Parallax

Hold a finger up in front of your face. Look at it with one eye with the other closed. Now look at it with the other eye. Notice that the finger appears to move relative to the background. Why? Because you are looking at it from a different angle.

If we look at a nearby star (a few light years away) in June, then look at the same star in December then it appears to have moved slightly, relative to the much more distant stars behind it, because we are looking at it from a slightly different angle.

The distance to nearly 2000 nearby stars can be measured accurately with this method.

The radius of the Earth's orbit around the Sun is about 1.5 x 10¹¹m (or 1 AU). The star Alpha Centauri appears to change direction by 4.2 x 10^-4 degrees when observed in June and December. How far away is Alpha Centauri?

Why is this method unsuitable for more distant stars?