# How stellar aberration is measured?

A simple calculation shows that stellar aberration due orbital motion of earth is roughly 20 arcseconds. My questions are:

1. Practically how this small value is measured?

2. Does this value is in the range of accuracy of a 11 inch reflective telescope with a camera?

3. And how this measurement originally was done by Bradley in the 18th century?

The Wikipedia article on angular resolution

https://en.wikipedia.org/wiki/Angular_resolution

is a source of many useful facts relevant for the question. For example, it was empirically established already by the English 19th century astronomer W.R. Dawes that the angular resolution $\theta$ in arcseconds is about $$\theta = \frac{4.56}{D}$$ where $D$ is the diameter of the lens' aperture in inches. A similar result may be calculated from the wave optics, too. If you substitute $D=11$ inches, you see that the angular resolution is better than one arcsecond.

Approximately one arcsecond is the limit one gets from simple telescopes in the atmosphere due to the atmospheric effects etc. It's not "safely smaller" than 20 arcseconds but it is still 20 times smaller.

Very good eyes' angular resolution is actually estimated as 20 arcseconds so the people with the sharpest eyes are marginally able to see the stellar aberration with naked eyes. The average healthy eyes' angular resolution is about 3 times poorer, 60 arcseconds.

At any rate, there was no problem to achieve the desired resolution with the 18th century (and even older) telescopes. In fact, any telescope that improves the eyes' resolution just a little bit is enough. State-of-the-art large terrestrial telescopes with adaptive optics

https://en.wikipedia.org/wiki/European_Extremely_Large_Telescope

are able or planned to be able to go to 0.001 arcseconds so there has still been a lot of progress since the 18th century.

Here's how to measure stellar aberration:

1. Take a telescope and point it straight up. Attach it to something massive and steady, like a chimney stack. Let the scope act like a pendulum. It's fixed at the top, and moves at the bottom. The plane in which it swings is the local meridian. That is, it only swings north-south, not east west.

2. With this setup, you can measure the zenith distance of a star throughout the year. You point the scope to the star as it transits the meridian. You measure how far the scope needs to deviate from the vertical, by comparing its position with a plumb line (which is precisely vertical).

3. Using the latitude of the observatory, you convert this measurement of the zenith distance to the star's declination.

4. You see how the zenith distance/declination changes over the course of a year.

Resolution of the optics isn't really the primary concern here. The reason is that aberration affects ALL of the stars in the field of view in almost exactly the same way. That is, it's not relative to background stars, as is the case with parallax.

Here's a second, easier way. It has less precision, but it's more practical, at least if you want to simply see the basic effect.

Take a long-exposure telescopic photo of the celestial pole. Use the highest possible magnification. The star trails in the photo are centered on the pole, so you can infer the pole's position with respect to the stars.

You repeat this over the course of a year. The position of the pole will trace out a cycloid-like curve on the sky. The width of the cycloid is caused (mostly) by stellar aberration. The change in the center of the cycloid is caused by precession and nutation.