The Scale of Things

"Space," says Douglas Adams' The Hitchhiker's Guide to the Galaxy, "Is big.  Really big.  You just won't believe how vastly hugely mind-bogglingly big it is.  I mean, you might think it's a long walk down the road to the chemist, but that's just peanuts to space."

If we talk about "space" as being anything in the universe outside the atmosphere of Earth, then space is very, very big indeed.  How big?  The diameter of the Earth is 12 000 kilometers.  The distance from the Earth to the moon is 400 000 kilometers.  The diatance from the Earth to the sun is 150 million kilometers.  The diameter of the entire solar system, as measured by the orbit of Neptune, is about 8000 million kilometers.  The distance from here to the nearest star (other than our own sun) is 40 million million kilometers.  The distance from here to the center of our galaxy is about 250 000 million million kilometers.  The distance to the great nebula in Andromeda, the nearest galaxy believed to be similar to our own, is 15 million million million kilometers.  And the distance to the edge of the known universe is around 100 000 million million million kilometers.

To allow astronomers to use reasonably small numbers in conversation when they're talking about the distances between planets, they use a distance called the Astronomical Unit.  One Astronomical Unit, or A.U., is just the average distance between the Earth and the sun, which works out to 149 597 870 kilometers.  A beam of light would take 8-and-1/3 minutes to cross this distance, which, to put it another way, means that anything we see happening on the surface of the sun actually took place 8 minutes and 20 seconds ago.  In terms of this unit, Pluto's orbit is only 40 A.U.s from the sun, and Mercury orbits the sun a scant 0.4 A.U.s away from it.  However, the nearest star is still 260 000 A.U.s from us, which means that such a large unit is still too small to use to talk about the distances to nearby stars.

Distances to nearby stars are measured by using trigonometric parallax.  Put simply, if you measure where in the sky a star is in December, and then measure its position again in June, it will have shifted a tiny tiny bit in relation to distant background stars.  This is similar to the way the position of a nearby object seems to shift in relation to the background if you look at it with your left eye, then with your right.  This tiny movement is called the parallax angle.  Even for the closest stars, the parallax angle measures less than one arc-second (1/3600 of one degree), which is about the diameter of the small white disk that the star makes on a photographic plate if you take a picture of it with a really big telescope.  The distance a star would have to be away to have a parallax angle of only one arc-second is called a parsec, and works out to a whopping 206 265 A.U.s; a star whose parallax angle was 1/2 an arc-second would be two parsecs away.  Such small angles can be measured if done carefully, and have been measured for most of the stars believed to be nearby.  Compared with the planets of our own solar system, the stars are extremely distant and extremely far apart.

The stars are so far apart, in fact, that astronomers and science fiction authors alike prefer to talk about interstellar distances in terms of "light-years."  A light-year is the distance that a beam of light, uninterrupted and in empty space, would travel in a year -- which is about 9 470 000 000 000 (nine million million, four hundred seventy thousand million) kilometers.  A star with a parallax angle of one arc-second works out to be 3.262 light-years away.  In terms of this unit, the nearest star (Proxima Centauri) is only 4.22 light-years away, which is a reasonably low and palatable number.

To put it another way, though, this means that anything we see happening on or near Proxima Centauri actually happened 4.22 years ago.  When we look out at Proxima Centauri through a telescope, we are looking 4.22 years into the past.  When we look at the center of our own galaxy, we're looking 25 000 years into the past.  When we look at the nearest spiral-type galaxy to our own, we're looking one-and-a-half million years into the past.  Thus, when we say the edge of the visible universe is about 10 000 million light-years away, we are also, in a way, saying that the universe is at least 10 000 million years old.

And, worse, we're not really sure about some of these great distances.  Out past about eighty light-years, parallax angles become so small that they can't be measured reliably.  Distances to more distant stars are guessed at by a means known as the standard candle.  Put simply, if you are twice as far away from a light source, you'll receive exactly 1/4 as much light from it.  If we know that all of the class G2 main sequence stars in our local neighborhood emit about 4 x 1027 Joules of light energy per second, and we know how much light we're receiving from a distant G2 main sequence star, we can calculate how far away that star would have to be if it's behaving like our local G2 main-sequence stars by emitting 4 x 1027 Joules per second and if there isn't any gas or dust between ourselves and the star.  Both of these assumptions turn out not to be true in all cases.  And as if that weren't bad enough, there are many distant stars out there that have no analog among nearby stars: there isn't a star within the range of trigonometric parallax that's anything like Betelgeuse or Deneb or many of the stars in the globular clusters that orbit our galaxy.

To sum it up, then:

1 A.U. = 149 597 870.61 kilometers
1 light-year = 63 239.7 A.U.s = 9 460 530 000 000 kilometers
1 parsec = 3.261633 light-years = 206 264.806 A.U.s = 30 856 780 000 000 kilometers


A Danish translation of this webpage has been made by by EnGlobe. It's available at http://encarsglobe.com/blog/Omfanget-af-Ting.html.