Wednesday, February 15, 2012

Distance Units in Astronomy

Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space. 
- Douglas Adams, The Hitchhiker's Guide to the Galaxy
I've had a few posts already concerning astronomy. Before I go on with more astronomy posts, I figure I'd have a sort of introductory post were I describe the different distance scales and units we use in astronomy. Not only should this be an informative post, it should also serve as a useful thing to link back to whenever I mention some of the terminology.

Here on Earth we use two main systems to measure distances. We have the English systems (inches, feet, miles) used in the United States, and the metric system (centimeters, meters, kilometers) used everywhere else. The English system is archaic, with odd conversions: 12 inches is one feet, but 5280 feet is one mile. The metric system is more modern and based on factors of ten, so you can always convert units quite easily, 1 meter = 100 centimeters = 1000 millimeters, etc. I grew up with the English system, but I like the simplicity of the metric and that's what we generally use in the sciences. However, things in astronomy tend to be very far apart and so we've ended up making some odd units.

The Astronomical Unit
When measuring scales in the solar system (or other planetary systems) it is best to use astronomical units (AU). The astronomical unit is defined as the average distance between the Earth and the Sun and corresponds to about 150 million kilometers (93 million miles). Now, we still use kilometers in some cases. For example, the distance between the Earth and the Moon is only about 384,000 kilometers or 0.00257 AU. Such 'small' distances are best kept in kilometers. Note that even though I say small, that's actually a considerable distance: the Earth's radius is about 6,731 km (more on this later).
Planetary distances in our solar system (and others) are best expressed in AU. For example, Mars is at about 1.5 AU and Jupiter is at about 5 AU. The outermost planet in our solar system, Neptune, is at about 30 AU. The gas and dust disk surrounding the nearby young star V4046 Sgr extends out to a radius of 370 AU, more than 10 times the distance between the Sun and Neptune.

The Lightyear
A lightyear is the distance that light travels in one year. Unfortunately, because it has 'year' in the name, most people think it is a unit of time. Light travels at a constant speed of 300,000 kilometers each second (186,000 miles a second). This is extremely fast and is the fastest speed that can be attained in our universe. You can calculate how much distance light would cover in one year and use that as a natural unit of distance. This corresponds to about 9,460,730,472,581 km (nearly 6 trillion miles). This is a huge distance, but stars are even farther than that: the nearest star, Proxima Centauri, is about 40,000,000,000,000 km (25 trillion miles), or more easily: 4.2 lightyears. The Galaxy itself spans 100,000 lightyears. The lightyear is then one of the more natural units to consider when talking about interstellar distances. However, there is another widely used unit to consider.

The Parsec
While the lightyear is easy to grasp among the general public, astronomers tend to prefer the parsec. It's definition involves the concept of parallax. When you look at something, you are using both eyes to perceive it and judge its distance. If you alternate closing one eye and opening the other, you will see the object appear to shift. How great the shift is depends on the distance between you and the object. We can apply this to astronomy as well. However, stars are so distant we have to use a wider baseline- our eyes are not separated widely enough. What we actually use in astronomy is the orbit of the Earth. In the simplest case, we take two images spaced half a year apart and compare them. Nearby stars will have shifted with respect to more distant background stars. Half of this angle is the parallax angle and is actually used to determine distances with simple geometry. One of my friends runs another astronomy blog tackling a single word in astronomy per week; you can check out his explanation of parallax here.

You can express angles in two ways: radians, as in 2pi radians in a circle, or degrees, as in 360 degrees in a circle. When you make the approximation that tan x or sin x is approximately x (for small values of x), you are assuming that x is expressed in radians. Parallax angles are small in astronomy, so this is perfectly valid, however we prefer to use arcseconds (1/3600 of a degree). How many arcseconds are there in 1 radian? Easy: 3600 times 360/2pi, or  206,265. So if we want a distance that corresponds to a parallax angle of 1 arcsecond as measured from the Earth, whose orbit is 1 AU, this distance must be 206,265 AU. This is the definition of the parsec, or pc: one parsec is 206,265 AU.

The parsec is widely used in stellar astronomy. The nearest star is about 1.3 parsecs, so this is a slightly more natural unit for stellar distances than the light year (1pc = 3.26 light-years). For one of my research projects, I set an outer limit of 100 pc and for another, 150 pc. However, the parsec is sometimes not enough to express distances so we turn to kiloparsecs (kpc) and megaparsecs (Mpc) for even larger distances. These are, as they sound, equivalent to 1,000 and 1,000,000 parsecs, respectively. The kiloparsec is useful for measuring large scales within our own galaxy; for example, the center of our galaxy is just 8 kpc away. Megaparsecs are more useful for distant galaxies; however, for very distant galaxies we tend to use another way to express distances- redshift.

Okay, so redshift isn't truly a unit of distance, but I'll describe it here. Hot gas emits lights at very particular wavelengths, depending on what gas it is. When it's cold, it absorbs light at exactly those wavelengths, too. When we look at stars and galaxies we see emission or absorption features corresponding to the gases present. However, sometimes these features are not at the right wavelengths. The phenomenon behind this is Doppler shift: when something is moving towards (or away from) you, the sound or light will get shifted in frequency. This works on the Earth as well, for example when you hear sirens speed past you- the pitch of the siren changes. The same is true for light in astronomy. Stars and galaxies moving towards us have gas features, known as spectral lines, shifted to shorter, or bluer wavelengths. The opposite is true for objects moving away from us- the lines are shifted to the red, or redshifted.

Within our Galaxy, this can be used to track the velocity of stars, but in general it doesn't tell us anything about distance. However, the situation is different for far away galaxies. It turns out that all but the closest galaxies are moving away from us. And when you measure distances through other ways (perhaps I'll describe these on some future post), you realize that the farther the galaxy, the greater the redshift or in other words- the faster it is moving away from us. Using these sorts of measurements, astronomers have determined that the universe is expanding in all directions. The result of that is exactly what we expect: galaxies are moving away from each other and the farther away a galaxy is, the faster it is moving. This is Hubble's law, which can be used to estimate distances:
d = cz/H0

Here z is the redshift, c is the speed of light, and H0 is the Hubble constant, which has a value of about 72 km/s/Mpc. The units of H0 are weird, but if you look closely the km/s cancels out from the speed of light and, since redshift has no units, all that's left is Mpc (megaparsecs). Because the speed of light and the Hubble constant are just conversion factors, one can just use redshift to describe distances to other galaxies. Things are a bit trickier in actual practice because of cosmological effects, but this is enough to get a handle on what astronomers mean when they refer to the redshift of galaxies.

Other Distance Units
The AU, the lightyear, and the parsec are the most commonly used distance estimates in stellar astronomy and redshifts are almost mandatory when dealing with other galaxies. However, you can still create useful units by comparing objects that we know in a lot of detail. Here are a few that are commonly used in stellar and planetary astrophysics.

Solar & Jupiter Radii
When measuring other stars it is sometimes useful to have a good comparison. In general, we use the Sun for all such comparisons. The Sun's radius is 695,500 km (432,450 miles). Sometimes, solar radii are useful in describing binary systems. For example, the binary system V4046 Sgr is comprised of two sun-like star that are just 9 solar radii apart. That's really close! Note that 1 AU is about 215 solar radii. For extrasolar planets or very low mass stars we use the radius of Jupiter (69,173 km) as a comparison. Note that this is about 1/10th the radius of the Sun. By using these units we get an easy to understand comparison between objects we know about.

Earth Radii
Remember I mentioned the separation between the Earth and the Moon is on average 384,000 km? One way to express this is to make use of Earth radius (6,731 km) as a unit. This means the separation between Earth and the Moon is on average about 63 Earth radii. Planetary radii (usually either Earth or Jupiter) are useful when studying extrasolar planets, as they give us a readily comparable size estimate. For reference, 1 solar radii ~ 10 Jupiter radii ~ 100 Earth radii. That's a nice relationship to keep in mind.

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