Depending on where we end up after Step 2, we’ll have to travel an average of about 2,000 light-years to get to M42:
Step 3 Distance: 2,000 light-years
Step 3 Time: About a week
The Orion Nebula, naturally enough, lies in the constellation of Orion the Hunter. The galactic center, where we started, appears in Sagittarius the Archer when viewed from Earth. These two constellations are on opposite sides of our night sky; in other words, the Earth and the rest of the solar system lie right between the Orion Nebula and the galactic center. As a result, by going to Orion, we’ve overshot our mark. Now we have to trace our way back home, in the direction of the center again, but this time taking a step of only 1,600 light-years—the distance to M42.
You might well wonder why we didn’t just go 1,600 light-years less in Step 2, so that we could avoid this next leg. The problem is that we didn’t know exactly where we were with respect to home—we might have missed to the right, to the left, up, down, whatever. Only by heading first to M42 can we figure out which way we’re off.
Step 4 Distance: 1,600 light-years
Step 4 Time: About a week
We’re almost home now—the distance to M42 is known within an error bar of about 100 light-years. From this vantage point, we should be able to recognize quite a few of the familiar constellations of the Earth. Some constellations, on the other hand, will be noticeably altered. The constellation of Canis Major the Great Dog, for example, contains Sirius, the brightest star in the night sky, at magnitude -1.4.
Now, Sirius appears that bright primarily because it’s relatively close in interstellar terms: the current estimate is about 8.6 light-years. Its absolute magnitude—again, the brightness it would have at the standard distance of 32.6 light-years—is thus about 0.0. It’s therefore considerably brighter than the Sun, to be sure, but nothing compared with the other bright stars in Canis Major, which are first and second magnitude stars at a distance of 400 light-years and up. Aludra (eta Canis Majoris), at magnitude 2.8, is about 3,000 light-years away. If Sirius were that far away, it would only be a small dot of light at around magnitude 10.0.
Since these stars are all so far away, most of the shape of the Great Dog will still be recognizable, aside from missing its brightest star. That does not mean that the constellation’s appearance will be totally unchanged, and therein lies the key to the last phase of our voyage home.
It’s an interesting game to take a photograph of your house, or some other place you’re familiar with, and try to figure out the exact vantage point it was taken from. You make an initial guess, say, and stand where you think it might have been taken from. But the picture doesn’t exactly match your actual view. Maybe two trees appear too close together; in that case, you’ll have to move to one side or the other, so that their separation matches that in the photo. Or maybe a couple of fenceposts have noticeably different heights in the photo, but to you, they appear to be nearly level with one another. Then you have to vary your altitude, again, until the fencepost heights match what you see in the photo.
If you’re at the center of the galaxy, there’s no way you can play that game with the constellations. The vantage point is too far away. The constellations depend on a lack of depth perception—they contain stars of all different distances from the Earth—and even if you could recognize them in principle, there would be too many stars in the way to pick them out. Similarly, if you had a photograph of your house taken from up in the airplane, it might be difficult to pick out which house was yours, let alone the exact angle and distance of the point where the picture was taken.
But from 100 light-years, things are different. The constellations are close enough to their usual forms to recognize, but not so close that they appear identical. There are enough cues to fine-tune your location. Finally, when you get to within a few light-years of the Earth, the constellation forms might no longer provide a usable basis for navigation, but now Sirius, at a distance of only 8.6 light-years, will do the trick admirably. At that distance, if you’re off by a single light-year, Sirius’s position in the sky will be in error by as much as 7 degrees, quite easy to notice and adjust for.
Now, it’s true that if your position could be off in such a way that Sirius is still in the right position in the sky, but we can address that simply by having a second nearby star to sight. If you know that your house is directly due south of city hall, that alone wouldn’t be enough to pinpoint your house’s location. Even if you could see city hall to the north, you might be too far or too close to it. But if you also knew that your house was due east of the theater, that would be enough. What we need is a nearby star, one that’s unmistakable so that we would recognize it and know where it ought to be, even when it’s out of place. What star would be that bright and close to us?
One of the clues that Sirius is so close is that it has a relatively large proper motion. Well, relative is relative; as I mentioned earlier, the stars are mostly so far away that they don’t appear to change their relative positioning when you observe them for a year, or for 10 years, or even for 100 years. The proper motion of even the fastest-moving star is only about the width of the full Moon in one century.
Fortunately, humans have been cataloguing the positions of the stars for millennia. The Greeks did it no later than the third century B.C., with Timocharis, and then more famously in the second century B.C., with Hipparchus (c. 190-120 B.C.). Hipparchus had, according to Pliny the Elder, observed a new star—a nova, that is—and in order to accurately record further observations, decided to commit to papyrus all the stars visible to the unaided eye, with their locations and their brightnesses, using the magnitude system that he invented.
Much later, in 1717, the English astronomer Edmond Halley (1656-1742) compared the then-current locations of the stars with those recorded by Hipparchus, and found that the positions of three of them differed by up to half a degree. Such a small discrepancy might easily have been chalked up to the lack of proper instrumentation in ancient Greece, but Halley thought that unlikely, given Hipparchus’s other achievements. By taking the old coordinates at face value, he interpreted the discrepancy as an actual change in location, taking place very slowly over nearly 2,000 years. Future observations have vindicated Halley’s judgment in this matter.
Because there’s no reason to think that these stars were intrinsically different from other stars, astronomers expected that the relatively large proper motion of these stars was due to their closeness, rather than their own native speed through the heavens. What strengthened their case was that the three stars were also quite bright, something else you expect when a star is nearby. One of the stars was Sirius, and the other two were Aldebaran, in Taurus the Bull, and Arcturus, in Bootes the Herdsman.
By using these three stars to calibrate our final positioning, then, we should be able to position ourselves to within a light-year of the Sun and Earth. From that distance, the Sun should be a brilliant star of magnitude -2.7—easily outshining anything else in the sky. That should allow us to head directly home. It’s hard to say exactly how far this last step should be, but it’s probably no further than the 100 light-years we talked about before:
Step 5 Distance: 100 light-years
Step 5 Time: About 8 hours
All told, adding up all five steps, we cover only a little over 30,000 light-years in just under four months, easily in time for dinner. Not bad!
The imaginary trip we just completed is only convoluted because of our incomplete knowledge of the Milky Way. Galaxies are fluid objects, all of the stars flowing amongst its neighbors, but only on time scales of millions or billions of years. In the short period of time that’s needed to get from the galactic center to the Sun in a ship that travels at 100,000 c, we can treat the galaxy as essentially static. For these purposes, it makes sense to think of a “map” of the galaxy.
Such a map may be coming, and relatively soon. The Hipparcos satellite has uncovered the distances to many of the nearby stars to about a several hundred light-years distance. Its proposed successor, the GAIA project, may be able to extend this horizon all the way out to the opposite edge of the Milky Way galaxy. If we had a complete map of the galaxy, we could make it home in a straightforward, one-step trip of about 25,000 light-years.