I need suggestions for "cutting & pasting" from the "command prompt" window, into Windows documents. So far, I've been able only to cut & paste into other command prompt windows. I'd like to paste my new BASIC computer program here. [Done - thanks, Mauro.]
I think this new program is the most valid physically. It varies the Barbarossa/Frey mass ratio, the orbital radius, and the time derivative of the orbital radius, consistent with observed positions, to minimize the unexplained work performed. Commonly, three parameters can be varied to make three functions (such as the components of the unexplained force on Barbarossa) become zero. However, I found that for most choices of Barbarossa and Frey among my Red sky survey "disappearing dots", the unexplained force remained large for all physically likely parameter values. One choice allowed a much smaller force, no more than 1/30 of the sun's gravity (which might be supplied by a relatively small, moderately distant moon).
Varying the orbit to minimize the unexplained force, usually produces a "gutter ball" solution with large eccentricity. Minimizing not the force itself, but the work done by that force, produces smaller eccentricities. My one very good combination of "disappearing sky survey dots" gave mass the ratio Barbarossa::Frey = 0.8770::0.1230, a midrange "barycentric" (not including Barbarossa's mass in the barycenter definition) radius 207.4 AU, and decreasing radius, -26 AU per radian (therefore e > 0.1). That is about as before, but I found that this very good combination occurs, with reversal of the Barbarossa and Frey identities on both the 1954 and 1986 plates. For the first time, objects on the 1987 plate fit perfectly, but again, with Barbarossa & Frey reversed from what I had supposed. The very first object I discovered, and named Barbarossa, becomes Frey on the 1987 plate.
This has implications for the Genebriera, Riley, Turner and U. of Iowa photos. The new predictions are close enough to the old ones, that these photos still are usually of the correct patch of sky, but now there might be other "disappearing" (i.e., not on sky survey) objects on these photos closer to the predicted positions; or, the Barbarossa/Frey roles might need to be reversed. So now, I don't know whether Genebriera, Riley, or either of them, were first to photograph Barbarossa prospectively.
My new program prints out predicted center of mass positions for these photos, and also contains the coordinates of the important "disappearing dots". It will be fairly self-explanatory for someone familiar with engineering mathematics and with BASIC or FORTRAN programming.
