Astronomy 162: Professor Barbara Ryden

Monday, January 13


``How far would I travel
To be where you are?
How far is the journey
From here to a star?''
- Irving Berlin

Key Concepts

(1a) Distances in the universe are important to know.

Distances are required to compute: (Besides, knowing the distance to a star is interesting in its own right.)

(1b) Distances in the universe are difficult to measure.

It took a long time to measure distances to the nearest stars.

(2) The distance to a nearby star can be found from its parallax.

Definition: Parallax is the change in the apparent position of an object which results from a change in the observer's position.

Simple example: Hold thumb at arm's length. Look first through one eye, then through other. Thumb's position changes relative to background. The closer your thumb to your eyes, the larger the jump in position.

More sophisticated example: Look at a star - first in June, then in December, six months later. Your location changes by 2 AU between these times. Therefore, the star's position changes relative to more distant background stars. The angle p (see the diagram below) is the star's parallax.

After measuring p, and knowing the size of the Earth's orbit, we can compute the distance to the star using trigonometry. Note that the distance to even the nearest stars (other than the Sun) is much larger than 1 AU; therefore, the angle p is small.

Measuring small angles:

Full circle = 360 X 60 X 60 = 1,296,000 arcseconds

1 arcsecond = angular size of dime 2 kilometers away

Important Equation: Computing a Distance from a Parallax

d = 1/p

d = distance to star, measured in parsecs

p = parallax, measured in arcseconds

The parsec is defined as the distance at which a star has a parallax of 1 arcsecond. In other units,
1 parsec = 3.26 light years = 206,000 AU.
Parsecs are the units most often used by professional astronomers in measuring interstellar distances.


The star Proxima Centauri has a parallax p = 0.77 arcsecond.

d = 1/0.77 = 1.30 parsec = 4.23 light years

Because stellar parallaxes are so small, they can only be measured accurately for relatively nearby stars. For comparison, the distance from the Sun to the center of our galaxy is about 8000 parsecs. Thus, we can only use the technique of stellar parallax to measure distances in our immediate neighborhood, not for the entire galaxy.

(3) On average, a nearby star will have a large proper motion.

Proper motion is the steady change in a star's apparent position on the sky, resulting from its motion through space. Proper motion is measured in arcseconds per year.

On average, close stars have faster proper motions than distant stars. (This is only an average statement: a star which happens to be moving directly toward or away from the Sun, for instance, will have no proper motion.)


Searching for stars likely to be nearby? Look for stars with large proper motion.
Prof. Barbara Ryden (

Updated: 2003 Jan 13

Copyright 2003, Barbara Ryden