Stellar aberration

" Stellar aberration was first observed by the British astronomer James Bradley in 1725. Bradley was looking for parallax effects. Parallax refers to the apparent motion of nearby objects against the background of distant objects as the observer moves. (Hold a pen at arms length and look at the projection of the pen against a far wall as you move your head. The changing projection is parallax.) Knowing the amount of parallax, by measuring the angular changes with respect to the distant background, and knowing the diameter of Earth's orbit, one has sufficient information to enable a simple calculation of the distance to the nearest stars.

The parallax effect can be understood from fig. 10.3.

Figure 10.3: The changing elevation, $\theta $, of a star above Earth's orbital plane as Earth moves in its orbit. (Not to scale.)
\includegraphics{fig/parallax.eps}

The maximum elevation above Earth's orbital plane should occur at position 2 and the minimum elevation at position 4, with positions 1 and 3 yielding different lateral angles.

However, Bradley found the maximum elevation occurred at position 3 and the minimum occured at position 1. The observed effect was of the order of 40'' of arc. It turns out that the nearest stars are so far away that their parallax is less than 1''. Although Bradley didn't know the size of parallax effects, the discrepancy in the positions at which maximum and minimum elevation occurred indicated that a new phenomenon had been discovered. We call it stellar aberration. It is also observable for all stars, not just a few close ones.

The elevation, $\theta $, of the star above the plane of Earth's orbit is known as the ecliptic latitude. The ecliptic is the name given to the plane of Earth's orbit and it's projection on the background stars. This is very well determined. Thus a star may be observed to describe a small ellipse in the sky, over the course of a year, if its ecliptic coordinates can be accurately measured. The semi-minor axis of this ellipse is usually called $\alpha $ and the semi-major axis $\beta$. See fig. 10.4. It is the effect of $\alpha $ that leads to the variation in ecliptic latitude.

Figure 10.4: The changing ecliptic coordinates of a star over the course of a year. (Not to scale.)
\includegraphics{fig/ab-ellipse.eps}
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(source: www.phys.uidaho.edu/~pbickers/Courses/310/Notes/book/node136.html)