Requiem for Relativity

Earth's ecliptic cuts Earth's equator at 23.5deg. From its track, one sees that Barbarossa's orbital plane cuts Earth's equator at 27.4deg. Also, Barbarossa's descending node is 26.4deg west of Earth's.

If the IRAS measurements of Source #1 (IRAS 11102-0701 or F11102-0701) were at quadrature, June 9, 1983, then the ecliptic was 27.4 * sin(90-12+26.4) - 23.5 * sin(90-12) = 3.55deg N of Barbarossa's track. When Barbarossa was Object #3, the ecliptic was 27.4 * sin(15.9) + 23.5 * sin(10.5) = 11.8deg N. This would move Barbarossa 1/329.5 * (cos(26.5) * 11.8deg - 3.55deg) = 77", perpendicularly to his track, northward, for the IRAS measurement.

I infer from Cal Tech's IRAS webpage, chapter:

"ISSA Explanatory Supplement
I. Introduction
B. The IRAS Survey" (2nd par.) and

"IRAS Explanatory Supplement
I. Introduction
C. Overview of Infrared Sky" (Fig. I.C.1)

that there were two measurements made at quadrature, June 9, (+/-)10days. (Barbarossa was in the 28% of the sky which did not get a third measurement.)

Extrapolating from the moderately nearby Object #1 (at -7.50" Decl per 1s RA), Source #1 lay 83" (perpendicularly) from Barbarossa's track, to the N. So, the correction for Earth parallax implies that Source #1 is only 6" from Barbarossa's track.

Source #2 (a galaxy) was, on the other hand, 37" on the wrong side of the track. This worsens to 37+77=114" with correction.

The DSS-1 plate does not show Barbarossa (i.e., Object #3). It does show the stars F1-F3. I found the DSS-1 plate by searching for the coordinates of Object #3, in the "ESO Digitized Sky Survey" on the website "archive.eso.org". Apparently the DSS-1 plate is in White light, not Blue or Red. This confirms that Barbarossa really is a wanderer, and not a narrow-spectrum nebula (if such exist). (DSS stands for Digitized Sky Survey.)

This ESO website also allowed me to confirm that Barbarossa *is* on the DSS-2Red plate, but not on the DSS-2Infrared plate. (The DSS-2Blue plate was unavailable).

I still don't know the date of the DSS-2Red plate. Can anyone help?

I looked at the Aladin plates, including of course the IRAS images, for my IRAS Source #1. There was a faint but definite 12-micron source centered, according to the pixels, within 10" of the coordinates given. There was a rather bright star very near there, which, I theorize, was confounded with Barbarossa (see above).

The documentation on the ESO website (above) says that the DSS-2Red plate is from the

"SERC Southern Sky Survey and from the SERC J Equatorial extension"

and that these were 1-hr exposures (a few were shorter). Disregarding a body's own orbital motion, a 3" track at opposition, is consistent with a 6-hr exposure for a body 330 AU from the sun, or a 1-hr exposure for a body 56 AU from the sun. Assuming the same 7% albedo, the diameter in the latter case would be 2300 mi. Pluto and Sedna were well away.

I still think Barbarossa is near 330 AU distant, and that this streak, only a few arcseconds away from the USNO-B coordinates of Object #3, is Barbarossa. The ESO DSS-2Red image shows a bulge on the south side of Barbarossa, which might signify a moon. Frey and/or Freya, at a few arcsec apparent distance and at suitable angles, could cause the horizontal and vertical asymmetry of Barbarossa's image. They also could alter the orientation, and increase the length, of the image's long axis.

So far, I've discovered that the DSS-2 Red plates (sometimes called "J Optical Red") were made with the ESO Schmidt telescope in La Silla, which was decommissioned in Dec. 1998.

Learning yesterday that the exposures were 1 hr, requires me today to revert somewhat to my first theory of the Frey & Freya orbits. At 330 AU, a 1 hr exposure has only a 0.5" track due to Earth's motion at opposition. Most of the photographic track is due to the apparent distance between the cold brown dwarf Barbarossa, and its double planet Frey & Freya, because these three objects are not resolved.

Frey & Freya formed by the same process as Earth and Luna. As I posted on Dr. Van Flandern's messageboard March 6 last year, this process causes an initial relative orbital speed (reduced mass model) equal to one of the main Tifft periods, 2.7 km/s. They are close enough that they came to maintain the same face toward each other.

Ganymede-like, their center of mass has a one-week orbit about the 0.016 solar mass Barbarossa, consistent with the needed 1,500,000 mile, apparent 11" circular orbital radius which, at opposition, allows frequent aliasing of Barbarossa by one moon or the other, a day before or after, at either end of the orbit. The discrepancy (imperfection) in aliasing, attributed to a year's stellar motion and converted by the USNO computer program into a "Proper Motion", will lie at either end of a narrow apparent ellipse, where Frey/Freya are close to Barbarossa's future/past position, and their dwell time is long. The plot of the discrepancies ("Proper Motions") should resemble the central part of a parabola. Of Objects #1-8, only Object #6 is grossly inconsistent with this: maybe somehow its "Proper Motion" is spurious. The "Frey minus Barbarossa" discrepancy is reversed in both direction and time, at the other end of the orbit, so both ends of the circular, inclined, apparently bilaterally symmetrical orbit give apparent "PMs" on the same rough parabola opening to the east with axis approximately parallel to Barbarossa's track. The orbital radius about Barbarossa is somewhat longer than Barbarossa's daily travel at opposition, so the smaller moon, Freya, farther from the Frey/Freya center of mass, aliases oftener, and closer. Accordingly, on the "PM ellipse" (omitting Object #6) Frey aliased only twice alone, Freya four times alone, and both simultaneously once. The two most distant aliasings, were those of Frey, and this was significant (see above) by Student's t-test.

The orbital speed of Frey/Freya's center of mass, is 25 km/s. Their relative orbital speed about each other, originally the Tifft period of 2.7 km/s (1.35 km/s each, in a crude equal-mass approximation) has increased (roughly, if their masses are equal) to 4 km/s (2 km/s each) because of braking energy loss, associated with tidal heating by Barbarossa (Frey & Freya keep the same face toward each other but not toward Barbarossa). Evidently this tidal heating has maintained Frey's & Freya's surface temperatures at 55K, or slightly higher, for 4.6 billion years, explaining my IRAS Source #1 above. Assuming equal masses, each 4x Earth, they would be 120,000 miles apart on center (up to 1" apparent) with an orbital period about each other of 3.5 days, for 2:1 resonance with the orbital period about Barbarossa.

Most of the lateral spread, and some of the longitudinal spread, of the streak on DSS2.713, is due to Earth's atmosphere ("one arcsecond seeing"). Another 0.5" longitudinal spread is due to Earth's orbital motion. For Frey/Freya this is sometimes (but not for this streak) doubled, when their orbital motion about Barbarossa is antiparallel to Earth's motion. The longitudinal spread is mainly due to the light from Frey + Freya, merged with the light from Barbarossa but apparently displaced, in this case ~ 3" northeast of Barbarossa. Frey+Freya combined are a +19.5 object. In one day, Frey/Freya orbit 360/7=51deg; arcsin(3/11)+51=67deg, appropriate for aliasing in the first quadrant, as observed for Object #3, with its (+) PMs in both RA & Decl.

Dr. Keller, is it possible Hubble has imaged the Barbarossa system?