Determining distances through parallax

You don't need to know trigonometry to follow the discussion below. But if you do know trigonometry, let me point out that all of the angles used are very small, and I use approximations valid for small angles.

The apparent position of nearby stars against the background of far-away stars changes as the Earth goes in its orbit around the Sun:

Here is what we see:

We can measure the angle, called the parallax, p of the star:

In this picture we measure the parallax p, we know the size of 1 AU, so we can compute the distance d to the star.

If the distance were twice as far, the parallax would be twice as small:

Thus the relation is

The constant depends on the units used for the parallax angle and for distances (meters, AU, ...).

Astronomers like to measure angles in seconds of arc. For this quarter, we are measuring distances in light years. (There are 360 degrees in a circle, 60 arc minutes in a degree, 60 arc seconds in an arc minute, see units page about angle measurements and light years.) With this unit of angle and distance, the distance fomula is:

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu