In order that we can move on and get to my point about the declination aberration equation described in the Astronomical Almanac, I will assume you agree with my last proposed statement (1) at least to the extent that you would not want to revise Bradley’s equation to include independent variables other than v, θ and θ_{0} in order to predict the value of c.
In the SR/GR forum, I was leading to a point involving the Astronomical Almanac’s (AA) Reduction for Annual Aberration equation used to estimate declination aberration. I did not feel that I should press this point because PAllen, et, al. suggested that I open a new thread in Astronomy after I introduced the AA declination aberration equation and plots of predicted declination aberration data for stars at θ_{0} = 90º, 75º, and 1º.
The point I had intended to make was that the AA declination aberration equation predicts that (θ  θ_{0}) = ( v/c).sin(θ_{0}).cos(α_{0}) in an ecliptic coordinate system. When θ_{0} = 90º, the AA equation predicts a different value for (θ  θ_{0}) than Bradley’s equation. The difference in predictions depends upon the right ascension angle α_{0}, when α_{0}  0º the difference in the two estimates for (θ  θ_{0}) are small but the difference in the two estimates become very large as α_{0} approaches 90º. This means that the AA equation would predict that a galaxy with a center on an ecliptic pole would appear to have stars with declination aberration close to 20.5 arc seconds when they are close to the plane where α_{0} = 0º and would have declination aberration close to zero for stars in the galaxy that are close to the plane where α_{0} = 90º.
Different predictions for declination aberration (θ  θ_{0}) of objects near an ecliptic pole from sources already approved by the mainstream is highly relevant to any attempt to assume that Bradley’s estimate for the Constant of Aberration (approximately 20.5 arc seconds) at all times is an “a priori” given independent variable that can be used with complete and unequivocal confidence in the equation c = v/tan(θ  θ_{0}) would yield a precise estimate for the value of c. I contend that the aberration of a body at an ecliptic pole must be accurately MEASURED through the use of an appropriately configured computerized telescope before the value (θ  θ_{0}) can be reliably determined. Also, if (θ  θ_{0}) is determined to be significantly different from 20.5 arc seconds then the Bradley model cannot be used to calculate a value for c.
