## Introductory Astronomy: Parallax

Determining the distance to a star is difficult because we cannot actually travel to the star and measure the distance directly. Instead, astronomers must be very clever and measure the distance indirectly. One of the ways they do this is by the method of Parallax. (This method is the same one that surveyors use on Earth to measure the height of a mountain or building.)

Parallax measurements take advantage of the fact that, as the Earth orbits around the Sun, relatively near-by stars appear to move with respect to the fixed, very distant stars (see the diagram below). This is the same thing that happens when you look at a close object with first one eye and then the other. For example, hold your thumb at the tip of your nose. Look at your thumb with first your right eye and then your left. Your thumb appears to move because your eyes are not at exactly the same place, so each eye views the thumb from a different angle. Now hold your thumb at arm's length and repeat the experiment. Your thumb will still appear to shift, but will not appear to move as much as it did when it was closer. The same thing happens to stars. The closer stars appear to shift more than the farther stars. The "fixed" background stars are not really fixed; they are just so far away that we cannot distinguish their apparent shift. The apparent shift of the stars is called their parallax.

Parallax is simply the apparent change in the position of an object due to a change in the location of the observer. In order to measure the parallax of stars which are very far away, we must use the largest baselinepossible. (The baseline is the distance between the two points where we take the measurements. For the experiment above with your thumb, the baseline is the distance between your eyes.) A larger baseline results in a larger shift, which means that we can measure the parallax of stars which are farther away.

The largest baseline we can use for ground based observations is the diameter of the Earth's orbit. Using the Earth's orbit, we make one measurement of the position of a star in, say, June, and the second measurement in December (6 months later). The smallest shift we can reliably measure from the Earth is 0.02 seconds of arc, which corresponds to a distance of about 50 parsecs. So, stars farther away than 50 parsecs do not appear to move and constitute the "fixed" background stars we use in the measurement.

Once we have measured the parallax angle in seconds of arc, we can use the simple parallax formula to find the distance to the star: