim! Thanks for your post. Almost everything I've thought, about what might happen this time, or what did happen the last two times, is posted to this thread, but here's a summary:
The phenomenon seems to involve yet-undiscovered physical forces, which are inconsistent with textbook "Relativity", and which I don't understand, but which reveal themselves through solar system resonances, asteroid alignments, previous geologic, oceanic and meteorologic events, and clues in ancient architecture and calendars. Because new physical forces are important to the phenomenon, the main cause of destruction might not be anything familiar like comets or solar flares. Then again, it might be, that a comet swarm resonates with this 6340yr period, or that something in the sun does. So, it might be mainly comets and/or solar flares, or it might mainly be something stranger, that no one knows about yet.
Sudden drastic cooling was important ~12680 yr ago. Tsunamis, but not severe climate change, were important ~6340 yr ago. Anyway, I bought some seedlings in 2009 to improve the windbreak around my house, to help keep it warm and reduce snowdrift. Vice President Gore deserves credit for alerting us all to the danger of climate change, even though he might have guessed wrong about the direction of that change.
I also bought Douglas Fir seed. It's recommended (the "Rocky Mountain" variety only) for the upper Midwest. It gave me excellent germination and fast growth. I have more Douglas Fir seedlings than I know what to do with. I'll give you some if you happen to come to my neighborhood (central Iowa). Or you can buy seed in moderately large quantities only (like an ounce or more) from the professional seed collector I bought from (no relation to me), Dean Swift in Colorado (the seed I got was from Lincoln National Park, New Mexico, at high altitude, i.e., cold winter climate, so at least one nursery in Michigan also uses it; my seed was from the bumper crop in 2004, stored in a deepfreeze).
The Russians have announced a comet-deflection project (see, Wall Street Journal Jan. 6, 2010). Maybe what they're not telling us, is that it's really about anticipated comet swarms in 2012.
Many people say, I ought to be saying prettyplease to the government astronomers instead of standing outside their "Circumlocution Office" and denouncing them like the elderly gentleman in last year's BBC movie version of Dickens' "Little Dorrit". If someone wants to try a milder approach to them, like the young "Arthur" character in "Little Dorrit", be my guest; maybe it'll work, though I doubt it.
The astronomy bureaucracy is so big, so rich (from taxing you), so arrogant, that nothing constructive will happen about 2012, until they're humbled, more or less crushed, and they won't be humbled until their conceit, selfishness, inadequacy and failure are perceived, by many people, as life-threatening. Then it will be tragically heavy-handed, it will be like Stalin blaming an agronomy professor for the Russian famines and punishing him by starving him to death in prison. The professor didn't deserve that, but it was partly his own fault: he was focused on fancy research; he was "in denial", not realizing that Russia's problem wasn't lack of technology, Russia's problem was chaos. They simply weren't getting into the fields (for various reasons ranging from administrative negligence to malfeasance).
With web searches, I found the names of many astronomers who have measured lightcurves of Monterosa and Arlon, though their data were published too summarily or cryptically, to allow calculation of the rotation axis, from what I could see on the internet. I found the email addresses of several, and emailed them asking what the axes were. So far none have responded.
Here is an opportunity for readers of this messageboard to do something constructive: independently of me, you can find out the email addresses of the researchers who have published lightcurves of Monterosa and/or Arlon, and ask them about the rotation axis (my recent posts explain why that's important). Then they'll realize that I'm not a "loner", and that there is some popular demand. |
Edited by - Joe Keller on 11 Jan 2010 17:00:52 |
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Jim
1607 Posts |
Posted - 07 Jan 2010 : 14:40:39
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| Hi Dr Joe, Its good to see you are aware of forces you don't understand and are unknown at this time, but, have you considered there might be something with the model you are basing all this conjecture on? Anyway, Have you used the Minor Planet Center as a data bank to find the info you want? I don't know how to setup a search at MPC but the application form looks good. And questions can be posted at MPS too. They should have what ever data there is and know more about the solar system the dean of a school. |
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Joe Keller
USA
747 Posts |
Posted - 08 Jan 2010 : 11:45:38
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I've been looking at the IAU Minor Planet Center website since last week and haven't found anything that suggests they would make an adequate response. However, anyone who thinks contacting them is worthwhile, is welcome to try. They direct the comments into bureaucratic pigeonholes (almost like "Press 7 if you think your data have been lost") practically advertising that a specialized inquiry like mine would be a waste of time. One can contact individual staff members only if one knows their email address, but the email addresses aren't listed, at least not anywhere I can find them. Incidentally, my form email to the Hubble Space Telescope was never answered.
The best I've been able to do this morning, has been to send them the following on their "Feedback form":
"I want to have all known data on the rotation periods and/or rotation axes of asteroids 947 Monterosa and 1717 Arlon. I have the wherewithal to estimate the rotation axes, if I have the lightcurves in decipherable form. This is important.
Sincerely,
Joseph C. Keller"
I won't get a satisfactory response to the above. I did it so I can say I've done it.
The way to get the real data, is to do what I suggested in my previous post. I suggest emailing the individual researchers directly (they can be found from web searches and/or from the IAU minor planet website), using one's real name, and ask about "the rotation axes of Monterosa and Arlon". (None of the ones whose email addresses I found, have answered yet, but the more different people email them, the likelier they'll be to look into the matter.)
Better yet would be to visit them personally in their offices, which is on my list of things to do, but there's nothing stopping anyone else from doing that before I can get around to it. I'm legally prohibited from leaving North America (US, Canada, Mexico), due to an alleged monetary debt owed to a wealthy person, so any visits to European astronomers will have to be by someone else.
There are four asteroids, all with the same rotation period, that align with Barbarossa at the end of the Mayan Long Count. At least two of these asteroids have the same rotation axis as well. If it could be shown that the other two also have that same rotation axis, I might be able to get some traction by advertising this to the educated public, perhaps through a leaflet campaign (I doubt I would get more than blank stares from professional astronomers, though). |
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Jim
1607 Posts |
Posted - 08 Jan 2010 : 13:46:47
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| Hi Dr Joe, Some times not getting a rapid reply is good. What I find most puzzling is both you and you and your bad astronomers are using the same model that seems to be the cause of most of the confusion and humor that astronomy has generated during the past 80 years or so. But, thats another matter;so-Why not simplify your requests? Ask if any data exists about the objects you want to know about. Ask who might know anything about whatever you are looking for like if you were shopping. Astronomers are people too. |
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Requiem for Relativity
