This made Cepheids useful as standard yardsticks. If all stars were the same brightness, then it would be easy to tell how far they all were; the dimmer ones must be further away, in direct accordance with the inverse square law—but they aren’t. It’s easy to determine a star’s apparent brightness, and if you can find its real, or intrinsic, brightness, you can determine its distance, or vice versa. By timing a Cepheid’s peaks, you could determine its intrinsic brightness, and therefore its distance.
Then, in 1923, Hubble followed up his observations of the Andromeda Galaxy by discovering a Cepheid variable in it. After tracking its brightness for some time, he determined that the Cepheid, and M31, were some 700,000 light-years away. That was considerably larger than the size of the Milky Way, and confirmed that M31 was a galaxy, separate from the Milky Way. Later, it was discovered that Cepheids come in different varieties, each with its own distinct relationship between period and luminosity. The Cepheid in M31 was intrinsically brighter than previously thought, and in order to appear as dim as it did, it had to be even further away.
The distance to M31, even now, isn’t precisely known, but based on the best available figures, it’s about 2.5 million light-years away. Since our estimated distance from the center of the Milky Way galaxy is only about 25,000 light-years, or just about 1 percent as great a distance, M31 is pretty much in the same direction in the sky, no matter where we are in the Milky Way. It therefore serves as a convenient and usable beacon for plotting the first main leg of our trip.
From the center of the Milky Way, M31 is probably not visible—it’s lost in the glare of the dense galactic nucleus. We have to go “up,” out of the plane of the Milky Way, in order to find it. M31, as it happens, is a bit south of the galactic plane, by about 20 degrees. From the center, we won’t necessarily know which way is south, so we’ll have to guess. If we guess correctly, then after travelling about 1,000 light-years or so, we’ll have cleared the nucleus by enough to see M31.
If, after travelling that 1,000 light-years, we don’t see M31, we have to conclude we went up on the north or “wrong” side, and sink back down to the south. By the time we get to the right point, we’ll have travelled 3,000 light-years total distance. Since there’s a 50-50 chance of going either way, the average distance it takes us, just to find our first beacon, is 2,000 light-years.
Step 1 Distance: 2,000 light-years
Step 1 Time: About a week
What do we do once we see M31? Here, we take advantage of M31’s great distance. If we head out of the galactic disc from Earth toward the south galactic pole, M31 is in the direction of Cassiopeia and Andromeda, and the center of the Milky Way is out to our left—”at 9 o’clock,” so to speak.
But if M31 is so far away, then it will be in the same direction as seen from just above the Milky Way nucleus, too. It will no longer be in the direction of Cassiopeia and Andromeda—those constellations only exist when we observe from the Earth—but they will be in that same direction relative to the Milky Way. If we continue to call the direction of M31 12 o’clock, then from the center of the Milky Way, we should travel toward 3 o’clock to get toward home. (See Figure 1.) It isn’t exactly at 3 o’clock, but such a precision is sufficient to get reasonably close. And since home is about 25,000 light-years from the center, that’s how far we’ll travel in our second step.
Step 2 Distance: 25,000 light-years
Step 2 Time: About 3 months
Assuming that our current understanding of the galaxy is correct, we should now be within about 2,000 light-years of home. But that is still far too great a distance to pick out the Sun. The Sun has an absolute magnitude of about 4.8, which means that as seen from a distance of 10 parsecs, or 32.6 light-years, the Sun would appear as a star of magnitude 4.8. Stars of that magnitude are fairly dim and cannot even be seen from many city skies.
But that’s as seen from 32.6 light-years away. Two thousand light-years is about 61.3 times further away, and leaves the Sun looking 61.3 squared, or 3,760, times dimmer. A dimming of 3,760 times is equivalent to an increase in magnitude of about 9.0 (recall that magnitude increases as brightness decreases), so from that great distance, the Sun looks like a star of magnitude 4.8 plus 9.0, or 13.8.
Looking for one star like that in a multitude is truly like looking for a needle in a haystack. For one thing, if the skies are anything like our own, there are something like a few dozen million stars of about the 14th magnitude. For another, the Sun is unlabelled. There’s no tag on the Sun that indicates that the Sun is our particular star. It’s an ordinary yellow-white star on the main sequence. Even if we restricted ourselves to those 30 million or so stars that are of about the right brightness and temperature, at least a few thousand could pass for the Sun. We can’t spend the time it would take to try each and every one. It’s not yet time to resort to trial and error; there’s far too much room for error.
However, if stars themselves are unremarkable, there are other things in the galaxy that aren’t. Some objects can’t be mistaken for anything other than what they are, even at quite a distance—for much greater a distance, certainly, than any star like the Sun. Many of the nebulae, for example, are quite distinctive. A great many of the nebulae turned out to be external galaxies, which don’t help us here, but then, many of them didn’t, but really were clouds of gas and dust within our own galaxy. If we could recognize one of them, it might serve as a second stop on our way home.
One of the most noticeable nebulae is the eta Carinae Nebula, in the constellation of Carina the Keel. (Carina is one of three constellations that were “created” by astronomers out of Argo the Ship when it was decided that Argo was too large and unwieldy to deal with, and is by far the most astronomically interesting of the three.) One of the stars in Carina, known as eta Carinae, was known in the early 19th century as an active but otherwise unremarkable variable star. It was ordinarily of the sixth magnitude (that is, barely visible to the unaided eye), but had been known to flare up occasionally to as bright as the third magnitude.
Then, in 1841, it brightened suddenly and dramatically. For a few months, it reached magnitude -1, brighter even than Canopus, which is usually the brightest star in Carina and the second brightest star in the entire night sky, after Sirius. From photographs taken by the Hubble Space Telescope it appears that, in 1849, eta Carinae underwent an explosion that nearly tore it apart. A lesser star would surely have perished; something like 10 or 20 solar masses were lost in an instant, astronomically speaking. In its wake, the nebula around eta Carinae was greatly embellished, and it is easily seen from decent skies on Earth (provided you are well-situated, in the southern hemisphere), even though it is around 10,000 light-years away. From 2,000 light-years, it would be large and obvious.
Unfortunately, being 10,000 light-years from the Earth is not much help, since we’re already within about 2,000 light-years. What we need is something much closer to home—ideally, closer than 1,000 light-years, but we’ll accept something a little further away, in exchange for a better fix on our location.
As it so happens, there is a bright nebula that’s much closer to the Earth than the eta Carinae Nebula. That is M42, otherwise known as the Great Orion Nebula. This patch of gas and dust, easily identifiable from dark skies as the middle star in Orion’s sword, hanging down from the bright belt, is a giant star factory.
The distance to M42 isn’t easy to determine. The distance to the stars can be determined using parallax, but that doesn’t work as well for diffuse objects like the Orion Nebula. There is, however, another method that takes advantage of M42’s known role as stellar birthplace.
The stars in the sky move with respect to one another. They move very slowly, so that it took a long time to discover this movement, called proper motion (and we’ll go into how long in just a moment), but they do move. Three of the stars around Orion are called “runaway stars” or “flying stars,” for their unusually high proper motions. These motions, if traced back about two million years, point right back to the Orion Nebula. Based on these and other observations, we can determine that the distance to M42 is just about 1,600 light-years. A bit further than we wanted, but certainly an improvement over the eta Carinae Nebula.