Before I get really far out with stellar distances, I urge you to get out in the very early evening to take in the great celestial hugging and tango going on between the naked eye planets Jupiter, Venus, and Mercury. As I told you last week in Starwatch, you must have an unobstructed view of the west-northwestern horizon to see it.

This weekend in the Butler sky, about 45 minutes after sunset in the low twilight of the west-northwestern sky, look for the three planets in a tight, spectacular little triangle just above the horizon. They’re within two degrees of each other, so close that your thumb extended at arm’s length can pretty much cover up all three!

Don’t wait too long in the evening to see the spectacle because all three slip below the horizon by around 10 p.m. Venus is the brightest of the three and Jupiter is the farthest away at more than 560 million miles. As this week continues the triangle breaks up, but all three planets will still be hanging together. Don’t miss this show. You’ll love it.

The three planets in the western sky are far closer to us than the rest of the stars we see. Stellar distances are too cumbersome to express in miles.

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. 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 six trillion miles for just one light-year. So if a star is 100 light years away that star would be about six hundred trillion miles away. That also means the light you see from that star took about 100 years to reach your eyes.

All that is great, but just how do astronomers know how far away these stars are? Admittedly it is a complicated and complex answer, especially for those stars and galaxies that are really out in the astronomical hinterlands.

For stars within about 3,000 light years from Earth, astronomers use the stellar parallax method for determining distance. Basically a picture of a star 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 is not too distant, you’ll see it shift a tiny bit against the background stars. The shifting of the star against the background stars creates what’s called a parallax angle. You can calculate a star’s distance using simple geometry that states opposite angles are equal plus some simple trigonometry.

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 that 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 the blurring atmosphere. That’s why the Hipparcos 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 about 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 its luminosity, which is the amount of light a star actually produces. In fact, they discovered that most stars could be put on a graph and fit 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 Cephied 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 vary in brightness over a period of a few hours to hundreds of days.

In all 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 a whole other 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.