[LeGrande]

The effect of aberration on the place of the sun is, therefore, the same as that which takes place on a star situated in the pole of the ecliptic.

Now you seem to be quoting the inverse angle from the sun to the earth which is fine. You two like to look at things from the back end don't you : )

[Ethan Clive Osgoode]

[LeGrande to mrjesse] The 20 arc seconds you are talking about is the displacement of the suns masses orbit around the barycenter.

[LeGrande] Now you seem to be quoting the inverse angle from the sun to the earth

Investigation of Change in the Computational Technique of the Sun's Physical Ephemeris

The solid curves represent the effect of aberration in arcseconds, and are clearly neither flat nor zero. Aberration effectively shifts the ecliptic longitude of the Sun, λ, westward on the sky (decreasing the value of λ). Like the light-time correction, the aberrational shift results in a slight change of viewing angle. The dot-dash curve in Fig. 1 can be considered to show P as a function of λ (plus a constant), since the latter increases by about one degree per day. So the curve can be used to provide a good estimate of how much P will change at different times of the year, if we subtract 20.5 arcseconds from λ (20.5 arcseconds being the mean aberration; the true amount of aberration varies from 20.14 arcseconds at aphelion to 20.85 arcseconds at perihelion).

Since the Sun’s axis is tilted by 7.25◦, we expect the effect of aberration to move the latitude at most by 20.5 arcseconds ×sin 7.25◦, or about 2.6 arcseconds, and be seasonally dependent. This is exactly what is seen.

The dashed curve shows the differences using the pre-2009 rotation computation but explicitly correcting for aberration. As expected, a nearly constant offset of −20.5 arcseconds is seen, with oscillations under 1 arcsecond mostly due to varying velocity as the Earth moves through perihelion and aphelion.