How Far Away is Vega?
By Bill Pellerin
Houston Astronomical Society
GuideStar Editor
At our annual Astronomy Day event, I’ll often point to Vega and say, “That star is 25 lightyears away and this means that the light takes 25 years to reach us.” But, how do we know that Vega is 25 light years away? How did we determine this?
This is an interesting subject. Even the distance to the Sun wasn’t well determined until the 1960’s when radar ranging was used to measure the distance. The process is easy, send a radio pulse to an object, and see how long it takes to get there and bounce back. If you know the speed of the radio pulse, and we do, it’s easy to calculate the distance using the formula we learned in high school — d=r*t. That is, the distance is equal to the rate (speed) multiplied by the time. Since the radio pulse has to travel to the object and back the calculation for this is d=r*t/2.
By Bill Pellerin
Houston Astronomical Society
GuideStar Editor
At our annual Astronomy Day event, I’ll often point to Vega and say, “That star is 25 lightyears away and this means that the light takes 25 years to reach us.” But, how do we know that Vega is 25 light years away? How did we determine this?
This is an interesting subject. Even the distance to the Sun wasn’t well determined until the 1960’s when radar ranging was used to measure the distance. The process is easy, send a radio pulse to an object, and see how long it takes to get there and bounce back. If you know the speed of the radio pulse, and we do, it’s easy to calculate the distance using the formula we learned in high school — d=r*t. That is, the distance is equal to the rate (speed) multiplied by the time. Since the radio pulse has to travel to the object and back the calculation for this is d=r*t/2.
Prior to that measurement of the distance to the Sun, the best measurement used trigonometry, time, and transits of Venus. Expeditions in the late 1700’s returned data sufficient to get the distance to the Sun to within 1% of the currently accepted value. (By the way, the last Venus transit any of us will ever see is visible in North America on Jun 5, 2012. If you miss this one the next one won’t be until December, 2117 – one hundred and six years from now.)
Once we become interested in knowing the distance to other stars, the problem gets more complicated. Astronomers talk about a ‘cosmic distance ladder’ when they are determining these distances and it is generally true that as we move up the ladder, to objects that are farther away, the accuracy of the distance measurement is less good. Closeby stars can be measured using stellar parallax – compare the position of the nearby star to the background, very far away, stars, wait six months for the Earth to move 186 million miles, and measure the star’s position again. Again, some simple trigonometry gives you the result. The idea is that you know the baseline, 186 million miles, and you know the angle of apparent movement of the star, so you can determine the distance.
The problem with this technique is that the angles are so small that it is difficult to get accurate measurements. If you measure the angle that the star appears to move 1 arc second (1/3600^{th} of a degree), the star is only 3.26 light years away – rather close. In truth, the closest star to us is about 4 light years away, so measurements to a fraction of an arcsecond are required to get the distance to any star in the sky. The star 61 Cyg was the first, in 1836, to have its distance estimated by this method. The estimate was 10.4 lightyears. Not bad. The current accepted distance to this star is 11.4 lightyears.
The parallax method was used much more recently by the Hipparcos satellite which was put into service in 1989. Because the Hipparcos satellite didn’t have to look through the turbulent atmosphere, it was much better at resolving the apparent angle of star movement, and was able to get accurate distances to stars as far away as 1600 lightyears. Newer instruments will be launched that will improve on this ability by a factor of 10 or so. By the way, the Hipparcos data tells us that the distance to Vega is 25.30 lightyears.
Farther out, estimates of the distances to stars are made by one of several techniques, but many of these rely on our knowing, or being able to estimate the intrinsic brightness of the star. Astronomers use the term ‘standard candle’ to mean a light source of known intensity. Once you know the actual brightness of the star it is easy to use the inverse square law to determine the distance. As we get farther from a star its apparent brightness is lower, and the apparent brightness decreases as one divided by the distance squared. The problem with this approach is the limitation of our ability to estimate the intrinsic star brightness. Here are some of the ways astronomers do this:

Spectroscopic parallax – one of the worst possible names for a technique in all of astronomy. This approach has nothing to do with parallax. The idea is that the star’s temperature is measured using a spectroscope (temperature and color are the same thing, so once you know the color of the star, you know its temperature). Based on stellar populations, and our knowledge about those populations, astronomers estimate the intrinsic brightness of the star. That done, getting the distance is simply a matter of calculating the distance to the star using the inverse square law.

Cepheid variable stars – Work done at the Harvard Observatory by Henrietta Swan Levitt early in the 20^{th} century, showed that the period of variability (the time from one peak in brightness to the next one) is related to the intrinsic brightness of the star. So, to get the intrinsic brightness, the astronomers measure the period of the variability. With that, the inverse square law provides the distance to the star. It was this technique that allowed Edwin Hubble to determine the distance to the Andromeda Galaxy.

Type 1a supernovae are a special class of supernovae for stars that are 1.4 solar masses. The 1.4 solar mass supernova is based on work done by Subrahmanyan Chandrasekhar in 1930. Since these supernovae all occur at the same mass, the brightness of each event is the same. These supernovae have been used to determine distances to galaxies.
It’s quite remarkable that we have been able to learn quite a bit about the stars from our little planet Earth in the Milky Way galaxy. There’s more to this story. Here are some references:
Measuring the Universe, by Kitty Ferguson, pub. Walker and Company, 1999 (available as a paperback)
Parallax, The Race to Measure the Cosmos, by Alan Hirshfeld, pub. W. H. Freeman and Company, 2001 (available as a paperback)