“Right! What’s a Parsec?”

For those who do not recognize the reference being made in the title, it is to an old Bill Cosby comedy routine depicting a conversation between God and Noah. During the course of the conversation, God provides the dimensions of the ark He wants built in cubits, prompting a somewhat incredulous Noah to say, “Right! What’s a cubit?”

Understanding the units used in a given measurement is pretty important business, and one of the most commonly-used units in astronomy and astrophysics is the parsec. A parsec is roughly 3.26 light-years, which translates to about 30.9 trillion kilometers or 19.2 trillion miles. While it is fairly common knowledge that a light-year is defined as the distance light traverses in one year, the origins of the parsec are considerably less well-known. Let’s address that here.

The term “parsec” is thought to have been introduced by British astronomer Herbert Hall Turner in 1913. The parsec is defined as the distance which would induce an annual heliocentric parallax shift of one arc second.

“Right!”

Okay, perhaps I should back up a bit and define some parts of that definition.

Parallax is a key component of the cosmic distance ladder, the chain of techniques used to measure distances on astronomic scales. No one technique in the distance ladder is effective over all distance scales, but overlap between the distance scales over which each technique is valid provides continuity. Parallax provides effective measurements of distances out to a range of about 1,600 light years. Beyond that, the shift becomes too minuscule to be accurately measured, although the ESA’s Gaia mission (just launched on December 19) should extend that effective range ten-fold. Measurements of even greater distances are largely dependent upon fixed relationships between the luminosity and periodicity of variable stars. (For more about the discovery of such techniques, see my earlier article “Henrietta Leavitte and the Cepheid Variables”.)

Conceptually, parallax is pretty straightforward to understand, since it can be related to everyday experience. To illustrate, let’s do a simple experiment. Close your right eye and hold your thumb out in front of you. Note the position of your thumb relative to some distant landmark. Now, leaving your thumb unmoved, open your right eye and close your left eye. Your thumb will appear to have made a jump to the left relative to the “fixed” background. Of course, you know that your thumb hasn’t budged, but is merely being viewed from a slightly different perspective as seen from each eye. If we wanted to get down to brass tacks, we could measure the angle that the thumb appears to have shifted, measure the distance between our eyes, and use a simple bit of trigonometry to measure the distance to our thumb.

Image from Wikipedia. Created by Srain at English Wikipedia.

Astronomers can use the same idea to measure the distances to stars, using even more distant stars as a relatively fixed background against which they can measure parallax shift. Of course, to get a measurable shift in angle, they need as long of a baseline (corresponding to the distance between your eyes in the example given earlier) as they can get. The best they can do is to use the diameter of the Earth’s orbit around the sun. Make a measurement. (In other words, snap a photo of the star in question through a telescope.) Wait six months. Make another measurement.  Apply some trig, knowing the diameter of the Earth’s orbit (about 300 million kilometers), and viola!  We have the distance to the star under investigation.  (I won’t bother going into how those calculations are done here. That can be seen in detail in the Wikipedia article on parsec.)

Nicolaus Copernicus first came up with this idea, but he didn’t have access to the technology to make it happen.  The first astronomical parallax measurement was made in 1838 by Friedrich Wilhelm Bessel (of Bessel function fame).

Well, then.  Now that we have the definition of parallax out of the way, let’s get on to arc second. This is merely a unit of angular measurement.  A circle can be divided into 360 degrees.  Each degree can then be subdivided into 60 arc minutes. An arc second is simply 1/60th of an arc minute, or 1/3600th of a degree.

Now we have all of the pieces in place to understand what a parsec is. Imagine a hypothetical star out there whose distance is just right to cause a parallax displace of one arc second.  The distance to that imaginary star would be one parsec.

Right? Right.

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About Glen Mark Martin

MCSE-Messaging. Exchange Administrator at the University of Texas at Austin. Unrepentant armchair physicist.
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