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Home > Articles > How To > Beginners > Measuring Astronomical Distances

Measuring Astronomical Distances
By Joe DalSanto - 2/23/2005

Measuring Astronomical Distances

By: Joe DalSanto

How often have you shown a friend some astronomical sight in your telescope, explained how large and how far away it is only to have them ask, “How do we know it’s really that large and far away?” Besides your own fascination with stellar distances, how do you explain this to non-astro friends? Nearly all of modern astronomy is dependent on accurate distance measurements. Without these, we could not determine the sizes, luminosities or other essential parameters of astronomical objects. How can we tell how far away the stars are?

As the idea of the earth circling the sun gained acceptance, early astronomers realized that the earth’s motion around the sun should produce apparent shifts of the nearer stars on an annual basis. That is, nearby stars should appear to move back and forth with respect to the more distant ones over the course of a year as the earth moves from one side of it’s orbit to the other. This parallax effect was not seen for quite some time as it is a very small shift, indicating great distances to even the nearer stars. The first reliable distances to the stars were measured in the 1830s. By this time, improvements in astronomical instruments allowed the precise, highly accurate measurements required to detect the tiny shifts of nearby stars. With these tiny angular shifts in hand, astronomers could construct enormously tall triangles with the diameter of the earth’s orbit as the base and the tiny angular shift as the angle opposite the base. The resulting height of the triangle, easily calculated thru trigonometry, gave us our first direct measure of the distances to the stars.

As these exacting measurements were slowly and laboriously obtained, it became evident that the stars were many light-years away. Therefore, this method had very definite limitations. The visual shifts were only measurable for stars out to about 100 light-years away, severely limiting our reach. In time, photographic methods improved the accuracy such that we could reach out to perhaps 250-300 light-years, but with steadily diminishing accuracy. Recent results from the orbiting Hipparcos satellite have greatly improved both our accuracy and reach but the trigonometric parallax method is still quite limited.

To extend our understanding of cosmic distances beyond a few hundred light-years, astronomers had to employ other methods which built on the parallax method as their foundation. Thus a “ladder” approach of distance-determining methods arose which utilizes various other branches of astronomy and allows us to reach out to objects thousands, millions, even billions of light-years away. Let’s see how.

The next major key to determining astronomical distances employed stellar spectroscopy. Nineteenth century astronomers had begun to classify stars by breaking their light into spectra and ordering the spectra by the various bright and dark lines present. As the twentieth century dawned, Ejnar Hertzsprung and Henry Norris Russell independently made a profound discovery. By studying the spectral types (closely related to actual temperatures) of stars whose distance had already been determined, they were able to show that stars do not come in all combinations of brightness and temperature. Instead, when plotted according to spectral type versus luminosity (in what became known as the “Hertzsprung-Russell, or HR diagram), the vast majority of stars lay along a band termed the main sequence of stars. Most stars spend most of their lives in this area of the diagram, slowly converting hydrogen into helium to produce their energy. However, there were some stars in most classes that were much brighter than typical for the main sequence. Since all stars of a spectral class have the same temperature, this implied that the brighter ones had to be larger, much larger, in order to be so much brighter. Thus were discovered giant and supergiant stars. As time went on, variances in spectral line widths provided additional information which resulted in the recognition of luminosity classes, from I for the largest supergiants to V for main-sequence stars, termed dwarfs.

The Hertzsprung-Russell diagram
Armed with this understanding of the stars, astronomers could now extend the reach of our distance measuring. It works like this: With a star’s spectrum in hand, we determine it’s spectral type and luminosity class. When plotted on a HR diagram, the star’s absolute (actual) luminosity can be read off of the vertical axis. (Of course the diagram had to be painstakingly calibrated but that’s another story). Comparing the actual luminosity just derived with the star’s apparent luminosity seen in the telescope we can easily determine it’s distance according to a well-established law of physics that specifies how light diminishes with distance. (This inverse-square law states that a star 4 times farther away will appear 4x4 or 16 times fainter, one 9 times farther will appear 9x9 or 81 times fainter, and so forth). Thus, virtually any star whose spectrum can be obtained is now within our reach, as we can determine its distance spectroscopically out to many thousands of light-years.

It didn’t take long for astronomers to realize that they could utilize another powerful method based on what they had learned in studying variable stars to reach even further. Certain classes of stars (primarily the famous Cepheid variables) displayed a remarkable property. Stars of this type with longer periods of variability were found to be brighter than those with a shorter period. Thus, regardless of their actual distance, these stars could be recognized by their period of variability. All that remained was to quantify the relation by determining the actual luminosity of Cepheids with various periods thru independent methods of stellar spectroscopy. (For example, a star of absolute magnitude 5 might have a period of 3 days while a star of absolute magnitude 7 might have a period 2 days). No matter how faint such a star appeared, if we could measure its period, we could then compare the observed brightness with the actual luminosity to determine the distance!

This method of using Cepheid variables as distance indicators was employed to prove that various nebulae were not part of our galaxy but in fact were enormous galaxies similar to our Milky Way in their own right. For example, when Cepheids were discovered in the Magellanic Clouds, their apparent brightness indicated a distance of roughly 175,000 light-years, well beyond the boundaries of our galaxy. When Edwin Hubble was able to identify Cepheids in the great spiral in Andromeda, he was able to determine an even greater distance (today’s value is about 2.5 million light-years). Recently, observations with the Hubble Space Telescope have identified Cepheids in galaxies as far out as 50 million light-years, solidifying our ability to measure distances within this vast region. We can then estimate distances to even farther galaxies by comparing their overall brightness with that of similar galaxies of known distance.

The final rung on the cosmic distance scale makes use of the property of the expansion of the universe. Nearly every galaxy appears to be moving away from us as indicated by a shift in its spectral lines towards the red end of the spectrum. This shift, painstakingly measured, quantified, and refined, gives us a indication of a galaxy’s distance based on the amount of the shift (farther galaxies have greater shifts). Once again, this method is calibrated by measuring the shift for galaxies with known distances before using it on galaxies with unknown distances. In this way we can state with some certainty that a faint galaxy or quasar may be billions of light-years from earth.

No less remarkable than the resourcefulness and determination of astronomers in measuring astronomical distances is the fact that we are able to unlock these clues from the universe from such limited visual information. The next time you (or a visitor to your scope) wonder about the vast distance to an object you’ve just seen, why not contemplate this? To paraphrase Isaac Newton, “If we have seen farther (literally!), it is by standing on the shoulders of (astronomical) giants”.

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