by Sarah Scoles

...till now.

How do we know how far away stuff in the universe is? There are very few things in space to which we can travel. It's not like we can say, "It took us X minutes going Y miles per hour to get to this quasar, so this quasar is Z miles away."

If all we get is light from objects in space, how do we know how far that light traveled to get to us?

This problem is one of the oldest in astronomy, although it wasn't always thought of as a problem. Until the 1500s, the concept of "space" didn't exist, as we currently think of it--people believed that there were "celestial spheres" surrounding the Earth, and that while the planets lived inside their own individual spheres, the stars all lived together inside a single sphere. The stars were thus believed to be located at a single distance from the Earth's surface (not very far above it).

Ah, the beautiful night sky (Credit: Wikipedia).



Later, in a high-tempered controversy known as The Great Debate, astronomers argued about whether "fuzzy" objects in space, which they only just had telescopes strong enough to discover, were nebulae or galaxies outside our own galaxy ("outside" the Milky Way being a brand new idea).

More recently, quasars, which are some of the most energetic objects in the universe, were thought to be weird stars within our own galaxy, before astronomers found that they were actually associated with very distant galaxies.

Since all we have to go on is an object's light, the only way for us to know about its distance is through its light. And that shouldn't be too hard, right? After all, we know how light dims as it travels. If you are 2 feet away from a lamp, it is 4 times as dim as it would be if you were 1 foot away (this is called the Inverse-Square Law). If you move 4 feet away, the lamp becomes 16 times as dim.

So we should be able to backtrack and say, "So if this star looks this bright to me, but it's actually this bright, its light must have traveled 10 light-years in order to dim this much."

The fundamental problem with determining distance is that, in general, you don't know how bright something would be if you were standing next to it...unless you're standing next to it.

A highly luminous star that is 1,000 light-years away could appear, from Earth, the same brightness as a dim star 100 light-years away. Light from an energetic galaxy, by virtue of how bright it appears to us, could be mistaken for a much-closer star.

So how do we determine how far away things are in space?

Astronomers use a set of methods collectively called the cosmic distance ladder.

I'm not making this up (Credit: David Darling).



A set of methods, rather than a single method, must be used because different tricks work for nearby objects than work for distant objects, although you first have to determine the distances to nearby objects before you can determine the distance to distant objects, which is where the ladder metaphor comes into play. But I think of the cosmic distance ladder as a toolbox: you can pick up a bolt and a washer, and you can finger-tighten them into place for a while, but eventually you'll have to use a wrench.

In the same way, we can directly determine distance up to a certain point before we have to resort to indirect methods. Inside the solar system, we can shoot radar and see how long the beam takes to get back to us. For nearby stars, the direct method takes advantage of the concept of parallax, or how the position of an object shift in the sky (from our perspective) due to our motion around the Sun. The less an object's position shifts, the farther away it is. When you're looking out the passenger window of a car, the road's shoulder is flying by you, but the mountain peak moves slowly across your view. If we can measure the angle by which an object appears to move due to our motion, we can determine how far away it is--this is parallax.

Paint (Credit: Richard Pogge).



But after not too far (at least in comparison to the scale of the universe), the angles become too small for us to measure.

Well, shoot. What do we do then?

That's whatare for. Standard candles are classes of celestial objects that have some known intrinsic luminosity (or at least a well-guessed-at intrinsic luminosity). If we know how luminous they are intrinsically, and we know how bright they appear to us, we can figure out how far their light has traveled, and thus how far away they are.Some standard candles are

Type IA Supernovae , which are the result of a white dwarf star's demise, and which appear always to explode with the same amount of energy.

, which are the result of a white dwarf star's demise, and which appear always to explode with the same amount of energy. Cepheid Variable Stars , which are much more massive (10x) and luminous (100,000x) than the Sun, and whose pulse speed is related in a predictable way to luminosity.

, which are much more massive (10x) and luminous (100,000x) than the Sun, and whose pulse speed is related in a predictable way to luminosity. RR Lyrae Variable Stars, which are less massive (0.75x) and only slightly more luminous (50x) than the Sun, and whose pulse speed is also related to luminosity.

So if we can measure the pulse speed, we can determine how much light the variable stars are actually putting out, versus what we are receiving, and then we can figure out the distance.

At extragalactic distances, when looking at other galaxies, we use the Tully-Fisher Relation, which allows us to translate the velocity due to the galaxy's rotation into an intrinsic luminosity.

There are, of course, other tools in the toolbox / rungs on the ladder, but these are some "popular" ones.



But, really, is it that simple? Can you really change an observable into an infer-able using an equation? Is the equation perfect and true every time?

Well, the equations don't always apply to all types of IA supernovae or variable stars. These standard candles are not as standard as once thought, and their properties (specifically, how many heavier elements they have inside) can vary, which would cause their luminosity to be different from what is expected.

So if you're inferring a distance from an inferred luminosity from an empirical measurement, the result must be subject to a lot of uncertainty, since it's two steps from a direct measurement.

What if one of those steps could be removed?

That's what Fritz Benedict and his team did, by using sensitive instruments aboard the Hubble Space Telescope--called the Fine Guidance Sensors--to measure the parallaxes of seven variable stars: five RR Lyrae variables and two Cepheids.

Actually measuring the distance to these stars decreases the uncertainty in their distances. Solidly known distances to these stars allow us to better determine how far away their homes, places like globular clusters and the Large Magellanic Cloud, are (calculations done in the paper cited below).

What science teaches us is that there is probably a joke book bigger than this (Credit: The Laugh Factory).





Who cares?

Figuring out how far away things are has, historically, led us to change our conception of the universe as a whole. It's always been bigger than we thought; things were always farther away than we thought at first. When we discovered that, we had to increase our conception of the size of the universe, and thus decrease our significance within it.

If no one cared about distances, we would still think that all stars were shiny stickers on a glassy sphere around Earth, or that our galaxy was The Galaxy, or that the universe is static and not flying "outward," whatever "outward" means in this context.

The point is, knowing anything about what objects are is fundamentally related to knowing where they are, since all we we can learn about objects is what we observe from afar. And in order to take the 'afar' part into account, and to learn what the objects actually are like and not just what they look like, we have to know how far 'afar' really is.

REFERENCES