Friday, August 2, 2013

Science Clock Series: Part VIII

Today's number comes from astronomy, and is given by:

\[\approx\text{distance to center of Milky Way (kpc)}\]
This one is pretty straight forward, though it requires a fair amount of exposition. The Milky Way, of course, is the galaxy within which we all live. As far as we can tell from our inside perspective, it is a barred spiral galaxy, like many others throughout the universe. 

The letters "kpc" stand for "kiloparsec," an astronomical unit of distance. "Kilo" is the SI prefix for a thousand, so we're dealing with a thousand parsecs. Just what is a parsec, though? A parsec is defined as the distance at which an object has an astronomical parallax of one arcsecond. Parallax is the way objects appear to move when you look at them from two different positions, when compared to even more distant objects.

(To see this effect, close one eye and line up your thumb at arm's length with an object across the room. Now switch eyes, and notice how your thumb is no longer in line with the object. This is the reason we have two eyes, in fact; our brain takes the slight differences in the angles between them and interprets it as distance. If you can measure the parallax of an astronomical object, you can mathematically work out its distance in a similar manner.)

An arcsecond, as I've discussed here before on this blog, is a unit of angular measurement (and a very small one at that). For comparison, there are 60 arcseconds per arcminute, and the full Moon (and Sun) are about 30 arcminutes in angular diameter. Thus an arcsecond is about 1/1800 the width of the full Moon.

This is a pretty small amount. And yet, there are no stars within 1 parsec of the Sun, so every star in the sky has a parallax smaller than 1 arcsecond. This is much, much too small to be noticed with the naked eye, and it wasn't until 1838 that the first measurement of a star's parallax was made by the German astronomer Friedrich Bessel. (The closest star to the Sun, Proxima Centauri, is 1.3009 parsecs away, or 4.243 light-years.)

Anway, that's how you define a parsec, but what does it mean in units your or I might be more familiar with? When you do the math a parsec works out to be approximately 3.26 light-years, or 30.9 trillion kilometers, or 19.2 trillion miles. A kiloparsec, then, is a massive 30.9 quadrillion kilometers, or 19.2 quadrillion miles, or 3,260 light-years.

This...is a long way. It is simply too large a distance for me to truly comprehend it. And yet we need such large units to meaningfully talk about our galaxy, which is around 31-37 kiloparsecs across (100,000-120,000 light-years). It's hard to put a solid number on it since the galaxy has no hard edge, but rather fades out around the edges. This gives it a radius of about 15-18 kiloparsecs, and as far as we can tell, the Solar System is located between about 8.0 and 8.7 kiloparsecs from the center of the galaxy (roughly 26,000 to 28,000 light-years), putting it about halfway out, nestled between two of the Milky Way's spiral arms.

Check back next time for a number from chemistry! Click here to jump directly to it.

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