Astronomical Distances

April 8th, 2009

I was reading some internet forum recently where someone suggested that since parsecs were based on local geometry (how stars appear to move in the sky because of the Earth’s own motion around the sun), no one would use the unit more generally.   Except that astronomers, do, all the time.   Sometimes movie directors do, too (look about 3 minutes in):

(For more on the “Kessel Run controversy”, and how Star Wars apologists justify the ridiculous error, confusing parsecs with a time.)

Anyway, astronomers, and people in general, like to use numbers between one and ten when possible, or into the hundreds.   So, you pick your distance units appropriately.   Here on Earth, we have miles and kilometers which work pretty well for walks, runs, and driving around a city or between cities.

In the solar system, it is customary to use astronomical units, or AUs.   An AU is the distance from the Earth to the Sun, approximately 150 million kilometers or 93 million miles.

Lightspeed units are sometimes used, too, and certainly for distances to other stars.   We use the relationship between time, rate (speed), and distance, so that distance is the speed times the time.   The speed of light in vacuum is some 300,000 km/s.   It’s around a lightsecond to the moon, a bit over eight light minutes to the sun (an AU), and light travels through the solar system in hours.   We could express a light-year in terms of miles (about six trillion) or kilometers (over 9 trillion), but you get a silly large number that people can only relate to in terms of the national debt.   Still, often science journalists do this because they assume the public knows miles and not light years, and only stick with light years for distances to the most distant quasars and galaxies.   Nearby stars are as close as 4 light-years away, and it is something like 100,000 light years across the Milky Way galaxy, and a couple of million light years to the Andromeda galaxy.   To keep the distances expressible in terms of numbers between one and thousand, we go to kilo light-years (1000 light-years) and mega light-years (a million light-years).   But astronomers tend not to use these units so much.   We prefer the parsec, actually.

So, about the parsec.   A parsec is a “parallax second.”   A star that moves through an angle of one arcsecond as the Earth moves one astronomical unit is at a distance of one parsec.   That’s about 206265 AUs, or about three and a quarter light years.   The equation relating the parallax p in arcseconds (the angle that a star appears to move due to the Earth’s motion across one AU) to distance in parsecs is simple: d = 1/p.   So, the distances to the closest stars first came from measuring parallax angles, and knowing the parallax immediately gives a distance.   Going to larger distances, astronomers use Kpc (kiloparsecs), Mpc (megaparsecs), and even Gpc (Gigaparsecs or billions of parsecs) for cosmologically large distances.

The terminology and scales are important to get right and understand.   It’s bad enough to hear about aliens coming from “another galaxy” when “another star system” is plenty far enough away, but it’s also just as crazy when the distances make no sense.   Knowing how far away stars and galaxies are helps avoid the problem above.   Also, translating things into light-years is a good reminder about how long it takes light to travel the same distance, letting you realize that when you look into space you look back into time, as well as the limit on travel time from relativity.

If you’re writing this stuff, and it seems confusing, best probably to stick with light-years which average readers have some intuitive grasp of.   Also easy then to talk about spaceship speeds in terms of fractions of lightspeed.   You only have to apply relativitity to figure out how long the trip seems to take from the perspective of someone onboard the ship (and until you get above half lightspeed it isn’t a very big factor), but it is easy from an external observer.   A ship traveling at one percent of light speed will take a hundred years to go one light-year, for instance.   But please use parsecs if you want to!   Astronomers do, and it sounds likes such a cool word that George Lucas used it, too, if incorrectly.

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