The Parallax Formula

Parallax is a method of using two points of observation to measure the distance to an object by observing how it appears to move against a background. One way to understand parallax is to look at a nearby object and note its position against a wall. If you look with just one eye, then the other, the object will appear to move against the background.

Parallax formula:


tan p= 1AU/d:

Since the star will be very far away, we can make the assumption that tanp is about equal to p. That simplifies our parallax formula to;

p=1AU/d, or in other words, d=1AU/p:

Astronomical units are not the most convenient units to work with, though, so instead we define a parsec to be the distance to a star that shows 1 arc-second of parallax angle. Our formula then becomes;

d=1p parsecs: