# How do astronmers measure distance to stars?

originally written as a response to a question from KidsAstronomy.com, Oct 10, 2000

```> How do astronomers find distances of stars from earth?
> what are some of the different methods?
```

Good question! Stars are _really_ far away, so ordinary techniques of measuring distances (yardsticks, tape measures, echoes) don't work. There is one truly fundamental method, called "parallax", another reasonably secure one which is usually called the "Baade-Wesselink" method, and a bunch of indirect methods. I'll give short descriptions of the two best methods, and some pointers to places you can look for further information.

"Parallax" refers to the apparent shift in the position of a nearby object relative to distant objects as the observer moves side-to-side. You can see it for yourself: hold your arm out straight in front of you, and point your thumb upwards. Close your left eye, and, looking with your right eye, line up your thumb with some distant object (a tree, a poster on the far wall of the room, etc.). Now, holding your arm still, close your eye and open your left eye. Look through your left eye at your thumb -- and you'll see that it isn't lined up with that distant object any more.

Your eyes are separated by only a few inches, so you can use them to detect a shift only for objects within a few feet of your head. But if you were a hammerhead shark, with eyes separated by three or four feet, you could detect a shift in the position of an object several hundred feet away. Back in the old days, battleships used to have special binocular-like devices, with the lenses separated by several feet. They allowed sailors to estimate the distance to enemy ships at a range of several miles (which allowed the gunners to aim their weapons accurately).

Astronomers need a very long "baseline" to detect the shift in the position of nearby stars. Fortunately, the solar system provides us with one: we can take the picture of a star when the Earth is one side of the Sun; then, six months later, when the Earth has moved to the OTHER side of the sun, we can take another picture. That gives us a baseline of about 300 million kilometers! With such a long baseline, we can measure accurately the shifts of stars up to about five hundred light years.

The Hipparcos satellite was specially designed to measure parallaxes from orbit: read about it at

The other method I'll mention briefly is named "Baade-Wesselink", after two astronomers who pioneered its use several decades ago. The basic idea is based on several fundamental physical principles:

• gases heated to thousands of degrees emit radiation in a precise, predictable manner, described by the "Planck" or "blackbody" equation
• nearby objects are brighter than identical distant ones by a predictable amount, described by the "inverse square law"
• stars are basically big spheres of hot gas

Putting it all together, if we can figure out the temperature of a star, and we can figure out its diameter, we can calculate how much light it gives off. Then, if we measure its brightness, we can use the inverse square law to calculate how far away it must be. Astronomers can do a pretty good job of estimating the temperature of a star by passing its light through a prism or grating and breaking it up into a spectrum. The hard part is determining the actual size of a star, since they are so far away that one can't simply look through an ordinary telescope and resolve the disk. But we've figured out some clever ways to estimate the sizes, and so can do a fair job of finding distances by this method.

It turns out that this method is often applied to stars which pulsate in size and brightness. Why? Well, it's not too hard to figure out the relative diameters of such a star at its maximum and minimum size (much easier than figuring out the absolute diameter), and this method can then be applied to the relative brightnesses.

I've searched for a better explanation of this method on the Internet, but with little success. These sites offer a bit of information, but none really does a good job of giving the whole picture:

I hope this helps.