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quote:Originally posted by Joe Keller
Sky Surveys Alone are Proof Beyond Reasonable Doubt
I now have (see above) four Barbarossa-Frey pairs on Red and Optical Infrared sky surveys...
The midrange radii for the first & last segments, were 211.9 & 210.9, so let's use r = 211.4 AU, and dr/dt = 0. The angular acceleration increased from 64 to 74 of my units (see above) which I can extrapolate to about 79 units for the interval 1997-2007 or 2009. This leads to the prediction:
0h Feb. 23, 2009: Barbarossa/Frey c.o.m. (geocentric)
11:26:33.95, -9:15:17.9 ...
To get a box, I changed two of the assumptions above. For each of the segments 1954-1987 and 1986-1997, I found, that constant radius which, with the 0.975::0.025 mass ratio, gave a perfectly straight arc; these radii were 214.5 & 210.1 AU, resp. Rather than average them, I extrapolated them, getting 207.9 AU to use for my 1986-1997-2009 prediction. This alternative treatment of the radius estimate, changed the predicted 2009 position only a few arcseconds; i.e. the equations form a poorly conditioned system, if solved for radius.
The other change in assumptions, was that I averaged the *apparent* dr/dt (i.e. secular deceleration due to distant third body) rather than extrapolated it. This changed the prediction more. Both alternative assumptions together give a new prediction
0h Feb. 23, 2009: Barbarossa/Frey c.o.m. (geocentric)
These predictions differ only 0.4 arcminute, in 12 yr.
I'm still working on stacking the sets of U. of Iowa photos. Aside from these, I have two photos from other sources. The first is from an unknown source at (? midpoint 7h UT) 2/16/2009, 400+ stacked exposures taken during a four hour interval with a telescope > 16 inches and Red filter. The second is from Joan Genebriera at 1h 2/23/2009, a single unstacked two minute exposure with a 16 inch telescope and Red filter, from Tacande Observatory on Tenerife.
Both these photos were aimed at my older coordinates, calculated before I found the error in my computer program. The predicted position of the c.o.m. is just beyond the north edge of the 2/16 photo and just within the edge of the 2/23 photo. However, objects likely to be Barbarossa & Frey were found in the 2/16 photo. (I found Barbarossa; the man who gave me the photo, already had found Frey, which I rediscovered independently.) The new prediction is slightly nearer what I found; this prediction is
7h Feb. 16, 2009: Barbarossa/Frey c.o.m. (geocentric)
On the 2/16 photo, I found a density, comparable to that formed by stars of Barbarossa's expected Red magnitude, at
(Neither photo has built in coordinates, so I measured by eye and with a ruler, comparing to the 1987 Red sky survey.) This density is near the breakup of the photo at its north edge and therefore is questionable. From the Frey position below, and the 40::1 mass ratio, I expect Barbarossa to be 0.43s W & 4.2" N of the c.o.m.; the measured position therefore is 0.96s W & 65.8" S of predicted.
However, the "Frey" (or "Freyprime") in the 2/16 photo, falls within 10" of the line through the 1986 & 1987 Freys, each referred to its own Barbarossa as origin. This is consistent with a binary orbit viewed nearly edge-on. Frey falls on this line, when the observed, not predicted, Barbarossa is used as origin; and with the solar orbital parallax correction. This is evidence that both the Frey and Barbarossa detections are real.
The observed 2/16 Frey is at
It is elongated to about 6 arcsec, like the 1987 sky survey Frey, but whereas in 1987 it was horizontal EW, on 2/16/2009 it was sloped 60deg downward NE-SW. These objects would move almost 3" in 4hr, so Frey and Barbarossa likely really are as bright as nearby stars of Red mag ~19 which appear slightly brighter.
Next I looked for Barbarossa & Frey on Genebriera's 2/23 photo. This unstacked photo has more hot pixels and the like, so I studied densities morphologically resembling the faintest (Red mag ~19) sky survey stars that could be seen on the photo. I used my "new" prediction above to estimate the c.o.m. motion, which was so small in < 7d, that almost any prediction would have been accurate enough. I also estimated Frey's binary orbital motion according to my previous graphical construction; Barbarossa's binary orbital motion would be 1/40 of that. The predictions for Genebriera's photo are
1h Feb. 23, 2009: Barbarossa (geocentric)
The predicted Barbarossa position, is ~10" within the north edge of Genebriera's photo. On this JPG image, I see starlike but very faint density there, possibly consistent with the more definite images of other Red mag ~19 stars farther from the photo's edge.
The predicted Frey position, corresponds to a starlike image, slightly fainter than a nearby star of Red mag ~19. The observed "Frey" is at
so is only 1.5" E & 6" S of predicted. Even this small displacement is consistent with my graphical orbital theory, because it is along a slope of ~75deg, not far from the 55deg slope of this part of Frey's binary orbit. I've explained the failure of the binary orbit to obey Kepler's second law, as the orbit of a visible "Freyprime" around a massive "Frey". In this theory, Freyprime would move as much as 12" per week, mainly parallel to the binary orbital track.
The U. of Iowa photos (I now have most of these files: ~10 per night, two minute exposure, robotic 15 inch telescope, clear filter, southern Arizona) taken 2/22-2/25, used a more recent aim point, so the positions of interest will be well away from the edge. Studying them is next on my list.