Light Aberration

For physical effects which depend not on the geometric relative position of two objects $B_1, B_2$ but on the apparent position of $B_1$ relative to $B_2$ one has to take light travel into account. The relativistic deflection of light by the Sun is only larger than $1''$ for angular distances from the Sun of less then $0^\circ5$ (see [S. Table 3.26.1]) and may be neglected for our purposes. The change in position during the light travel time (for example $20''$ between Sun and Earth) can be calculated by iteration by determining the geometric position at time $t_1=t_0-R(t_0)/c$ where $R(t_0)$ is the distance between $B_1$ and $B_2$ at $t_0$ and $c$ is the speed of light [S. 3.314-315]. The light aberration is caused by the relative speeds of the observer $B_1$ to the light coming from object $B_2$ and the aberrated position of $B_2$ moving with relative speed $\mathbf{v}$ can be calculated by $\mathbf{r_2}=\mathbf{r_{20}}+R\mathbf{v}/c$ [S. 3.317].