Celestial Programming : Aberration of Light

The motion of an observer causes the apparent position of objects to be offset slightly from their geometric position. For the Earth orbiting the Sun, the maximum effect is about 20.5 arcseconds. An observer's velocity relative to the center of the Earth can add about another .3 arcseconds.

$$ \begin{align*} \tau &= |\vec{u_4}|/c' \\ \beta &= |\dot{\vec{E}}|/c' \\ \cos D &= \frac {\vec{u_4} \cdot \dot{\vec{E}}}{|\vec{u_4}| |\dot{\vec{E}}| } \\ \gamma^{-1} &= \sqrt{1 - \beta^2} \\ f_1 &= \beta \cos D \\ f_2 &= [1 + f_1/(1 + \gamma^{-1})]\tau \\ \vec{u_5} &= \frac{\gamma^{-1}\vec{u_4} + f_2\dot{\vec{E}}}{(1+f_1)} \end{align*} $$

Where \(\dot{\vec{E}}\) is the velocity of the observer, \(\vec{u_4}\) is a unit vector in the direction of the observed object, \(\vec{u_5}\) is the observed position of the object, and \(c'\) is the speed of light in AU per day (173.1446326846693 AU/d).