Over the many years I’ve been writing this column, I've rattled off the distances to many celestial objects. I don't often use miles to express stellar and galactic distances, because the numbers would quickly become cumbersome. Instead, I use light-years because the numbers are smaller, and they're also a reminder of just how long it takes for the light from the stars to reach our eyes. All light travels at the speed of 186,300 miles a second in the vacuum of space. A light-year is defined as the distance that light travels at that speed in one year.
Given that there are about 31.5 million seconds in a year, you can calculate that a single light-year equals around 5.8 trillion miles. So, saying a star is 70 light-years away, which is pretty typical for stars we see with the naked eye, means that star is about 406 trillion miles away. That's 406, followed by 15 zeros! Also, by definition, the light we see from that star tonight left that star 70 years ago. We actually see the star the way it looked in 1950. If we see a star tonight that's 3,000 light-years away, we see it as it was in 980 B.C.! Whenever you look at the stars, you're looking back into the past, sometimes the very distant past!
So how do astronomers know how far away these stars are? Unfortunately, it's not a short and easy answer. For stars that are less than 2,000 to 3,000 light-years away, you use the stellar parallax method for determining distance. You take a picture of a star when the Earth is on one side of the sun in its orbit, and then you take another picture six months later when the Earth is on the other side of the sun. If the star is not too distant, you'll see it shift a tiny bit against the background stars.
This process comes down to simple high school trigonometry. The shifting of the star against the background stars creates what's called a parallax angle. Using basic geometry rules that say opposite angles are equal, you can draw a triangle between the Earth, the sun and the star. You 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 (the distance between the Earth and the sun), 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 challenging because it's such a tiny angle. You also have to assume that the background stars you're using to measure the stellar parallax angle are stationary. In reality, they're shifting as well!
Measuring the distance to stars using stellar parallax is also extremely difficult from the Earth's surface because you have to put up with the blurring effects of our atmosphere. That's why satellites have launched into orbit to measure the stellar parallax more precisely and calculate distances to thousands of stars.
Stars farther than 3,000 light-years away require other methods to figure out stellar distance. One method is 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 much about a star. From these rainbow-like 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 its luminosity, which is the amount of light a star produces. They discovered a distinct pattern when you plot a graph of spectral type vs. luminosity. Most stars fit right along a nice curve. The beauty of this is that by just getting the spectrum of a star you can determine its luminosity. Once you know the luminosity, figuring out the distance is an easy math equation using the straightforward inverse-square law of light.
For really distant stars, Cepheid variable stars are used. This was a huge discovery made by Henrietta Leavitt early in the last century at Harvard University. She studied thousands of variable stars, stars that varied regularly in brightness over a few hours to hundreds of days. In all of her observations, she discovered that the variable stars called Cepheids were extraordinarily regular and extremely bright, shining 500 to 10,000 times the sun's luminosity.
They varied in brightness due to cycle changes within the star. Leavitt found a near-perfect relationship between a star’s period of variation and its average luminosity, or light output. Cepheid variables could then be used as mile markers in deep space because of their brightness. If you spot a Cepheid variable, you can determine how far away it is just by observing its period. Once you have the period, you can get its luminosity, and from there, relatively simple math can be used to determine the distance of extremely far away places!
The famous astronomer Edwin Hubble used observations of Cepheid variable stars in what was then known as the Andromeda Nebulae to determine that Andromeda was a whole other galaxy, over 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, but he could not have done it without Henrietta Leavitt and her Cepheid variables. What a great celestial yardstick!
Mike Lynch is an amateur astronomer and professional broadcast meteorologist for WCCO Radio in Minneapolis/St. Paul and is author of the book, “Stars, a Month by Month Tour of the Constellations” published by Adventure Publications. Send questions to firstname.lastname@example.org.
The Rochester Astronomy Club welcomes new members and puts on public star parties. Their website is rochesterskies.org.