Celestial Programming : Approximate Anual Aberration Correction

This is an approximate anual aberration correction algorithm taken from "Concise telescope pointing algorithm using IAU 2000 precepts" by Patrick Wallace. The accuracy is within .3 arcseconds for 100 years past J2000. A more precise algorithm requires computing the velocity of the Earth, which often requires considerable amounts of data and computation. This algorithm produces very good results with only a handful of opperations. If the accuracy needs to be extended to a longer period, one may use a truncated version of VSOP87D to compute the Earth's ecliptic longitude, then add 180° to get $\lambda_{\odot}$.

$$ \begin{align*} t &= JD - 2451545 \\ \lambda_{\odot}&= 4.895 + .0172021 t \ (radians)\\ \vec{v}_{BCRS}&= \begin{bmatrix} \cos \alpha \cos \delta \\ \sin \alpha \cos \delta \\ \sin \delta \end{bmatrix} \\ \vec{v}_a& \simeq \begin{bmatrix} +.000099 \sin \lambda_{\odot} \\ -.000091 \cos \lambda_{\odot} \\ -.000040 \cos \lambda_{\odot} \\ \end{bmatrix} \\ \vec{v}_{GCRS}&\simeq \vec{v}_{BCRS} + \vec{v}_a \end{align*} $$