A while ago, Robert Sheckley wrote a book called Dimension of Miracles. It's about a guy named Carmody who finds himself, through some colossal joke, at the center of the Milky Way galaxy. And somehow, he has to find his way home.
What if this were your problem? Suppose that you had a spaceship capable of travelling at, say, 100,000 c (that is, 100,000 times the speed of light). Since we're a matter of a few dozen thousand light-years from the galactic center, that speed should be sufficient to bring you home in a matter of months. (Let's ignore for now the relativistic effects.)
But only if you knew where you were going. If you had to exhaustively travel to each star and check for the earth, you'd have to travel nearly a trillion light-years, and even in your fast ship, that would take millions of years. So that cannot be done; you have to travel smart. You have a reasonable, high-quality telescope at your disposal—say, a 10-inch (250 mm) apochromatic refractor. What signposts and path would you use to get you and Carmody safely back home? Think about that for a moment, before reading on.
Here's one way to proceed. I'd go up out of the disc and look for M31. If it isn't easily visible, I will conclude that I've gone up on the northern side (as it is defined back on earth), and sink back down to the southern side (for the purposes of this discussion), carefully avoiding any monstrous black holes or massive radiation.
Now, if I orient my spaceship so that M31 is at 12 o'clock, then the stars of Sagittarius (and hence the sun as well) should be at about 2 o'clock. I'll go for some 10,000 parsecs in that direction. At roughly that distance, now M42 should easily be identifiable, and we can go there as a rest stop. We are now some 500 parsecs from home.
At this point, we've overshot—we've gone too far, in exchange for finding an easily identifiable beacon, M42. We now regain our bearings. Taking care to orient ourselves toward the south galactic pole, we again find M31 and call it 12 o'clock. Home should then be generally in the 9 o'clock direction. At some point, we should pass within a few dozen parsecs of the Pleiades. My simulations suggest that these should be fairly easily recognizable from their tiny dipper shape (though this may be mirror-reversed from what we are used to). We are now just over 100 parsecs from home.
From the Pleiades, Antares is still distinguishable as the heart of Scorpio the Scorpion, though it is not quite as well-ordered as it is from the earth. Still, if we travel in the direction of Antares for 110 parsecs, we should be almost home, within a couple of dozen parsecs.
Finally, here, the constellations of Leo the Lion and Ursa Major the Great Bear should be vaguely recognizable. It will take some minor trial and error to position yourself until those constellations look just right; further adjustments will put Sirius in the right location with respect to Orion. That should do it, you should be within a fraction of a parsec from the sun, and it should be a blindingly bright star.
Welcome home, Carmody!
Copyright (c) 2000 Brian Tung