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PAllen
#13
Feb12-12, 05:55 PM
Sci Advisor
PF Gold
P: 5,060
Quote Quote by Ken More View Post
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 θ0 in order to predict the value of c.
No, here I don't want the discussion to be about measuring or predicting the value of c at all, no way, no how. It has nothing to do with explaining how AA values are computed from SR aberration formulas. You may independently add something to thread on measuring c using aberration that does not involve calculations or tables in AA.
Quote Quote by Ken More View Post
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 θ0 = 90, 75, and 1.

The point I had intended to make was that the AA declination aberration equation predicts that (θ - θ0) = (- v/c).sin(θ0).cos(α0) in an ecliptic coordinate system. When θ0 = 90, the AA equation predicts a different value for (θ - θ0) than Bradley’s equation. The difference in predictions depends upon the right ascension angle α0, when α0 - 0 the difference in the two estimates for (θ - θ0) are small but the difference in the two estimates become very large as α0 approaches 90. 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 α0 = 0 and would have declination aberration close to zero for stars in the galaxy that are close to the plane where α0 = 90.
And this set of issues is purely about your misunderstanding both the Bradly and SR aberration formulas and the application to AA computations and has nothing to do with predicting c. It was felt since none of us in that forum had a copy of AA (and we cannot take your presentation of it as accurate), explaining how all this is consistent in detail would better be done by someone here who might have a copy.

You consistently call the Bradley formula a declination formula. This is purely a falsehood, and this has been explained at least 6 times to you. It is formula for total angular deviation of an object whose position is orthogonal to earth's motion, and the direction of deviation is in the plane formed by the earth's velocity vector and the light path. The AA is all about the equatorial coordinate system (as witnessed by terms declination and right ascension). The angular difference in the Bradley formula translates in somewhat complex ways to declination and right ascension change.
Quote Quote by Ken More View Post
Different predictions for declination aberration (θ - θ0) 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 - θ0) 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 - θ0) can be reliably determined. Also, if (θ - θ0) is determined to be significantly different from -20.5 arc seconds then the Bradley model cannot be used to calculate a value for c.
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So I suggest here we first focus on the issue that there is actually no discrepancy whatsoever between AA computations and SR aberration, since the former is derived from the latter. Until this misunderstanding is addressed, all the rest is irrelevant.