NavList:

Hello Robin. You wrote:
"Finding the GC pole using classical spherical trigonometry seems to be quite a bit tougher. Can anyone enlighten me has to how it would have been done in practice?"

Hmmm. Sounds like spherical coordinate rotations. As a preliminary, I would calculate the distance between the stars. Standard law of cosines:
cos(D) = sin(Dec1)*sin(Dec2) + cos(Dec1)*cos(Dec2)*cos(dRA).
We need that anyway. Next calculate the position angle of star 2 from star 1:
sin(PA) = -sin(dRA)*cos(Dec2)/sin(D).
Next I switch to a coordinate system in which star 1 is located on the equator at longitude 90 degrees and star 2 is at latitude equal to D (the distance between them) and also located at 90 degrees longitude. In those coordinates, the "north" pole of the great circle containing them, call it PGC, is at latitude 0 and longitude 0. Next I rotate about the axis passing through S1 and the center of the sphere by an angle equal to the position angle PA. The point PGC rotates up to latitude=PA, still at longitude=0. Then I rotate around an axis perpendicular to the first passing through the original location of PGC and the center of the sphere by a rotation angle equal to the declination of the first star, Dec1. The two stars are then at their proper declinations and have the proper difference in RA. The PGC's Dec and RA follow from the general spherical coordinate rotation equations and are given by
sin(Dec0) = sin(PA)*cos(Dec1)
tan(RA0-90) = tan(PA)*sin(Dec1) [with some quadrant check]
Finally rotate the whole thing about in right ascension. That's just a simple offset adding the right ascension of star 1 onto the calculated RA of PGC:
RA0' = RA0 + RA1.

Does that work? I haven't checked signs and all that since it's not a practical problem, but the principle seems fine.

-FER

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