# Distances to Stars

It is crucial to be able to measure the distances to stars if we are to derive intrinsic luminosities. There are several methods for measuring distances to stars, but the most reliable by far (when it can be applied) is Trigonometric Parallax.

Hold a finger up in front of your nose, close one eye and note where the finger appears on the back wall. Now close the other eye (and open the one that was closed before) and note that the finger appears to move on the back wall. This is the parallax effect - the apparent motion of a nearby object compared to distance background objects because the change in viewing angle.

• If you do this same experiment now holding the finger at arm's length, you will notice that the apparent motion of the finger against the background is smaller (unless you have really short arms).

• For nearby stars we also measure a parallax - an apparent annual motion of the stars compared to background stars that is really a reflection of the Earth's motion around the Sun.

The asterick is a nearby star which is apparently moving back and forth every year compared to the more distance background stars. Note the star at the lower right which has a proper motion.

• Here is another view of trigonometric parallax for stars:

The distance to the star is inversely proportional to the parallax angle (which is usually indicated by the symbol ).

• There is a special unit of distance called a parsec. A star whose annual parallax angle is 1 arcsecond is is at a distance of {\bf 1 parsec}.

What is an arcsecond ( )?

So

This is the angular size of a dime seen from 2 miles.

• The distance to a star in parsecs is when is measured in arcseconds.

• How far away ARE the nearby stars? The closest star (aside from the Sun is called Proxima Centauri with a parallax of . This means it is more than 1 pc away:

• Even the largest parallax (that for the closest star) is small. The atmosphere blurs stellar images to around so astrometrists'' are trying to measure a tiny motion of the centroid of a stellar image as it moves back and forth each six months. In the previous diagrams the parallax motions have been hugely exaggerated.
• From the ground it is possible to measure parallaxes for stars out to around 80 pc -- this corresponds to very tiny motions.

So, a star at 80 pc has a parallax angle of only   arcsec.

• Within a sphere with a radius of 10 LY (3 pc) there are only 10 known stars

• Note that most of the nearest stars are faint in apparent brightness and much less luminous that the Sun.

Michael Bolte
Mon Jan 26 12:32:25 PST 1998