July 1999

How Far Is That Star?

The next time you gaze up at the night sky at all those twinkling stars, remind yourself that they are so far away that their light needed years to reach you. Even the very closest star, Alpha Centauri (we'll ignore our home star, Mr. Sun) is seen as it appeared four years ago. The distances to the stars are vast.

Okay, wait a minute. How do these wise-guy astronomers know that the stars are so far away? You'd need a pretty big yardstick, pal.

It makes sense to be a little skeptical, since the distances are extraordinary. The techniques that astronomers use for determining astronomical distances are as various as they are ingenious, but let me tell you of an old and rock-solid method. It's called parallax.

Parallax is a pompous word for an easy idea: triangulation. Hold your thumb up at arm's length and look at it with just one eye. Then look with your other eye. Your thumb will seem to shift its position against the wall. Viewing something from two different perspectives causes it to seem to move between two positions, at least compared to its background.

And here's the point: the closer the object, the greater the shift. Move your thumb closer to your face and look again, one eye and then the other. A bigger change, no? In a speeding car, trees near the road whiz by, but mountains creep past oh-so-slowly. Same idea.

Well, great! If we can observe a star from two different locations, it should appear in two different positions with respect to stars farther away. The greater the difference in the star's two positions, the closer it must be. Piece of cake. The straight-line distance between Kitt Peak National Observatory and Cerro Tololo Inter-American Observatory (in Chile) is, maybe, 9,000 kilometers. If a telescope at each observatory photographs the same star, they can compare images...

Oops. The star would be in the same position in both images. No shift at all. It turns out that stars are too far away for parallax detection to be that easy; 9,000 kilometers is not a long enough baseline. Our observatories must be farther apart than that. So what do we do?

These astronomers are so clever. Just use one telescope, but wait for the Earth to move in its orbit around the Sun. In a single year, our planet moves in a vast circle (ellipse, really) with a diameter of 300 million kilometers! That should be far enough! If a star is watched carefully for an entire year, it should appear to make a tiny loop. More distant stars should make smaller loops. The stars themselves aren't moving; the loop comes from our changing view of a star as we "loop" around the Sun.

Astronomers knew that this should work as far back as the sixteenth century. The problem was that not everyone believed that the Earth moved in the first place. Detecting the annual parallax motion of the stars was proposed early on as a proof of heliocentrism (a Sun-centered Solar System). Some (such as Tycho Brahe, who should have known better) thought it was too foolish to try.

A few astronomers did try, though, and were disappointed when they found no such motion. Some astronomers explained the failure by saying that the stars must be incredibly far away. Others said, "Baloney. The stars can't be that far away. Clearly the Earth does not move!"

Luckily, heliocentrism caught on for other reasons, and astronomers kept struggling to detect stellar parallax. (Like Tycho, Galileo refused to look. He felt that his explanation of the tides was evidence enough that the Earth moved.)

Their goal, however, would remain elusive until the nineteenth century. The first parallax shift of a star was detected in 1838 by an astronomer named F. W. Bessel (right), at the Konigsberg Observatory in Prussia. The star was actually a binary called 61 Cygni, a gravitationally bound pair of red dwarf stars. Bessel found that these stars were making annual loops with a radius of .29 arcseconds, corresponding to a distance of 10.3 lightyears (in other words, the distance light would travel in 10.3 years).

(What's an arcsecond, you ask? It's a sixtieth of an arcminute, of course, which is a sixtieth of a degree. A degree is about the width of your thumbnail, held at arm's length. It's not surprising that earlier astronomers had such a hard time detecting such a tiny shift!)

At last, we had a solid distance to a star, and others quickly followed. While even today we can only detect the parallax of stars within about a hundred lightyears, there are plenty of stars within that distance that we can now study. By studying these stars, we have learned different tricks for measuring distances to stars too far for parallax. Recently, the Hipparcos spacecraft was able to determine the parallax of thousands of stars, including a recheck of old 61 Cygni. The result: 11.4 lightyears, good to a twentieth of a lightyear.

One last thing: Ever heard of a parsec? This is an old unit of distance, derived from parallax. It's short for PARallax-arcSECond. A star with a parallax shift of one arcsecond would be one parsec away (but no stars are this close).
A star with a parallax of half an arcsecond would be two parsecs away, a third of an arcsecond means three parsecs, etc. A parsec is about 3.26 lightyears. You can hear Han Solo mention parsecs in Star Wars, but I have no idea what he's talking about.

Steve White
Nightly Observing Program
Kitt Peak Visitor Center

P.S. I found another neat diagram that illustrates what the parallax shift of a star looks like. Also, if you want to know how astronomers find distances to stars too far for parallax, check out Part II of this article. - S

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Telescope Operators/Guides for Nightly Program:
Adam Block (ablock@noao.edu) Lead Observer
Steve White (swhite@noao.edu)
Flynn Haase (fhaase@noao.edu)
Richard Barchfield (richardb@noao.edu)

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