Requiem for Relativity

The Aladin server is fine now. Maybe I missed the plate among the pile of "windows" on my "desktop".

Object #1 also is missing from its Aladin plate. Of the three nearest dim stars having either R1 or R2 < +19.0, one is obvious, one (USNO-B 0827-0286485) is a definite smudge (galaxy?) at its catalog location just S of where Object #1 should be, and one is a fainter smudge.

A nearby Red +16.66/17.29 star (USNO-B 0827-0286507) resembles a nearby R+18.62/18.68. The nearly equal R1 & R2 magnitudes argue against a very variable star, and for obscuration.

The abovementioned USNO-B 0827-0286485 seems to have a vague moon on each side: they are 20" apart on a line 20deg to the equator. Both this line and the one mentioned above for Object #3, slope like Barbarossa's alleged orbit.

The Aladin server has been "down" for 3 hrs now, but before then, I confirmed that USNO-B catalog objects with discrepant Red magnitudes such as mine, generally are absent from the plates, or at least displaced. Within 20 arcminutes of Object #1, the USNO-B catalog has 12 other objects with one Red mag <18.99, one Red mag >19.50, both PMs greater than 80 in absolute value, and (for determinacy) uncertainty of position less than "999" in both axes. Before the server went down, I had time to evaluate 10 of these:

One was a typical dim star at exactly the published location. One lay on a point (i.e., streak) of a bright star (much as Object #4 lay on an arm of a spiral galaxy). Two resembled Object #2: there was nothing near their catalog location. One resembled Objects #1 & 3: it lay 10" from a pair of stars or galaxies (the brighter was in the USNO-B catalog - as was the brightest of the three objects near Object #1). Five of the objects, lay about 5" from other, faint and/or blurred, solitary, uncataloged objects. Thus only one of the ten random objects meeting the criteria, was in a complicated situation like Objects #1 & 3 ( p = (6*10 + 4) /(14*13*12/3!) = 0.18 ).

Regarding Object #3, an estimated 40,000 asteroids of more than a few km size, gives only one per square degree of sky; perhaps three per square degree in this part of the ecliptic. Furthermore an asteroid at opposition, even 4 AU from the sun, would get 100x the apparent retrograde angular speed, from Earth's motion, as Barbarossa. Only half this would be canceled by the asteroid's own orbital speed. Even a Kuiper belt object at 34 AU, would get 10x the retrograde speed, as Barbarossa.

Alternatively, the streak near Object #3 might be a roughly edge-on spiral galaxy. The Zwicky, Herzog & Wild Catalog of Galaxies (1961) vol. 1, pp. i,36-38, indicates that a few degrees north of Barbarossa (south of -3.5deg Decl was not covered) even the densest clusters have only about 1000 galaxies per sq deg, down to about magnitude +18. The streak south of Object #3 looked like roughly a +18 object. Even in the densest cluster, the chance of finding a +18 galaxy within a 5" radius, would be only 1000*(pi/720^2)= 0.006. Only half of galaxies would be spiral, only half of those sufficiently edge-on, and only 1/3 of of those, aligned within 30deg of Barbarossa's orbital path, so, p < 0.0005, or, for four Objects, p < 0.002. However, a galaxy would give about the magnitude observed: if the 5" length is the bright core analogous to the central 40,000 lt yrs of M31 (which subtends 1 degree at 2.4*10^6 lt yr), then the magnitude would be log(720^2)*2.5 + 3.4 = 17.7.

I checked the IRAS infrared source catalog, using overlapping disks of 1deg radius to cover Barbarossa's track from 10h59m to 11h35m. The number of IRAS sources within 10deg of the track's midpoint, implies expectation of 0.50 sources closer than 1' to the track. The number of sources found in the swath of the overlapping disks, extending 0.866-1.000deg to either side of the track, roughly confirmed this.

Two IRAS sources (p=0.09, Poisson test) were found closer than 1' to the track (J2000 celestial coordinates):

Source #1. IRAS 11102-0701 (repeated in the "Faint Source" IRAS catalog, as F11102-0701, with ostensibly slightly more accurate coordinates, which I use), 55" from the segment between Objects #1 & 2; RA 11h12m44.9s Decl -7deg17'50". For the source in the original IRAS catalog (without the "F") the flux in Janskys was 0.633 +/- 12%, 0.657, 0.400 & 1.00 in the 12, 25, 60 & 100 micron bands, resp. (no error bars given for last three values). In the "faint source" IRAS catalog (with the "F") those fluxes were 0.657 +/- 9%, 0.301 +/- 31%, 0.120 +/- 29% & 0.644 +/- 29% (all but the longest wavelength's fluxes, are said to be 94-98.5% reliable in the "F" catalog). The source is 17" from a mag +11 red star, USNO-B1 0827-0286738. The IRAS satellite's field of view perpendicular to the ecliptic was 0.75 to 3' (narrower for shorter wavelengths), and 4.5 to 5' parallel to the ecliptic. The uncertainty of the source's position (in the "F" catalog) is 28" parallel to the ecliptic and 2" perpendicular thereto (due to experimental design, all sources had more uncertainty parallel to the ecliptic, but for this source, the difference was especially great). (In the original catalog, the uncertainties were 70" & 8", resp.)

Source #2. IRAS 11210-0823 (I haven't yet checked the "F" catalog), 33" (perpendicular) from the segment between Objects #3 & 4; RA 11h23m32.1s Decl -8deg39'30". The flux in Janskys was 0.256, 0.250, 1.950 & 4.650 at 12, 25, 60 & 100 microns. This source overlies the same face-on spiral galaxy as does Object #4. The original catalog uncertainties are 40" parallel & 11" perpendicular to the ecliptic.

IRAS, in 1983, mapped the sky four times in ten months. Special software was employed during part of this time to find asteroids (positional discrepancies apparent within hours)(S Green et al, Icarus 64:517+, 1985). Earth's motion would give Barbarossa net apparent motion only 2% that of an asteroid.

I have to leave this public library computer; more to follow.

If the effective observation date of IRAS was 1983.5; if Source #1 (above) was Barbarossa; if Barbarossa's orbital period is 6828 yr; and if the track of Objects #1-8 is that of Barbarossa, then the position of Barbarossa for 2007.25 is:

RA 11h8m14.1s Decl -6deg44'11.5"

Apparently school let out early in Story County due an impending storm, so I have to leave yet another public library computer today; more to follow.

I asked the librarian: it was a conference afternoon! Now the kids are gone to supper and I'm back on the computer here, after looking up some facts in the Encyclopedia and making some calculations.

I neglected Earth parallax when I could assume that observations always occurred at opposition. If the relevant IRAS observation (launch Jan. 2003: 10-month mission ended before the end of 1983) was made, effectively, June 9, then the correction for Earth parallax and for the aberration of light, changes Barbarossa's "J2000" position for 2007.18 (approx. March 9, when Barbarossa is, approx., at opposition and on the meridian at midnight) to:

RA 11h8m53.6s Decl -6deg49'07.8"


This is based on extrapolation from the most recent sighting, rather than the great circle below.

If the USNO-B catalog plates were made at Barbarossa's opposition +/- 1 month, there would be up to (10.5' Earth parallax + 0.3' aberration of light) * sin(Barbarossa's inclination 26.4 - Earth's inclination (23.45*cos10.5)) * sin30 = 20" deviation to either side of the track. This is roughly what was observed. The corresponding 0.5 * 10.8' * cos(23.45)/cos( = (+/-)20s deviation in RA, would be enough to regularize the periods of the Freya sightings (Objects #1, 3-6 & .

Graphically, the best great-circle fit to Objects #1-8, gave a root-mean square deviation of 13.4" (perpendicularly) from the line (subsequently confirmed as 13.40" using successive approximations on my IBM 486). I tried undoing the USNO-B catalog's automatic Proper Motion correction to the coordinates: using successive approximations on my IBM 486, the rms deviation became 12.2".

I chose the points by the criterion of closeness to a line. Yet subtraction of the USNO's presumably fictitious Proper Motion correction, removed 20% of the variance.

The likely correction to Barbarossa's predicted present (2007.18) RA, from the uncertainty of IRAS observation dates, is between 0 and -11s, maybe -13s (the corresponding correction to Decl for Barbarossa's track, is approx. -7.5 arcsec Decl per sec RA). Estimating Barbarossa's orbit causes an even bigger uncertainty: the most different likely alternative, is a circular orbit with 4400 yr period, which would alter Barbarossa's predicted present RA by -120s.

So, I give not only estimated present coordinates, but also a search great circle which is known more confidently. (At roughly 10 degrees from the ecliptic, Barbarossa's track appears as almost a perfect great circle now, at opposition.) This is the great circle determined by least-squares successive approximations with Objects #1-8. It passes through the points:

RA 11h 08m 00s Decl -6deg 43' 36.7" &
RA 11h 10m 00s Decl -6deg 58' 37.9"

A straight line segment between these points, on rectilinear coordinate paper, will deviate by less than 3", from great circle to chord.