how did James Bradley discover light aberration? I do not understand his timing method. James
The magnitude of the aberration could be v/c? 
The speed of earth is about 30km/s.  That means the deviation from the real position of a star is about 30/300000 rad =180*3600/3.14159/10000 ~20arcsecond.
That is a horrible value.
Could the effect of parallex, proper motion and light aberration of a star be separated clearly?
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Sure. Aberration is always the same. Parallax depends on the distance, and the phase is different.
Why is their phase different? They all have a one year period.
Generally we should not worry about the light aberration, right? Even space telescopes have reference stars. The position of the reference stars are fixed. So although there are detectable wobble(20&quot;) in one year , because we use reference stars, this kind of effect is removed every day immediately. Every night, when the night assistant lets a telescope point at some direction, he has to use reference stars to calibrate that night's pointing.
Am I right?
That is a horrible value.


That value for aberration of starlight is "horrible" in two ways: One, in that's is very small. And two, in that it's large enough to interfere with parallax measurements.

In the late 1600s, scientists had already adopted the heliocentric model, and so were looking to measure the distance to the stars via parallax. Robert Hooke was among the first to attempt it, and probably the first to claim a measurement of the parallax. His observations were not very convincing at that time, but he probably did observe some effects from aberration of starlight (though they didn't know such a thing existed back then).

In the early 1700s, Bradley attempted to make a more precise measurement of parallax, and did obtain significant data, but the variations in the star positions were out of phase with the model. Using the speed of light estimate by Ole Roemer from Hooke's time, he correctly proposed that this was not parallax, but a speed-of-light phenomenon, now known as the aberration of starlight.

More info here:

http://arxiv.org/pdf/1208.2061.pdf

It took another century, until early 1800, for Bessel to measure the first parallax.

Basically, aberration of starlight produces the same variation in the positions of all stars, a periodic elliptic "wobble" that is the same for all stellar objects. Parallax produces a similar kind of wobble, but the amplitude depends on the distance to the star, and the phase is different from the aberration's.

There are also other effects, such as nutation, which introduce further perturbations.

http://cseligman.com/text/history/bradley.htm



Aberration per se is easy to explain via the old analogy to running through the rain. When you're standing, rain falls vertically. When you're running, rain appears to come from a different direction. Same with starlight. Like in this diagram (by Professor Courtney Seligman, linked above):



Now, small as that value is, it's still 20 arcsec. The resolving power of early telescopes (and modern amateur telescopes) is 1 arcsec or better - which is more than enough. What you need is a very solid mount with good setting circles. Lacking that, you could build a telescope with a fixed position, very rigid, forever pointing at the same place in the sky - that's what Hooke did - and then you're only limited by resolving power.

In any case, the precision required was quite doable with 1700s technology. An amateur could do it today, at very low cost - what you need is persistence to follow through with a long term project.


  Could the effect of parallex, proper motion and light aberration of a
  star be separated clearly?


Sure. Aberration is always the same. Parallax depends on the distance, and the phase is different.



EDIT:


  Why is their phase different? They all have a one year period.


Go to the site by Prof. Seligman, link above, and look at the two diagrams showing the aberration and the parallax. In point B (in April), the star is in the middle of the ellipse due to parallax, but it's at the right-hand tip of the ellipse due to aberration.

Broadly speaking, parallax is a position-based effect, whereas aberration is a speed-based effect. It makes sense that they are out of phase by 90 degrees (remember trigonometry?)



Proper motion appears as a long-term drift of stellar positions that remains even after you subtract aberration, parallax, nutation, etc. There's a back-and-forth-back-and-forth from aberration and parallax, whereas proper motion keeps going in one direction only.

You could measure proper motion with relatively short term observations, but it only works for stars that are nearby and are moving fast. If you're willing to wait decades, proper motion is much more easy to measure.

EDIT:


  Generally we should not worry about the light aberration, right?


Yeah, sort of. You know, at any given moment, the size and the direction of it. So you could simply subtract it from the measured position of the star you're watching.

OTOH, it was an additional source of error, until speed of light and the Earth's orbital parameters were very precisely determined. Perhaps it still contributes to the noise added to the data, to some extent - I'm not entirely sure here.