[Joe Keller]

I've spent much of my time this week accurately confirming that J. Genebriera did indeed image Frey on March 25, 2007 (00:42 UT) and that S. Riley did indeed image Barbarossa on April 1, 2007 (07:39 UT). The J2000 coordinates of Genebriera's object are

11 26 22.2 -9 4 59

and of Riley's

11 26 25.0 -8 57 26.

(I can't access Aladin from this library so the Riley coordinates are from measuring on the screen with a ruler and therefore slightly rough; 3mm on the screen is 1s RA.)

The center of gravity slowed only 0.69% between the second and third segments, i.e., [Objects C3 & C 1987, Objects D & D2 1997] and [Objects D & D2 1997, Riley & Genbriera Objects 2007]. This corresponds to about 2s RA. The direction changed only 0.0046 radian (i.e., 0.46%) between the two segments. These deviations are smaller than likely would arise from observation bias: I searched entire 15x15' square images for "disappearing dots" and parts of adjoining squares also, rarely finding more than one or two starlike "disappearing dots" per square.

The direction changed 0.86% between the first and second segments, i.e., [Objects A2 & A 1954, Objects C3 & C 1987] and [Objects C3 & C 1987, Objects D & D2 1997]. The center of gravity slowed 3.3%.

The correction for Earth parallax was made by interpolating the sun's position according to old volumes of the American Ephemeris & Astronomical Almanac in the Iowa State Univ. library. For 1954 I had to use the formula therein to convert to J2000 coordinates. On an IBM486 computer I wrote a "BASIC" program to find the rectangular coordinates of every object precisely. I adjusted the objects' distance from the sun (presumed the same for all) so that the angle subtended between 1954 and 2007 equalled that for a body with a slightly elliptical orbit of period 2688 yr (my best estimate of the period of progression of the 5:2 Jupiter:Saturn resonance) when at said distance from the sun.

Then I adjusted the mass ratio of Barbarossa (i.e., A2, C3, D & Riley) and Frey (i.e., A, C, D2 & Genebriera) to 0.62:0.38, at which the torsion of the great circle was about constant: that is, the (small) break between the first (32.9 yr) and second (10.1 yr) segments was about twice the break between the second (10.1 yr) and last (10.1 yr) segments.

Corrections for proper motion of reference stars, between the 1987 date of the SERC-Red reference plate, and 2007 or 1954, all were negligible (1997 had its own Aladin reference plate). The aberration of light from the objects is negligible because it affects the reference stars as well; the aberration of sunlight is negligible because the sun's position is needed only for the small Earth parallax correction. The correction for the different distances of Barbarossa vs. Frey from the sun, is negligible.

The decreasing angular speed could be due to the influence of a small distant moon. The moon(s) seem to orbit Barbarossa in a plane near that of Barbarossa's orbit, so any torsion of the great circle would be relatively small.
The strange shapes of both Genebriera's and Riley's objects might be due to rings like Saturn's. The Roche limits for these bodies, a likely distance for rings, would be 1-2" depending on densities. The bodies' diameters should be about 0.8". A barely detectable planetary disk could make a spot smaller than that of a star of equal bolometric magnitude.