Measuring Stellar Distances

Three useful units – which we use depends on how far away the object is. Being able to convert quickly is useful to know.

• Relatively small distances – Astronomical Unit, AU = average distance between Earth and Sun  (1 AU=150 million km)
• Light Year. 1 ly is the distance light travels in a year at a speed of 300 million m/s.

Find the distance in km between us and our nearest star Proxima Centauri (4.3ly away) You might like to speculate how long it might take a spacecraft travelling at a maximum possible 25,000km/h to reach it.

• One parsec (pc) is defined as the distance to a star that shifts by one arcsecond from one side of Earth’s orbit to the other. These angles are incredibly small. They’re too small for degrees to be a practical unit of measurement. There are 3,600 arcseconds (60 minutes x 60 seconds) in one degree. To provide some perspective: one arcsecond is equivalent to the width of an average human hair seen from 20m away.

The nearest star is Proxima Centauri, at 1.3 pc. The Andromeda Galaxy, the closest spiral galaxy to our own, is nearly 800 kiloparsecs away.

If we imagine ourselves taking measurements of an imaginary star at six monthly intervals, it seems to have moved with respect to the Sun, 1 AU away.

Putting this another way:

Explaining Trigonometric Parallax.

• Because of the Earth’s revolution around the Sun, nearby stars appear to move with respect to very distant stars which seem to be standing still.
• Measure the angle to the star and observe how it changes as the position of the earth changes. In the second diagram if the observation point is at the top of the picture, six months later it will be at the bottom, 2 AU’s away
• You can use your fingers to show trigonometric parallax. Shut one eye and hold your finger about eighteen inches in front of your face. Observe a distant object and the finger. Keeping still, look with the other eye. The finger represents the near star and appears to have moved with respect to the background. If you ask a friend to hold up his finger and repeat the observation, it would seem to have moved much less.
• The parallax or apparent shift (from the Greek for ‘alteration’) of a star is the apparent angular size of the ellipse that a nearby star appears to trace against the background stars. Because all parallaxes are small (the stars are very far away), we can use the small angle approximation as shown. If we measure the distance to the star in AU. (astronomical units), then the parallax is given by:

For example – the six month parallax angle for Alpha Centauri is 1.52 seconds of arc. You might like to calculate how far away this is in light years.