General Astronomy

# Distance Units in Astronomy

“You’ve never heard of the Millennium Falcon?…It’s the ship that made the Kessel Run in less than twelve parsecs.”

The quote, as any Star Wars fan would know, is from Han Solo boasting about the speed of his ship to Obi Wan Kenobi in the Mos Eisley Cantina. But you may have wondered what a parsec is. As we’ll see, the most famous smuggler in the galaxy is actually unit confused!

In astronomy, we typically work with objects that are enormous in size compared to things we experience in our everyday life. Meters work well for things we might measure on Earth, but aren’t suited for measuring the distance to a star or the size of a galaxy—the numbers become too large and cumbersome to work with. There are a couple of commonly used measurements of distance in astronomy: the astronomical unit (AU or au), the light year, and the parsec (pc).

The astronomical unit is roughly the distance from the Earth to the Sun. This is about 150 million kilometers (93 million miles). The light-year is the distance that light travels over a period of one year in a vacuum, which is about 9 trillion kilometers (6 trillion miles). It is NOT a measurement of time. Light years are more often used in popular science than in professional research.

The last common unit of length is the parsec, which is frequently used in professional astronomy. It takes a little understanding of parallax to see how it is defined. Parallax is the apparent change in position of an object when viewed from two different lines of sight. This concept can be easily demonstrated by holding out your thumb at arm’s length and looking at it through your right eye only, and then your left eye only. You will notice that your thumb appears to change its position with respect to a distant background (see diagram below). In fact, if you did this with an object at various distances, you will notice that its apparent shift in position decreases with distance. You can start to see how an astronomer might use this to determine distances.

If we observed a star from two different points on Earth’s orbit we would see an apparent shift in its position with respect to other more distance background stars. This shift is maximized if we make two observations six months apart, since this would correspond to viewing a star from opposite sides of Earth’s orbit. One half of this apparent shift is called the parallax angle. The units used are degrees with a sixtieth of a degree called an arcminute and a sixtieth of an arcminute an arcsecond. For example:

1° 34’ 3”

This tells us that an object has a parallax angle of one degree, 34 arcminutes, and 3 arcseconds. We are now ready to understand the definition of a parsec.

The diagram shows the position of Earth six months apart on its orbit, along with corresponding lines of sight to a nearby star. We can imagine building a right triangle with one leg as the Earth-Sun distance, one as the distance of the star from our Sun, and the hypotenuse. Using a little bit of trigonometry, it can be shown that:

Where theta is the parallax angle (half the total shift in position). Since the angles involved are small, we can approximate the tangent of theta as simply theta. Finally, we define the parsec as the distance to an object with a parallax angle of one arcsecond (1”). This distance is about 3.26 light years. So, with some unit conversion, we can relate the distance to an object and its parallax angle as:

Where “d” is in parsecs and theta in arcseconds. So, it appears Han Solo is confusing a unit of distance for a unit of time (but see this).

The nearest star, Proxima Centauri, is 4.24 pc away, which means it has a parallax angle of less than 1 arcsecond. Note that the human eye has an angular resolution of only 1 arcminute, so we are unable to detect this apparent shift without the aid of a telescope. Below is a table of distances to various astronomical objects from the Sun:

 Object Astronomical Units (AU) Light Years Parsecs (pc) Earth 1 1.581 x 10-5 4.848 x 10-6 Jupiter 5.203 8.227 x 10-5 2.522 x 10-5 Pluto 39.482 6.243 x 10-4 1.914 x 10-4 Polaris (North Star) 2.801 x 107 433 133 Proxima Centauri 268,136.44 4.24 1.30

Using parallax, astronomers have been able to map out numerous objects in the Milky Way galaxy. The European Space Agency launched the satellite Hipparcos in 1989. Over its three and a half year mission, it measured the motion and parallax of over 100,000 stars in our galaxy with high precision (~2 milliarcsec). Another 2.5 million stars were added with lesser precision by 2000. The successor to Hipparcos, Gaia, was launched in 2013 and can measure parallax with an even higher precision in the microarcsecond range. It will be able to generate a 3-D map of over 1 billion objects in the Milky Way including stars, exoplanets, and even asteroids in our solar system.