Parallax

How do astronomers measure distances to stars? One way is to measure what is called the parallax angle of the star which compares the position of the star to more distant, background stars. Parallax is a part of astronomy called astrometry which is the measure of stellar distances and motions.

• p is the parallax angle measured in arcseconds (1 arcsecond is 1/3600 of a degree)
• r is the distance from the Earth to the Sun (astronomical unit)
• d is the distance from the Sun to the star (in essence from the Earth to the star since r<<

In trigonometry, p is actually the arctan of r/d, but for small angles, tan(p) is approximately p. Astronomers then define a unit of measure called a parsec to make calculations easier.

• One parsec is the distance a star would have to be from the Sun to create a parallax angle of 1 arcsecond (1") as seen from Earth (r = 1 AU)

Notice that the parallax angle is only one-half of the total angle created for the star's position in January and June.

What's nice about this equation, is it works for any distance r as long as r is measured in AU. There was talk about placing a space probe near Jupiter's orbit to create a much larger baseline. Remember, that r for Jupiter is approximately 5.2 AU which means the angle p would be 5.2 times larger than at Earth. Larger angle are obviously easier to measure than small angles.

The closest star to the Sun (Earth) is Proxima Centauri. Its parallax angle is approximately 0.75" which means it is about 1.3 parsecs from Earth. All other stars have a larger distance, so they have much smaller parallax angles, which is why it would be better to measure parallax farther out in the Solar System.