Last time, we looked at measuring distance within the solar system and to stars in our galactic neighborhood. Scientific expeditions in 1761 and 1769 included historical figures Charles Mason and Jeremiah Dixon, surveyors of the Mason-Dixon line, and British explorer Capt. James Cook. Their efforts helped establish the sun-Earth distance (an average of 93 million miles) and the stellar parallax method used to estimate distance to "nearby" stars.

Stellar parallax works pretty well until the angle of shift for a given star becomes so small that a reliable estimate cannot be calculated. To overcome the limitations of stellar parallax, astronomers developed new methods based upon the physical properties of light emitted by stars.

Along with his studies of the variable star Algol, John Goodricke also discovered another variable star in the constellation Cepheus in 1784. Known as Delta Cephei, this star is the prototype for a class of stars called Cepheid variables. Cepheid variable stars pulsate in brightness, producing unique light curves that make them easy to detect. Following the groundbreaking work of Henrietta Leavitt and Ejnar Hertzsprung, Cepheids became standard candles for distance measurements.

Before we continue, let's understand two terms that will appear later — apparent magnitude and absolute magnitude. Apparent magnitude refers to the brightness of a star as it appears from Earth. If that star could be viewed from a distance of 32.6 light years (10 parsecs), its apparent magnitude then becomes known as its absolute magnitude. Absolute magnitude is the standard measure of a star's luminosity or intrinsic brightness.

Employed at Harvard College Observatory to count stars on photographic plates, Leavitt noticed that some stars varied in brightness. After collecting data on more than 1,700 stars in the Small Magellanic Cloud, she found 25 Cepheids. Some of the Cepheid stars pulsated with longer periods than others. Continuing her study, she sorted Cepheids from shorter to longer period. The long period stars at the top of the list turned out to be the brighter ones and the shorter period, dimmer stars were on the bottom. She reasoned that the longer the period, the greater the luminosity of a star. In 1912, she confirmed her findings of the Period-Luminosity relation, but because the distance to stars in the Small Magellanic Cloud was unknown, an actual value for the luminosity part of the equation could not be determined.

In 1913, Ejnar Hertzsprung measured distance to Cepheid variable stars within the Milky Way galaxy using a technique called statistical parallax. By applying the inverse square law of light to his distance estimates, Hertzsprung was able calibrate the star's distances with their Period-Luminosity relation. The inverse square law states that a star at twice the known distance of another will appear one-quarter as bright. Three times as far is one-ninth as bright and so on. By identifying a Cepheid and recording its period, one can determine its luminosity. Then, by using the baseline for absolute magnitude, one can calculate how far away a star of a given absolute magnitude would need to be in order to show the apparent brightness observed.

In the mid-1920s, Edwin Hubble observed Cepheid variable stars in a large nebula in the constellation Andromeda. His calculations conclusively proved that the nebula was, in fact, a separate galaxy far beyond the Milky Way. Our home galaxy was just one of what he called "Island Universes." We now know that there are likely to be hundreds of billions galaxies in the universe.

Light emitted by distant objects is subject to the Doppler effect. Visible light is just one portion of the electromagnetic spectrum. When looking at the light emitted by a star or galaxy, astronomers can tell if the object is approaching or receding. Light from approaching objects is shifted toward the blue end of the spectrum. For objects receding, the light is shifted toward the red end of the spectrum. An everyday example of the Doppler effect can be heard in the sound waves emitted by a passing police siren — the frequency shifts as the squad car approaches, passes nearby and then moves away.

Astronomers seeking to measure more remote distances and gauge the rate of universal expansion have used Type Ia supernovae as their standard candle-distance indicator. A proposed model for Type Ia supernovae points to close binary systems in which one star gravitationally siphons off material from its neighbor. As this process continues, a point is reached where the mass gained by the star causes it to become unstable triggering the supernova outburst. So far, all Type Ia supernovae detected produce identical light curves allowing us to determine their luminosity or intrinsic brightness.

Today, we can cross check our calibration of distances through stellar parallax and the standard candles of variable stars and Type Ia supernovae. Future discoveries will update our understanding and lead to progressively more reliable measures of distance. As for me and my struggles with topographical maps, estimating distances and the time needed to make a trip, I'm putting a GPS unit on my holiday wish list.

Peter Lipscomb is the director of the Night Sky Program for the New Mexico Heritage Preservation Alliance. Contact him at plipscomb@nmheritage.org.