Requiem for Relativity

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11 years 11 months ago #21363 by Joe Keller
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Asteroids 511 Davida, 39 Laetitia, 947 Monterosa, 1717 Arlon: indicate date Jan 4, 2013 with full-range half-max Nov 22, 2012 - Feb 23, 2013

In posts years ago, I noted that these four asteroids have rotation periods clustering near the shortest value known. These periods are remarkable not only because they are short, but because they are so nearly equal. These four comprise the entire cluster: the other short periods known, differ much more.

Years ago, I noted that these asteroids align (i.e. roughly equal heliocentric ecliptic longitudes modulo 180deg) in about Dec 2012. Just today I found time to return to this topic.

I got their heliocentric J2000 ecliptic longitudes (I rounded these to the nearest 0.01deg) from the online JPL ephemeris, for the dates Dec 1, Dec 31, Jan 30, and Mar 1. These data allowed very accurate third degree Newton's forward-difference interpolation. Davida's longitude is near 360 at these times; the other longitudes are near 180. So, I added 180 to Davida's so that I could consider agreement modulo 180, i.e., collinearity with each other and with the Sun.

The minimum standard deviation of the set of four longitudes, is 3.408deg, at Jan 4.4 GMT, 2013. The standard deviation is sqrt(2) times this (i.e. the variance is twice the minimum) at Nov 22, 2012 and at Feb 23, 2013. The mean longitude (mod 180) of the four, at the time of minimum variance of their longitudes, is 177.62deg.

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11 years 11 months ago #13872 by Joe Keller
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Davida, Laetitia, Monterosa, Arlon: resonance at 6339.49 Julian yr

This resonance has nothing to do with any Jupiter resonance. It is a resonance that has appeared only during the last few years. Also, it involves large prime numbers, unlike the asteroid-Jupiter resonances.

The JPL Horizons online ephemeris, current today, Dec 18, 2012, gives periods for these asteroids with the osculating elements in the headers of their ephemerides; the Wikipedia articles on them also give periods. The two sets of periods differ considerably, so let's use the periods of latest epoch. For 511 Davida, 39 Laetitia, and 1717 Arlon, these would be from the Wikipedia articles, which cite JPL data as the source for all three, and give epochs Aug 27 2011, Dec 31 2006, and May 18 2008, resp. For 947 Monterosa, the current JPL header gives a more recent epoch, Sep 30 2012, than the Wikipedia article. Using the periods of most recent epoch, all supposedly from JPL data, we have:

Davida 5.63009883 yr
Laetitia 1682.713 d = 4.607017 yr
Arlon 1188.041866925004 d = approx. 3.252681361 yr
Monterosa 4.5609 yr

I find that exactly 1126 (prime factorization 2*563) Davida periods

= 6339.49128 Julian yr

= 1949.004707 (1949 is prime) Arlon periods

= 1376.051 (prime factors: 1376 = 2^5 * 43) Laetitia periods

= 1389.96 (prime factors: 1390 = 2 * 5 * 139) Monterosa periods

where only significant or almost-significant digits have been carried. Using the JPL periods of older epoch (1998 for Davida, 1988 for Laetitia, 2005 for Arlon & Monterosa) there is no such resonance. This suggests that only in the last few years have these asteroids converged to a period resonance.

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11 years 11 months ago #13873 by Jim
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Dr Joe, It is good to see you are back at the JPL site. You can fix these problems here that's for sure if you keep focused on the stuff being generated(or maybe I'm delusional).

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11 years 11 months ago #21344 by Jim
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Dr Joe, It is good to see you are back at the JPL site. You can fix these problems here that's for sure if you keep focused on the stuff being generated(or maybe I'm delusional).

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11 years 11 months ago #13875 by Joe Keller
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Last night, December 21, 2012, I saw Bolon descend, and there were nine companions.


Last night I was standing by the doghouse of my dog, KeeKee, and looking at Jupiter. Early this morning I realized that Jupiter is Bolon.

Months ago I saw a list of Mayan Gods. Several of their names were short phrases containing the word Bolon. Likewise many Greco-Roman temples were inscribed with this or that appellation of some major God such as Jupiter, Zeus or Hera, derived from some attribute or aspect, for example "Jupiter Thunderer" or "Zeus of Hospitality", etc. The Mayan name-phrases containing the word Bolon, might have referred to what were understood to be different appellations or aspects of the same major God. This makes it likely that the Mayans would have referred to the planet Jupiter by the name Bolon.

The December issue of Sky & Telescope has an article titled "Jupiter Rules the Night" about Jupiter's opposition Dec 2. Tortuguero Monument #6 says that on Dec. 21, 2012, "Bolon descends with nine companions" (translations vary slightly but my paraphrase is typical). "Descend" might mean simply "set in the west" or might mean "move westward, rather than eastward, relative to the stars, in retrograde motion [or even more specifically, 'after opposition' also]". All of this will be true for Jupiter during Dec. 2012.

Sundown at the Pyramid of the Moon in Teotihuacan (Wikipedia's coordinates: 19.6996N, 98.98440W, approx. 2000 ft. el.) on-center (i.e. zero elevation, airless model) is 23:58 GMT on Dec 21. Jupiter's apparent (airless model) J2000 coordinates then, from that observation point, are RA 67.12125, Decl 21.01891 (converting the JPL's equinox of date, to J2000 using the NASA Lambda utility).

This position places Jupiter just north of the Hyades. The Bright Star Catalog (on VizieR) lists nine stars currently nearer to this Jupiter position than Aldebaran is, and with Visual magnitudes less than +5.00. In order of nearness to the position:

kappa1 Tauri Vmag +4.22
epsilon 3.53
upsilon 4.28
omega2 4.94
delta3 4.29
delta1 3.76
delta2 4.80
tau 4.28
75 Tauri 4.97 (Flamsteed number only)(4.66 deg from Jupiter's position)

The next nearest star with Vmag < +5.00, besides Aldebaran, is a star lacking a Flamsteed number, 4.85 deg away. Specifying the number of "companions" this way, implies that the makers of the Mayan Calendar, were confident that they knew Jupiter's longitude with an error of no more than the order of 4.85 - 4.66 = 0.19 deg. In 1200 years, Jupiter travels about 360 * 100 = 36,000 degrees, so this is of the order of a part in 200,000, or less if the Mayan calendar is older. A modern value often given for Jupiter's orbital period, 4332.1 d, implies 0.05 d maximum error, a part in about 90,000. Earlier on this thread, I have posted evidence that the makers of the Mayan Calendar had accurate knowledge of stellar proper motions.

The next brightest star on this list would be kappa2 Tauri, Vmag +5.28, which is 0.31 mag dimmer than the dimmest of the above nine. The mean magnitude of the nine, is 4.34, with standard deviation 0.50 and range 1.44. Near the threshold of unaided eye observability, the distinction between +4.97 and +5.28 would seem large enough to make this the magnitude boundary which defines the "nine companions".

Nine stars brighter than +5.00, within a radius of 4.66deg, amounts to 0.13 such star per square degree. The Bright Star Catalog lists only 1604 stars with Vmag < +5.00 in the entire sky of 41,253 square degrees, i.e. 0.039 per sq. deg.

Such competent astronomers hardly would choose the term of their calendar frivolously. They were limited by inexact knowledge of the time of the event of which they were trying to warn, so they chose to end it on the last preceding solstice or equinox, to give future scientists another proof of competence.

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11 years 11 months ago #13876 by Joe Keller
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(continuation of yesterday's post)

For at least several days before Dec 21, there also are exactly nine stars in the online Bright Star Catalog, brighter than Vmag +5.00, and closer to Jupiter than Aldebaran is. These earlier sets of stars differ though; almost all of the stars were different, only a few days before Dec 21.

On the other hand, after Dec 21, Jupiter moves westward slowly toward stationarity. It happens that the set of stars brighter than +5.00 and closer to Jupiter than Aldebaran is, changes little. As observed from the Pyramid of the Moon in Teotihuacan, Jupiter's stationarity in Right Ascension is at 10:00 GMT Jan 30; Jupiter then will be (graphically, from my plot; remembering to use the NASA Lambda utility to correct the JPL coordinates for Jupiter to J2000 from equinox of date) 2.4 degrees away, azimuth 292 (clockwise from N) from the mean of the positions of the nine Dec 21 "companions". At the winter solstice, Jupiter was 1.4 deg away, az. 16.

I also find that Jupiter comes to stationarity in RA, only a few arcminutes from the Vmag +4.94 star, omega2 Tauri. The J2000 coordinates for Jupiter then, and for the star, are (RA, Decl) = (64.37655,20.74515) & (64.3150,20.5786), resp. (VizieR's online version of the Bright Star catalog automatically includes proper motions to the date of inquiry).

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