How do we know how far away stars are?
In the nearly 20 years that I've enjoyed sharing my love of astronomy with you, I've rattled off many, many distances to many stars and galaxies.
If we tried to express the distances in miles the number would quickly become extremely cumbersome. Light years do a better job because the numbers are smaller and we're reminded of just how long it takes for the light from the stars to reach your eyes.
All light travels at the speed of 186,300 miles a second and a light-year is defined as the distance that light travels at that speed in one year. Given that there's about 31.5 million seconds in a year, you'll come up with almost 5.9 trillion miles for just one light-year.
If you see a star tonight that's 70 light years away, which is fairly close for a star, it's taken that light 70 years to get here.
If you're a frequent star flyer of this column you know that I've reminded you time and time again about the distances you're witnessing every time you gaze into the night sky. But, how do astronomers know the distances to all of the inhabitants of the cosmos?
Do they just point their telescopes at stars, examine them, then scratch their heads and say, “Because I have a PhD, I estimate that this star is 100 light years away and that one over there is 5,000 light years away?” No, there's a little more to it than that.
About 100 years ago astronomers got a fairly good estimate of stellar distances using the famous Hertzsprung-Russel diagram, developed in the early 1900s by Ejnar Hertzsprung of Holland and Henry Norris Russel from the United States.
They studied the spectrums of thousands of stars, which are like fingerprints. If you take starlight and send it through a spectrograph, you can spread out the various wavelengths that make up that light and learn a lot about a star. From these rainbowlike displays you can see signatures of different chemical elements, temperature, and much more.
Hertzsprung and Russel found a definite relationship between the spectral type of a star and it's luminosity, which is the amount of light a star produces. In fact, they found that most stars could be put on a graph and that they fit right along a nice curve. The beauty of this is that by just getting the spectrum of a star you could determine its luminosity. Once you know the luminosity, figuring out the distance is an easy math equation using the very simple inverse-square law of light.
A more direct way of estimating stellar distance is the stellar parallax method that uses basic high school trigonometry. Here's how it works:
A photo of the star in question is taken when the Earth is on one side of the sun in its orbit, and another picture is taken six months later when the Earth is on the other side of the sun. If the star isn't too distant, you'll see it shift a tiny bit against the collected background of far more distant stars. The shifting of the star against the background stars creates what's called a parallax angle. Using the rules of geometry that say opposite angles are equal, you can then make a triangle between the Earth, the Sun, and the star. You then take the parallax angle and cut it in half. Since you know what that angle is and you know the length of one side of the triangle, it's simple “trig”. The distance x (to the star) = 93,000,000 miles divided by the tangent of the parallax angle.
As simple as the math is, the practice of measuring that parallax angle is very difficult and you're also making assumptions. First of all, these parallax angles are extremely tiny. Not only that, you're assuming that the background stars you're using to measure the stellar parallax angle are stationary. In reality they're also shifting as well, but only a tiny, tiny bit.
Measuring the distance to stars using stellar parallax is also extremely difficult from the Earth's surface because you have to put up with our blurring atmosphere. That's why the Hipparchos satellite was launched in 1989 to measure the stellar parallax and distances to hundreds of stars, followed by the Gaia satellite in 2013. Despite its success, the satellite's accuracy falls off with smaller parallax angles and larger stellar distances past about 30,000 light years.
For really distant stars, like those in other galaxies, Cepheid variable stars are used. These are stars that vary in brightness over time. In the early 1900s Henrietta Leavitt, an assistant in the astronomy department at Harvard University, made a huge discovery. She studied thousands of variable stars that varied in brightness over a period of a few hours to hundreds of days.
She discovered a class of variable stars that was extremely regular in brightening and dimming, and extremely bright, shining 500 to 10,000 times the sun's luminosity. They varied in brightness due to cycle changes within the star.
There's a near perfect relationship between a star's period of variation and its average luminosity, or light output. Cepheid variables could be then be used as mile markers in deep space because of their brightness. If you saw a Cepheid variable star in a distant corner of our sky you can could determine how far away it is just by observing its period of variation. Once you have the period you can get its luminosity, and from there it's simple math to determine the distance of some really far-off places.
The famous astronomer Edwin Hubble used observations from Leavitt's Cepheid variable stars in what was then known as the Andromeda Nebulae to determine that Andromeda was a whole other galaxy, more than 2 million light-years away.
Until then, our Milky Way was thought to be the only galaxy in the universe. This is Hubble's discovery and he got all the credit, but he couldn't have done it without Henrietta Leavitt and her Cepheid variables. What an unsung hero she was!
Mike Lynch is an amateur astronomer and professional broadcast meteorologist for WCCO Radio in Minneapolis/Paul and is author of the book, “Stars, a Month by Month Tour of the Constellations” published by Adventure Publications available at bookstores at http://www.adventurepublications.net
