Measuring the Distance of Stars

Astronomers have come up with various different techniques to estimate how far away any given star is.

The first technique uses triangulation (a.k.a. parallax). The Earth's orbit around the sun has a diameter of about 186 million miles (300 million kilometers). By looking at a star one day and then looking at it again 6 months later, an astronomer can see a difference in the viewing angle for the star. With a little trigonometry, the different angles yield a distance. This technique works for stars more than 100, up to about 1000 light years of earth.

Another method uses brightness measurements. It turns out that a star's colour spectrum is a good indication of its actual brightness. The relationship between colour and brightness was proven using the several thousand stars close enough to earth to have their distances measured directly. Astronomers can therefore look at a distant star and determine its colour spectrum. From the colour, they can determine the star's actual brightness. By knowing the actual brightness and comparing it to the apparent brightness seen from Earth (that is, by looking at how dim the star has become once its light reaches Earth), they can determine the distance to the star.

Stellar motions: All stars are in motion, but only for nearby stars are these motions perceivable. Statistically, therefore, the stars that have larger motions are nearer. By measuring the motions of a large number of stars, we can estimate their average distance from their average motion.

Moving clusters: Clusters of stars travel together, such as the Pleiades or Hyades star clusters. Analyzing the apparent motion of the cluster can give us the distance to it.

Inverse-square law: The apparent brightness of a star depends both on its intrinsic brightness (its luminosity, or how bright it really is) and its distance from us. If we know the luminosity of a star (for instance, we have a measured parallax for one star of the same type and know that others of the same type will have similar luminosities), we can measure its apparent brightness (also called its apparent magnitude) and work out the distance using the inverse-square law. There are several variations on this, many of which are used to measure distances to stars in other galaxies.

Interstellar lines: The space between stars is not empty, but contains a sparse distribution of gas. Some times this leaves absorption lines in the spectrum we observe from stars beyond the interstellar gas. The further a star is, the more absorption will be observed since the light has passed through more of the interstellar medium.

Period-luminosity relation: Some stars are regular pulsators. The physics of their pulsations is such that the period of one oscillation is related to the luminosity of the star. If we measure the period of such a star, we calculate its luminosity. From this, and its apparent magnitude, we can
calculate the distance.

Thank you for your extensive answer, Contrex.

Of the methods you mentioned, do some yield more accurate measurements than others? You mentioned that the upper limit of accuracy for parallax measurements is about 1000 light years; do we know the upper limits for some of these other methods--tens of thousands of light years, or even hundreds of thousands, for example?

http://www.google.co.uk/search?num=100&hl=en&safe=off&q=measuring+stellar+distances+accuracy&btnG=Search&meta=

Also there is Cepheid Variables - these are a certain type of star that blinks with a certain very consistent frequency relating to size, and size determines lumonsity. So if you can spot one, and determine its brightness and period of blink, you can pretty accurately determine its distance from you. This was the approach EdwinHubble used in 1929 to show Andromeda definitely wasn't in our galaxy, but was a galaxy in its own right.

http://zebu.uoregon.edu/~soper/MilkyWay/cepheid.html

By the way, astronomers and cosmologists don't tend to dwell in distance using light years for most purposes - we deal in red-shift. Rather than say X is 12,345,678 light years away we say it has red-shift of 2.

"Red Shift" involvement in celestial locating
I don't know if you really want to get into it this deep but there is a US Govt. site that publishes red shift values (aparent speed of recession or "Z") for many (like thousands of) celestial objects. (New computer and somehow I have lost the link )

Perhaps somebody could link shapeless to the Automated Red Shift Lab.

Or Google "Red Shift" and follow it around.

The red shift is a deadly accurate method. Just ask any State Trooper with a "Doppler type" (radar) gun.

Fascinating stuff. Thanks for your input, all!