Aberration

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+ +

+
+ Next: Different Sorts of Mean Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Parallax and Radial Velocity +

+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. +

+ +

+
+ Next: Different Sorts of Mean Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Parallax and Radial Velocity +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit