Parallax decreases with Distance
As the distance to a star increases, the its parallax decreases. This is easy to see in the following two figures:
(Click on the image to view at full scale [Size: 165Kb])
In the upper figure, the star is about 2.5 times nearer than the star in the lower figure, and has a parallax angle which is 2.5 times larger.
This movie demonstrates parallaxes graphically (beware: it is big, don't try to download it over a slow network connection).
This gives us a means to measure distances directly by measuring the parallaxes of nearby stars.
We call this powerful direct distance technique the Method of Trigonometric Parallaxes.