Requiem for Relativity

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p. 4

(schematic drawing of "disappearing dot" on plate scans, here)

FINDING BARBAROSSA AND FREY

Finding an excess of such discordant magnitudes near the (+) CMB dipole, and several on a line, almost parallel to the ecliptic, I next checked online sky surveys for disappearing dots. (A Harvard astronomer told me how to open the "FITS headers" of these files.) Eventually, on all relevant Red (three of these) and Optical Infrared (one of these) plate scans, I found disappearing dots of comparison Red or Optical Infrared magnitude +17.5 to +19.5, for Barbarossa and its moon, Frey. Some more distant dots might be another moon, Freya, and there is evidence that Frey's orbit precesses due to Freya plus a third, unseen moon, Lowell. Thus I found evidence of three of the "nine companions" of the Mayan "Bolon". The mass ratio Barbarossa::Frey is 40::1.

I estimated Frey's orbit about Barbarossa, at 1.6AU and 20yr. All dots were fairly starlike, often with the Eberhard effect. Though Frey's orbit is vague due to uncertain, contradictory identifications, the precision of Barbarossa's trajectory is, considering that I found only about one disappearing dot per 15x15 arcminute frame, very significant.

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p.5

(schematic drawing of x, y, z vs. t graphs, here)

FINDING BARBAROSSA'S ORBIT

Prof. Taff's textbook on celestial mechanics teaches that orbit determination often is inaccurate because the equations usually are poorly conditioned, i.e., small input errors cause large output errors. However, only six parameters are needed to define the trajectory, and with four observations, I have eight parameters (4x2 = 8 coordinates).

My procedure was to guess Barbarossa's heliocentric radius at the 1997 observation, and guess the first and second time derivatives then too, which gives the radius for all the observations, because for these observations the effects of any realistic third or higher time derivatives of the radius, are negligible, vs. the observation accuracy. Then I drew a smooth curve (specifically, a unique sinusoid+constant of a reasonable predetermined frequency) through the 1954, 1986 and 1997 x-coordinates, and likewise through the y- and z-coordinates. I assumed that the orbit would make all three curves pass through the appropriate value at 1987. The result is semimajor axis 344AU, eccentricity 0.6106, true anomaly 90deg within a few days of Dec. 21, 2012; ascending node 293, inclination 12.9, longitude of perihelion 86. The J2000.0 celestial coords. for 12h GMT Dec. 21, 2012 are RA 11:27:46.95, Decl -9:22:53.1 (barycentric sidereal period, approx. 6339.93 yr).

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p. 6

(world map with -9deg lat, and Sacramento, S. Arizona, & Tenerife marked, here)

ATTEMPTS TO PHOTOGRAPH BARBAROSSA PROSPECTIVELY

The first to attempt to photograph Barbarossa prospectively, was Joan Genebriera of Spain with his 16-inch telescope on Tenerife, March 2007. A week later, in April 2007, Steve Riley of California attempted, with his 8-inch telescope near Sacramento. My prediction of Barbarossa's position, and my interpretation of electronic photos, have improved over the last three years, but the results of all attempts so far, to photograph Barbarossa prospectively, can be summed up by the word, "equivocal".

In December 2008 the Univ. of Iowa began allowing me, with the help of Prof. Robert Mutel, to hunt for Barbarossa with their 14 inch robotic telescope in southern Arizona. One batch of photos was stacked by Prof. Mutel, another by Mauro Lacy of Argentina (Alan Grow of Rolla, Missouri helped Lacy retrieve the files from the U. of Iowa database). Both Lacy and Grow are professional computer programmers who donated their time. So far only Visual band photos have been obtained from this 14 inch robotic scope, and these are equivocal.

The Red and Optical Infrared band magnitudes of Barbarossa on the sky surveys are about +19, but on Blue it is absent, therefore dimmer than about +21. By analogy with other red objects like Sedna or Mars, I can guess that Barbarossa's Visual magnitude is +20.

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p. 7

(schematic of photographic plate design, here)

BIGGER TELESCOPES ARE NEEDED

The successful sky survey photos of Barbarossa were with 48-inch telescopes, operated in the Red or Optical Infrared bands, with exposures near an hour, using hypersensitized photographic emulsion plates. The nearest I've gotten to repeating that experiment, is two photos donated in 2009 by an unknown amateur using a 17 inch telescope; one of these was in the Red band, integrated over almost four hours by an unknown algorithm (because my orbit extrapolation was less accurate then, I got only an equivocal detection among edge artifacts).

The other electronic photos have been no more than 20 minute exposures; most have been ten stacked one-minute exposures. Such brief exposures, arbitrarily discarding the brightest photos at each pixel (otherwise there are too many false detections) would miss an intermittently self-luminous object. Near the detection limit, cataloged stars sometimes were textbook starlike, fragmentary, and totally absent, all in the same photo.

The online visible and optical infrared electronic (CCD) sky surveys, because of their small patches, happened not to cover Barbarossa's positions at the right times. They did help prove that the sky survey detections were not stars.

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p. 8

(diagram of pure hydrogen Jupiter size, vs. heavier element Earth size)

THEORY CANNOT SAY HOW BRIGHT BARBAROSSA IS

Extrapolating quantum mechanics from the laboratory, published theoretical calculations say that if Barbarossa is pure hydrogen, it is about Jupiter's size. On the other hand, when heavier atoms are present, gravitational atomic collapse involves many ionic species, tends to occur sooner, and is so complicated that no calculations have been published. Even if Barbarossa's composition were known, its size wouldn't be. As for albedo, there is a published estimate, that some cool brown dwarfs have albedos of 1% or less.

Barbarossa might be much older than the solar system, or might have formed by accretion or had some other unexpected cooling mechanism. If Barbarossa's temperature is near equuilibrium with solar radiation at that distance, then its (surface) temperature is near that of background interstellar dust and therefore hardly detectable. However, I have found a possible bow shock wave for Barbarossa, on infrared sky maps.

Distant objects, e.g. Sedna, tend to be almost as red as Mars. Barbarossa's appearance on all red and optical infrared sky surveys, but none of the blue, suggests that it is even redder than Mars.

text of Joseph C. Keller's poster for Oct. 10, 2009 CPAK conf. (U. of California - Irvine), p. 9

(diagram showing definition of angular momentum, here)

BARBAROSSA HAS THE MISSING ANGULAR MOMENTUM

Paul Wesson noticed the approximate constancy of the ratio, (angular momentum)/(mass squared) for almost all astronomical systems, large and small. Barbarossa has about ten times Jupiter's mass, and therefore 65 times Jupiter's angular momentum, yet only 0.01 times the solar system's mass. Barbarossa's inclusion brings the solar system's angular momentum up to the norm for its mass.

SUNLIKE STARS OFTEN HAVE "BARBAROSSAS"

Published statistical analyses say that cool, almost undetectable brown dwarfs are commoner than hot ones. Even so, the very nearby sunlike star, Epsilon Indi, happens to have not one, but two, relatively hot brown dwarf companions. Our Sun's Barbarossa and Frey resemble Epsilon Indi's companions, in their distance from each other and in their distance from their star. "Hyperjovian planets" amount to very cool brown dwarfs. Emitting little infrared, if far from their stars (little gravitational wobble) they are impossible to detect.