Measuring distance can take time

In the 10-year plus history of this starry column in the Eagle, I’ve rattled off distances to many stars and galaxies.

The distances are so far that the miles are too cumbersome to express. Light years do a better job because the numbers are smaller and you’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 in one year. Given there’s about 31.5 million seconds in a year, you’ll come up with around 5.8 trillion miles for just one light-year when you number crunch.

So if you see a star tonight that’s 70 light years away, which is pretty typical for the distance of a star you can see with the naked eye, that would equate to about 406 trillion miles.

Also by definition, because it’s 70 light years away, the light we see from that star tonight left that star 70 years ago, so what we actually see is that star as it looked back in 1944. If a star is 3,000 light years away, we see it as it was in 986 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? Do they just point their telescopes at stars, examine them, then scratch their heads and say, “Because I have a PhD, I think that 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, but it’s not all that complicated, at least for the not too distant balls of gas we call stars.

For stars that are less than about 2,000 light years from Earth, 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 simple geometry rules that say that opposite angles are equal, you can then make a triangle between the Earth, sun and the star. You take the parallax angle and cut it in half.

Because you know what that angle is and you know the length of one side of the triangle it’s simple trigonometry.

The distance to the star equals 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. You’re assuming the background stars you are using to measure the stellar parallax angle are stationary. In reality, they may be 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 our blurring atmosphere. That’s why the Hipparchos satellite was launched in 1989 to measure the stellar parallax and distances to hundreds of stars.

Despite its success, the satellite’s accuracy falls off with smaller parallax angles and larger stellar distances past 500 light years. Stars beyond that require another method.

That method uses 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 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 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.

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.

Leavitt studied thousands of variable stars, stars that vary in brightness over a period of a few hours to hundreds of days. In all of her observations she discovered that the variable stars called Cepheids were extremely 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 see a Cepheid variable star in a distant corner of our sky you can determine how far it is just by observing its period. 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 of Cepheid variable stars in what was then known as the Andromeda Nebulae to determine that Andromeda was another galaxy, more than two 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.

Celestial happening

The Leonid Meteor Shower peaks this Monday night and Tuesday morning.

It’s actually one of the minor meteor showers of the year, although if you’re in the countryside and have dark skies you may see 15 to 20 meteors an hour.

They’re best seen from around 1 a.m. to the start of morning twilight.

Lie back on a lawn chair and roll your eyes all around the sky slightly favoring the eastern half of the sky.

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 available at bookstores and at www.adventurepublications.net.