We're now gliding through the first week of astronomical spring. Consequently, the Andromeda Galaxy, a faint thumb smudge of light lingering above Andromeda the chained princess' outstretched arm, will soon set with the Sun. One can see it now low in the western evening sky just after twilight fades to black. Though this galaxy is vast and extends more than 120,000 light years across, it is about 2.2 million light years away and therefore is little more than a blemish in our sky.
We take this opportunity to discuss the most compelling aspect of astronomy: how astronomers know what they know about the Universe. Namely, how can we possibly know that the Andromeda Galaxy is 2.2 million light years away?
A light year, incidentally, is the distance light travels in one year through a vacuum. As this speed slightly exceeds 186,000 miles a second, a light beam propagating through space traverses 5.8 trillion miles! To give one an idea about how much space separates objects, the closest star to our solar system, Proxima Centauri, is 4.2 light years away. The most distant stars we observe with the unaided eye are about 3000 light years away. With that in mind, it seems all the more extraordinary that we know that the Andromeda Galaxy, the closest major spiral galaxy to our own, is 2.2 million light years away: a measurement made less than one hundred years ago.
We begin with a famous relation in astronomy; something called "The Distance Modulus," which relates a star's apparent magnitude (apparent brightness), absolute magnitude (actual brightness), and distance. If one knows two of these values, one can determine the other. This modulus is quite intuitive. We measure a star's apparent magnitude directly just by observing it on Earth. This brightness value does not yield information about its actual brightness, however. For all we know, a given bright star could be comparatively faint, but close; conversely, a faint star could be quite intrinsically brilliant, but far away. If we can figure out the star's distance, we would know its true brightness. Or, if we can somehow ascertain a star's absolute magnitude, we can compare it to its apparent magnitude and measure its distance.
The trick is knowing a star's intrinsic brightness. And, with a certain type of variable star, Cepheid variables, we can directly know its brightness by observing its variability period. Cepheid variables are giant stars that pulsate, growing larger and then smaller and then larger again over a period that can last many weeks. Conveniently, the variability period: the between successive minima (least brightness) or maxima (greatest brightness) depends on its intrinsic brightness. The brighter the Cepheid variable, the longer the variability period. As brightness relates directly to a star's luminosity, or energy output, these correlation between the variability period and brightness is called "The Period-Luminosity Relation."
This relationship was first established by a survey of Cepheid variables in the Small Magellanic Cloud, a satellite galaxy to the Milky Way approximately 160,000 light years away. It was noticed that the brighter Cepheid variables in the SMC had longer periods than the dimmer ones. As astronomers assumed that the stars within the SMC were at equal distances from Earth, they determined that the Cepheid variable's luminosity affected the star's variability period.*
Edwin Hubble, certainly not an obscure astronomer, measured the distances to Cepheid variables within the Andromeda Galaxy and, by extension, to the Andromeda Galaxy itself He knew the absolute magnitude by the amount of time they needed to cycle through one variability period. He then compared it with the star's apparent magnitude, discernible through his powerful telescope. He determined that the Andromeda Galaxy was about 900,000 light years from Earth. Though this measurement was enough to place the Andromeda Nebula, as it was then called, well outside the Milky Way Galaxy's boundaries, it was less than half the currently accepted value. Astronomers later learned that there are two classes of Cepheid variables, each of which has its own period-luminosity relation. Hubble used 'cluster variables,' which yielded an incorrect distance to the Andromeda Galaxy.
When the two classes were defined, and the measurement to the Andromeda Galaxy refined accordingly, astronomers realized that that splotch of light in the sky we had called the Andromeda Nebula was 2.2 million light years away! The most distant object one can observe with the unaided eye.
Today, we know that the Andromeda Galaxy is just one of billions of galaxies. And, by cosmological standards, Andromeda is so close it is almost the Milky Way Galaxy's Siamese twin. However, calculating Andromeda's distance served as a stepping stone toward the vast cosmic reaches well beyond: reaches that even today we haven't fully fathomed.
*We know the stars in the Small Magellanic Cloud are not equidistant from Earth. However, we can assume they are for the purposes of this observation. People in Los Angeles are not all precisely the same distance from us, but Los Angeles is far enough away that we can make a safe assumption that they are.
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