Looking Up: How do astronomers know the distance to a star?

I am often asked this question. The answer is relatively simple, and involves different techniques based on the distance to the star. Today we will discuss the first technique used by astronomers to measure the distance to nearby stars.

Lets use the four bright stars in a line in the picture to get us going along what astronomers call the “Cosmic Distance Ladder.” We'll call the far left blue star #1, the next one to the right will be #2, then #3 and #4.

We can see all four stars are relatively bright. This almost always means the stars are closer rather than really far away. Some dim stars are nearby but bright ones usually are definitely nearby.

So the first tool in the astronomer's distance estimation box is for nearby stars. It works very well for stars up to about 3,200 light years away. Remember one light year equals 6 trillion miles. However, the universe is extremely large, and just our own galaxy is about 100,000 light years across. So 3,200 light years is relatively close.

This first tool is called "parallax." You can demonstrate parallax by just holding your thumb out at arm's length in front of a wall. Look at your thumb first with one eye closed, and then the other one closed. It will seem to jump from side to side. This is because of the difference in the angles that you see your thumb from the left eye vs the right eye.

You will recall how parallax can be used to measure distance from your high school trigonometry class. It is simple triangulation. When you know the length of one side of a triangle, and you know the angles at each side of that length you know how long the other two sides are. Hence, if you could establish a base line, and two angles to a star from earth you know how far each side extends -- thus giving you the distance.

Well okay, but how do we get the baseline, and angles to a distant star? This turns out to be pretty easy. You just use a very high-resolution telescope to take two pictures of a star. The pictures will be taken 6 months apart. So the earth is on one side of the sun for the first picture, and the other side for the second picture.

We know with great precision how far the earth is from the sun so that gives us the distance across our base line.

The high-resolution telescope then pinpoints the exact location of the star against its background for each of the two photos. That gives us the angles that the light from the star is following in reaching the earth for each of the two points in time. Now we can easily calculate the distance to the star.

A special telescope orbiting the earth called "Hipparcos" was used for these measurements. As I said earlier, this works well out to about 3,200 light years, which includes over 100,000 stars. (Before Hipparcos we could only go out to about 400 light years with this method). The angles get to be incredibly small beyond that, and astronomers then use other tools in their distance measurement box which we will discuss in future articles.

So lets go back to our picture above. Here is what parallax tells us about the 4 bright stars in the upper left:

• Star #1 - It is 506 ly away. (A blue/white type "A" star.)
• Star #2 - It is 897 ly away.  (A blue/white  type "O" star).

Hipparcos recorded an uncertain number for its distance, so we used another measurement to get its distance called a spectroscopic fingerprint, which we will discuss in the future.

The object is really a double star. Two stars situated close to each other, separated in telescope much larger than mine by only 0.8  arc sec. One star is brighter at seventh magnitude than the other which is 9th magnitude.             

• Star #3 - It is 248 ly away. (A yellowish type "K" star.)
• Star #4 - It is 331 ly away. (A blue/white type "O" star.)

Lying in deep space beyond the four bright stars is the red emission nebula, NGC 6357. It lies 5500 ly away. Again, how astronomers determine distances for an object this far is another story for another time.

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Ted Wolfe is a member of the Everglades Astronomical Society. Organized in 1981 it serves the Naples community, providing information in all aspects of amateur astronomy. Its goals include educating the general public, school children and other groups to the wonders of the universe. The society meets at 7 p.m. every second Tuesday of the month at the Norris Center (public invited). Regular viewing visits to a special, dark sky site in the Everglades are held each month, allowing the general public to observe the night sky through telescopes, under pristine conditions. For more information, visit the website at http://naples.net/clubs/eas. A Blu-ray disc for viewing on TV is now available which features 70 of Ted's deep space images with original background music. For more information, go to www.naples.net/clubs/eas/sales.html.