What is the most basic method of determining stellar distance?

Answer 1

Parallax. If you hold your finger in front of your face and close one eye and look with the other, then switch eyes, you'll see your finger seem to "shift " with respect to more distant objects behind it. The effect is called parallax.

Astronomers can measure parallax by measuring the position of a nearby star very carefully with respect to more distant stars behind it, then measuring those distances again six months later when the Earth is on the opposite side of its orbit. The shift is tiny... less than an arcsecond even for the nearest star (an arcsecond is 1/60 of an arcminute, which is 1/60 of a degree). In fact, I have heard (but only heard it once and never been able to find a reference to verify it, so label this as "interesting hearsay not necessarily to be believed ") that some of the early Greek astronomers specifically looked for parallax from the stars to work out whether the Earth orbited around the Sun. But their instruments could not measure the very small parallaxes nearby stars exhibit. Since they thought nearby stars were much closer than we now know, the fact they observed no parallax implied that the Earth did not orbit the Sun. Whether this is true or not, it was not until telescopes were invented that astronomers could measure parallaxes at all accurately.