Aberration

The finite speed of light combined with the motion of the observer around the Sun during the year causes apparent displacements of the positions of the stars. The effect is called the annual aberration (or ``stellar'' aberration). Its maximum size, about $20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ , occurs for stars $90^{\circ}$ from the point towards which the Earth is headed as it orbits the Sun; a star exactly in line with the Earth's motion is not displaced. To receive the light of a star, the telescope has to be offset slightly in the direction of the Earth's motion. A familiar analogy is the need to tilt your umbrella forward when on the move, to avoid getting wet. This Newtonian model is, in fact, highly misleading in the context of light as opposed to rain, but happens to give the same answer as a relativistic treatment to first order (better than 1 milliarcsecond).

Before the IAU 1976 resolutions, different values for the approximately

$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ aberration constant were employed at different times, and this can complicate comparisons between different catalogues. Another complication comes from the so-called E-terms of aberration, that small part of the annual aberration correction that is a function of the eccentricity of the Earth's orbit. The E-terms, maximum amplitude about $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ , happen to be approximately constant for a given star, and so they used to be incorporated in the catalogue $[\,\alpha,\delta\,]$to reduce the labour of converting to and from apparent place. The E-terms can be removed from a catalogue $[\,\alpha,\delta\,]$ by calling sla_SUBET or applied (for example to allow a pulsar timing-position to be plotted on a B1950 finding chart) by calling sla_ADDET; the E-terms vector itself can be obtained by calling sla_ETRMS. Star positions post IAU 1976 are free of these distortions, and to apply corrections for annual aberration involves the actual barycentric velocity of the Earth rather than the use of canonical circular-orbit models.

The annual aberration is the aberration correction for an imaginary observer at the Earth's centre. The motion of a real observer around the Earth's rotation axis in the course of the day makes a small extra contribution to the total aberration effect called the diurnal aberration. Its maximum amplitude is about $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ .

No SLALIB routine is provided for calculating the aberration on its own, though the required velocity vectors can be generated using sla_EVP and sla_GEOC. Annual and diurnal aberration are allowed for where required, for example in sla_MAP etc. and sla_AOP etc. Note that this sort of aberration is different from the planetary aberration, which is the apparent displacement of a solar-system body, with respect to the ephemeris position, as a consequence of the motion of both the Earth and the source. The planetary aberration can be computed either by correcting the position of the solar-system body for light-time, followed by the ordinary stellar aberration correction, or more directly by expressing the position and velocity of the source in the observer's frame and correcting for light-time alone.