How Parallax Works
To understand how parallax works, hold your thumb in front of your face. Alternately open and close each eye and notice how your thumb appears to move back and forth with respect to the background wall. Now move your thumb closer to your face and notice how this effect increases as the distance between your eyes and thumb decreases. This apparent motion (you did not really move your thumb) is called the parallax. The brain subconsciously uses information from both eyes to estimate distances. Because the distance estimates require observation from two points, people who have lost an eye will lack this depth perception. A parallax is any apparent shift in the position of an object caused by a change in the observation position.
As the earth orbits the Sun, astronomers can observe a nearby star at six-month intervals with the Earth on opposite sides of the Sun. The nearby star appears to move with respect to the more distant background stars. Note that the star (like your thumb) is not really moving. The parallax effect is an apparent motion caused by the motion of the observation point (either to the other eye or to the opposite side of the Sun). The closer the star, the larger will be its apparent motion. This parallax, when combined with the principles of geometry and trigonometry, can be used to find the distance to stars that are relatively close. Closer stars will have a larger parallax.
Astronomers measure the parallax in the form of an angle. For even nearby stars these angles are quite small. The closest star to the Sun, Proxima Centauri, has a parallax angle of less than 1 second of arc. A second of arc is 1/3600th of a degree (1°=60 minutes of arc=3600 seconds of arc, 1 minute of arc=60 seconds of arc). At a distance of 3 mi (5 km), a quarter will have an angular diameter of roughly 1 second of arc. Measuring such small angles is obviously difficult, but astronomers have managed to overcome the difficulties, detecting parallax for the first time in 1838.
The parallax angle is defined as one half of the apparent angular motion of the star as the earth orbits from one side of the Sun to the opposite side. This definition is the same as the apparent motion that would be observed if the two observation points were the Sun and Earth. Once this angle is measured, the distance between the Sun and the star is the earth-Sun distance divided by the tangent of the parallax angle.
To simplify this calculation astronomers use a distance unit called a parsec (short for parallax-second). A parsec is the distance to a star that has a parallax angle of exactly one second of arc. One parsec is 206,265 times the distance between the earth and Sun, 3.086X1013 kilometers, or 3.26 light years. The distance to a star in parsecs is then simply 1 divided by the parallax angle measured in seconds of arc.