In every text and other source I have consulted, there is always the same explanatory diagram with lines drawn from the earth at two opposite points in its orbit through the nearer star and ending at the field of more distant stars. The geometry of the diagram is clear to me, but my question is this. Looking up at the sky, you canít tell which stars are nearer and which farther. As a concrete example, when Bessel took the parallax of 61 Cygni, the first parallax ever measured, how did he know that 61 Cygni was closer than the stars against which he was measuring its angular shift six months apart, since prior to his measurement no stellar distance had ever been determined ? This strikes me as a mystery of logic, with the additional editorial mystery that not one book addresses this question, which leads me to believe that the answer is obvious but I am just missing it. Any help with this will be greatly appreciated.
Yes, it could be a bit of a chicken-and-egg dilemma. But there are ways to give astronomers an idea of what stars may be closer, and to at least try to measure their distances.
First, assume most of the stars you see (unaided or through a telescope) are very far away and form the "distant background" of stars. That's a fairly safe assumption (although there may be a few that are relatively close - but those are the exceptions).
Now, the positions of stars were charted for centuries - starting in earnest with Hipparchus at about 150 BC. As instruments became more precise, positions of stars became better known. So when a star was seen to have changed its position between observations separated by several years, that star gets some notice. Because if any star is seen to change its position in the sky in just a few years, that star must be very close. Even if the star is moving quickly in our galaxy (compared to other stars), for us to actually see the movement implies its fairly close proximity to earth.
So 61 Cygni was noticed as a very fast mover (with large 'proper motion') in 1804. Efforts were then launched to try and measure its distance (once again, assuming stars in the same telescopic field of view are very far in comparison) and in 1838, Bessel was successful.
That's one way to obtain a good candidate for close proximity to earth - large proper motion. These days, spectral classification is also used, since we know how intrinsically bright a star of a certain spectral classification is, and if we then measure it's apparent brightness, we know its approximate distance. If it's close enough, we can refine that estimate through parallax. Of course, there are other methods, which I'm sure you can easily find, but those are the main ones for the closest stars.
Hope that helps.
Prof. James Gort