Parallax

describe the method of heliocentric parallax to determine distances to nearby stars
recall the definition of one parsec (pc)

How can we measure how far away stars are? There are several methods. For relatively nearby stars we can use parallax.

Hold a pencil up in front of your face. Look at it with one eye with the other closed. Now look at it with the other eye. Notice that the pencil appears to move relative to the background. Why? Because you are looking at it from a different angle.

If we look at a nearby star (a few light years away) in June, then look at the same star in December then it appears to have moved slightly, relative to the much more distant stars behind it, because we are looking at it from a slightly different angle.

The distance to nearly 2000 nearby stars can be measured accurately with this method.

The radius of the Earth's orbit around the Sun is about 1.5 x 10¹¹m (or 1 AU). The star Alpha Centauri appears to change direction by 4.2 x 10^-4 degrees when observed in June and December. How far away is Alpha Centauri?

Why is this method unsuitable for more distant stars?

The Parsec

We have seen how we can use parallax to find the distance to nearby stars. We do this by measuring the annual parallax angle then using trigonometry to find the distance.

• Angles are measured in degrees. There are 360 degrees in a circle.
• For small angles we use minutes also. A minute is a 60th of a degree.
• For very small angles we use seconds also. A second is a 60th of a minute.

This may seem a very tiny angle but it is measurable with the sensitive instruments that astronomers use.

Imagine that a star has parallax angle of 1 second in 6 months. (i.e. a 3600th of a degree) We say that such a star would be a distance of one parsec away. So how far is a parsec in metres?

This seems like such a huge number it is hard to imagine it. Consider this though;

A light year is the distance that light travels in a year ( at 3 x 10⁸ m/s)

So 1 parsec = 3.08 x 10¹⁶ / 9.47 x 10¹⁵ = 3.26 light years. (useful to remember 1 parsec is about 3.2 light years). Other useful distances include the megaparsec Mpc and the kiloparsec kpc.