How Far is a Star?

61-cygniTake a look at your index finger held out arm’s length.  Now watch your finger as you alternately close one eye, then the other.  See how it appears to move back and forth against the more distant backdrop?  This effect is called parallax, and it’s the same effect astronomers use to directly measure the distance to nearby stars.

With the stars, of course, it’s a little different.  They’re a lot further away.  So closing one eye and then other won’t cut it: you need a much bigger side-to-side displacement.  In fact, astronomers use the baseline between the Earth and the Sun… a distance of some 300 million kilometers… to detect the parallax of nearby stars.

The image below shows the basic idea.  When the Earth is on one side of the Sun, say, in July, a nearby star appears in a slightly different place relative to the background stars than it does when the Earth is one the other side of the Sun in January.  The tiny angular change, along with the known distance from the Earth to the Sun and a little basic trigonometry, directly gives the distance to the star.

stellar parallax
But even with this large baseline, the apparent movement, or parallax, of a nearby star relative to more distant stars is much smaller and harder to measure.

These little angular shifts are extremely small, even for nearby stars.  The nearest star, Proxima Centauri shows a parallax of 0.77 arc-seconds (an arc-second is 1/3600 of a degree).  That’s about the angular size of a penny at a distance of 5 km.  Because of the difficulty in measuring such small angles, astronomers can only measure a parallax of about 0.01 arc-seconds.  That’s enough to accurately measure the distance to stars out to a few hundred light years… a tiny distance compared to the 50,000 light-year radius of our galaxy.

While ancient astronomers understood the concept of parallax, no one was able to detect these tiny angular shifts.  Some, including the great Tycho Brahe in the late 16th century, believed the lack of parallax was evidence the Earth was fixed in space and was likely the center of motion of the heavens.  The first measurement of parallax was made by Frederick Bessel in 1838.  He saw the shift of the star 61 Cygni (shown at the top of this article).

Space satellites can measure stellar parallax quite accurately.  The amazingly productive Hipparcos satellite, launched by the European Space Agency in 1989, was designed to make much more accurate measurements of stellar parallax than Earth-bound telescopes.  Hipparcos measured the parallax of more than 120,000 stars out to a distance of 1,600 light years.  The upcoming Gaia satellite will do even better, directly measuring the distance to stars tens of thousands of light years away.

By the way, if a star was at a distance which produced a parallax of 1 arc-second as seen from Earth, it would have a distance of 1 parsec.  A parsec, which works out to about 3.3 light years, is the unit of distance used by most professional astronomers.  Light-years are for us amateurs.

That’s it for today.