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## The Question

(Submitted April 15, 1997)

How do astronomers know for sure that stars are really as far away as they state?

Thank you for writing the "Ask an Astrophysicist" service with your question. The methods astronomers use to measure distances to the stars is a piece of fundamental and active work in astronomy with important implications for how we understand the Universe around us.

Measuring the distances to stars is kind of like a house of cards: we use one method to get nearby stars, use a new method for further away stars which depends on our first measurements of nearby stars, then yet another method at further distances, and so on.

The first method astronomers use to measure distances to stars is called parallax. If you hold your finger in front of your face and close one eye and look with the other, then switch eyes, you'll see your finger seem to "shift " with respect to more distant objects behind it. The effect is called parallax.

Astronomers can measure parallax by measuring the position of a nearby star very carefully with respect to more distant stars behind it, then measuring those distances again six months later when the Earth is on the opposite side of its orbit. The shift is tiny... less than an arcsecond even for the nearest star (an arcsecond is 1/60 of an arcminute, which is 1/60 of a degree). In fact, I have heard (but only heard it once and never been able to find a reference to verify it, so label this as "interesting hearsay not necessarily to be believed ") that some of the early Greek astronomers specifically looked for parallax from the stars to work out whether the Earth orbited around the Sun. But their instruments could not measure the very small parallaxes nearby stars exhibit. Since they thought nearby stars were much closer than we now know, the fact they observed no parallax implied that the Earth did not orbit the Sun. Whether this is true or not, it was not until telescopes were invented that astronomers could measure parallaxes at all accurately.

Astronomers have been carefully measuring parallaxes for stars for centuries, and with remarkable precision. But it is painstakingly slow work with only a few thousand stars having well measured parallaxes. In 1989, the European Space Agency (ESA) launched a satellite called Hipparcos to accurately measure the parallax of some 120,000 stars (plus about another million or so stars with good, but lower precision). Hipparcos measurements increased the number of stars for which parallaxes are measured by a vast amount. Visit the Hipparcos web page for more details:

Parallaxes give us distances to stars up to perhaps a few thousand light years. Beyond that distance, parallaxes are so small than they cannot be measured with contemporary instruments. So astronomers use some more indirect methods beyond a few thousand light years. Rather than describe them in detail, let me point you to a good reference: George Abell's "Exploration of the Universe ". Your local library probably has a copy... and if it does not, almost any good astronomy textbook will also include this information.

The methods beyond a few thousand light years include:

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. See: