How Far is ‘Far’ When it Comes to Stars

Distances to stars are huge. That should not surprise us. Space is big. Unbelievably big. How do we know the distances between our sun (a star) and those other stars in the night sky? 

Stellar nursery, Orion’s head, in infrared, taken by Spitzer Space Telescope, ASA,
JPL-Caltech, D. Barrado y Navascués (LAEFF-INTA) (PD).

Figuring out how to measure those distances was not easy. One of the first attempts to measure the distance to the stars involved a rather understandable, but horribly incorrect assumption. Dutch astronomer, Christiaan Huygens (1629–1695), gave us this early attempt. He believed that a star’s brightness in the night sky could tell us how far away it is, and he had used this theory to figure out our distance to the star Sirius. 

Huygens made a number of small holes in a screen and faced it towards the sun. Each hole was a different size and let in a different amount of sunlight. By examining the brightness of the sunlight coming through holes of varying sizes, he had found the hole where, when the sun shone through it, its brightness was closest to the intensity of Sirius. 

Huygens thought that all stars have the same brightness when viewed from the same distance. He was quite clever with this method of determining the distance to Sirius. Knowing that the brightness of a star diminishes as it gets farther away, Huygens had calculated that since the hole through which the Sun’s brightness equalled the brightness of Sirius was 1/27,664th the diameter of the Sun, Sirius would have to be 27,664 times as far away as the sun is from Earth. 

But he had made a critical mistake. He had incorrectly assumed that Sirius was equally bright as our sun. Today, we know that this bright, nighttime star is about 25 times as luminous as our sun. 

If Sirius is so much brighter than our own star (the Sun), that means we can’t measure a star’s distance just based on their brightness as measured from Earth. For example, some of the closest stars are invisible to the naked eye—the eye without the aid of a telescope. The seventh-brightest star in our night sky is called Rigel (at the foot of Orion) and rests some 773 light years away—more than 180 times as far as our closest neighbor, Proxima Centauri, which is invisible without the aid of a telescope. When placed side-by-side at the same distance, Rigel would be at least some 57,000 times brighter than our own sun. 

Actually, it wasn’t until we had an alternate method for determining distances to stars that we were able to tell how bright Sirius actually is. 

The First Big Step 

A more accurate way of measuring our distance to stars comes from how we measure long distances here on Earth. For instance, surveyors are able to tell the distance to the far side of a canyon, or to a remote mountain peak, without actually going there. They do this by measuring the direction of a distant object from two different locations a known distance apart. The line connecting the two points of measurement is called a “baseline.” For example, a surveyor may find that a distant mountain peak is due North from his current location. Then, the surveyor will measure out a distance to another site—say 20 meters away—and take a new reading on the mountain peak. Let us say the new direction is 10° West of due North. Knowing the length of the baseline—in this case, 20 meters—and the difference in angles—here, 10°—a surveyor can calculate the distance to the remote object using the principles of trigonometry. Their process is called “triangulation.” 

Once astronomers determined the distance from Earth to our sun with a fair degree of accuracy, they were able to determine the distance to the nearest stars using the same kind of triangulation. 

The baseline was huge—the entire diameter of Earth’s orbit, for example, from January 1 to July 1. As Earth orbits the sun, it moves from one side of the Solar System to the other, and  Earth’s position at January 1 is approximately 300 million kilometers (186 million miles) from its position on July 1. The line connecting those two positions is our baseline. 

GPS uses triangulation to locate us, too. Such triangulation works, though, only for objects within about 100 light years (the distance light can travel in 100 years, or about 588 trillion miles). Beyond 100 light years, it’s hard to get an accurate measurement. 

Beyond 100 light years, we take advantage of another phenomenon: that when we view the same star on January 1st and then on July 1st, it will appear to move because it’s being viewed from a different angle. This effect is called “parallax,” and it can help us measure stars that are farther away.

Parallax 

Try this out. Hold your pointer finger up in front of your face and close your left eye. Look at your finger and the objects across the room in the distance. Now, close your right eye, and open your left. Did your finger move? Your finger appears to have moved only because you are now looking at it from a different angle. 

This is the concept of parallax. It’s another way of looking at triangulation. In the example above, the baseline is the distance between your two eyes. 

Parallax is the same reason why, when driving along a country road and looking out the side window,, the telephone poles seem to whip past, while the distant hills seem to hardly move at all. 

When measuring parallax, we need to measure angles by more than just degrees. If we remember our high school math class, we recall that a circle is divided into 360 degrees. Each degree is divided into 60 minutes. And each minute of arc is divided into 60 seconds—similar to the time divisions on a clock. When a star seems to shift by one second of arc when viewed first in January (one one side of the sun) and then again in July (on the other side), the distance between the star and the middle of the baseline is said to be one parsec (parsec being short for “parallax second of arc”). Astronomers use this unit rather than light years. A parsec is 3.26 times the length of a light year. 

how we measure the distances to stars
Illustration of the use of parallax in astronomy. Produced for the Hubble Space
Telescope project, NASA, ESA, A.Feild, STScI (PD).
Spectroscopic Parallax 

First of all, so you’re not confused later,”Spectroscopic parallax” has nothing to do with triangulation or the parallax mentioned above. This term was invented merely because it involved figuring out the distance from the energy spectrum emitted from a star. Adding the word “parallax” was a bit of a misnomer, but the term has persisted and can be understood as “spectroscopic distance determination.”

Here’s how it works:

Once astronomers knew more about the types of stars and how they relate to one another, they were able to use the brightness of what are called “main sequence” stars to determine their distance. Main sequence stars are the “adults” of the stellar family before they grow into giants, or even supergiants, towards the end of their lives. This “adult” stage is where stars spend most of their lifetime. If we know the color of a main sequence star and other elements found in their light spectrum, we can judge their distance away based on the apparent brightness of that star. Color tells us a lot about a star, like how much energy the star is releasing. When we see an iron pulled out of a fire glow cherry red, for example, we know that it is hot, but not nearly as hot as the painfully scintillating glare of a bluish- white welder’s arc which can cut right through that iron. The color of a main sequence star tells us not only its surface temperature, but also something about its mass, diameter and natural brightness. Smaller stars burn more slowly, don’t get as hot and have a reddish hue. Bigger stars burn far more quickly, get far hotter and have a bluish hue. 

All main sequence stars of the same reddish hue have roughly the same natural brightness. So, a brighter, reddish main sequence star will be closer to Earth than a dimmer, reddish star. The same applies to all the other stars on the color scale. 

Where “triangulation” parallax works out to about 30 parsecs (~100 light years), spectroscopic parallax can work out as far as 10,000 parsecs. 

Back to Brightness 

There is another way to figure out very large distances—for example, the distances to other galaxies. There is one type of star that cycles in both brightness and color over time with such a consistent rhythm that astronomers have found a way to use this behavior to measure the distance to that star. These stars are called Cepheids. Scientists discovered that, as the star cycles from bright to dim to bright, the length of time between peaks of maximum brightness correlate with its intrinsic brightness. If we know the apparent brightness and the Cepheid period, we can determine the distance to the star. 

Cepheid stars helped us discover that stars exist beyond our galaxy. Before 1924, scientists thought the universe consisted of only our own Milky Way. This all changed when Edwin Hubble discovered a Cepheid star in the Andromeda nebula. 

how we measure the distances to stars
An artist’s impression of the planet orbiting Proxima Centauri. Notice the two
stars above and to the right of Proxima Centauri; these are the two main stars of the
Alpha Centauri triple star system. Illustration by ESO, M. Kornmesser (CC BY 4.0).

Hubble used this star to determine the distance to the Andromeda nebula, and it appeared to lie outside our galaxy— proving that the Milky Way was not the only galaxy in the universe. 

Andromeda was not merely a cloud of interstellar gas; it was its own galaxy with billions of stars, very much like the Milky Way. It turned out, many nebulas already known to astronomers were actually separate galaxies! The distance to Andromeda is about 778,000 parsecs, or 778 kiloparsecs (2.54 million light years) away. Andromeda may be the closest large galaxy to our own Milky Way galaxy, but our two large galaxies are like tiny drops in an ocean of a universe filled with billions of galaxies spanning 93 billion light years. 

how we measure the distances to stars
Andromeda galaxy (M31), our sister galaxy with which our own Milky Way
galaxy will merge in the next few billion years. Photo by Adam Evans (CC BY 2.0).

Scientists have refined and added to these three methods of measuring the distances to stars numerous times—too many to describe in this short article. We’ve come a long way in understanding the size of our universe since Huygens’s experiments with Sirius. But even today, we have a great deal more to learn about stars and the universe. 

Peter Thompson an Astronomy enthusiast. Self-taught, he is constantly studying and researching this beautiful science. He shares his journey on Astronomy for Beginners.

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