How far away are you?

“It is a mistake to look too far ahead. Only one link in the chain of destiny can be handled at a time.” –Winston Churchill

And yet, when you look out, you can’t help but wonder how far away these points of light in the sky are.

Some things are easy. Our Solar System, for instance. Just by knowing Newton’s Laws of gravity and observing the positions of the planets over time, we can determine the distances to any of the planets, our Moon, or our Sun to incredible (better than 99.999%) accuracy.

But what about the stars? They’re much, much farther away than anything in our Solar System, and they can be awfully deceptive. After all, take a look at these two famous stars from the Southern Hemisphere: alpha centauri and beta centauri!

Alpha Centauri is one of the closest stars to us, at a distance of only 4.37 light years. There’s a very small uncertainty on that, too. Why? Because it’s close enough to measure by the most reliable method of all: parallax!

As the Earth orbits the Sun, its position changes by about 300,000,000 km over the span of six months, as we move to the other side of the Sun. While most objects in the sky are very, very far away, the closer ones will appear to change position by a very small (but measurable) amount. The angle the position appears to change by corresponds directly to the distance an object is away from you.

(And you can read a further explanation here.)

But what about that star almost as bright, that’s very close to it: Beta Centauri?

Beta Centauri is very, very strange! Yes, it’s blue, but there are actually two stars there. Moreover, they’re both blue giants! And what’s more, is that Beta Centauri is about 350 light years away!

But when something’s too far away to measure a parallax well, we really get stuck! We can’t measure a distance directly; we have to estimate it. And the more interesting (and unique) an object is, the harder it is to figure out its distance!

Take Betelgeuse, for instance. Distance estimates range from 180 to 900 light years, a 400% difference!

And what’s more, is if you use two different methods of estimating the distance to Betelgeuse, you’d get two different distances! In other words, astronomical distances are easy to get right in terms of a “ballpark” figure, but to get it exactly right with complete confidence is a very, very rare thing. Why? Because the estimates we can come up with are only true on average. In reality, there’s a lot of natural variation in these objects.

It’s kind of like looking at a picture of a human, “knowing” that humans are six feet tall, and then figuring out how far away that human is. Only, of course, not all humans are six feet tall!

This same problem for stars and humans affect even entire galaxies!

Which brings me to a spectacular pair of galaxies: The Antennae Galaxies, known as NGC 4038 and NGC 4039. These are two of the closest merging galaxies we have, at a distance of just 45 million light years. But if you had asked me their distance 10 years ago, I would’ve told you 65 million light years!

Why, as ESPN’s Gregg Easterbrook notes, were we off by so much?

Because the only reliable way to measure the distance to a galaxy is to look at the individual stars in it, measure their brightness, and figure out (based on the brightness of identical, known stars) how far away they are. Only with the new camera on the Hubble Space Telescope were we able to do that for the first time!

In other words, that old 65 million light-year estimate had a huge uncertainty!

It turns out that many of our great astronomical measurements have huge uncertainties, and distances are some of the toughest to get right!

Even Andromeda, the closest big galaxy to us, has undergone a major revision! We used to think it was 500,000 light years away, based on Cepheid stars. Then we discovered a new type of Cepheid, and the distance was suddenly measured in the millions of light years, not the hundred thousands. And — using the same technique of red giant measurements we just used for the Antennae Galaxies — we now know that Andromeda is 2.54 million light years away, with an uncertainty of less than 3%.

The moral of the story? Coming up with an estimate is easy. Coming up with an accurate estimate, where you understand and are honest about your uncertainties, is much, much more difficult.

Want to start some trouble along these lines? Ask an astronomer how many stars there are in the Milky Way galaxy…