Oh, and he also finds out that the trip to the galactic center, to collect his winnings, was a one-way trip. He’s on his own for the way back—well, he and his talking advisor.
To summarize the situation, Carmody is oodles of light-years from the Earth, he’s been abandoned by the strange people who brought him here, and he has a gadget that, when confronted by a carnivorous dinosaur, advises him to turn himself into a plant.
And somehow, he has to find his way home.
What if this were your problem? To make it somewhat tractable, suppose you’re at the center of the Milky Way, and you have a spaceship capable of travelling at, say, 100,000 c—that is, 100,000 times the speed of light, which itself is about 300,000 km/s. The Sun, and the Earth around it, are just about 25,000 light-years from the galactic center. That means that a ship travelling at the speed of light would take 25,000 years to get home, so one travelling 100,000 times faster would take only about 3 months. (We’ll ignore the relativistic effects for the time being.)
But you can only get home that fast if you know precisely where to go. The Milky Way contains some 400 billion stars (give or take a hundred billion or so). The nearest star to our own is Proxima Centauri, a little more than 4 light-years away. If you visited each star in the galaxy, in exhaustive fashion, and each step between stars was 4 light-years long, you would have to travel 1.6 trillion light-years. Even at 100,000 times the speed of light, that would take 16 million years, and let’s face it, neither you nor Carmody has that long to dawdle around. Worse yet, over those 16 million years the stars are bound to move around a bit, and it’ll be hard to keep track of where you’ve been, and where you haven’t.
Perhaps, however, the local stars are only spaced 4 light-years apart because the Sun is in, relatively speaking, the boondocks of the galaxy. Stars near the center of the galaxy, where things are busier, are bunched together much closer—perhaps about 1 light-year apart on average. But even if every step was 1 light-year in length, that would still only decrease the total travel time to 4 million years.
Very obviously, then, if we’re going to get home from the center of the galaxy within a single ordinary lifetime, we’ll have to make use of some knowledge of the galaxy itself—and only information that we have access to at the current time. No fair assuming that we’ll someday have a complete map of the galaxy, down to the last star, and using that instead. The first thing to try, possibly, is that since we know the Sun is not at the center of the galaxy, there’s no point in trying the stars there. And since the galactic center is so tightly packed, that allows us to eliminate quite a few stars.
In fact, knowing that we’re approximately 25,000 light-years away from the galactic center means that we don’t have to examine any stars out to a distance of almost 25,000 light-years—but not quite. After all, we don’t know that figure too precisely. It might be 23,000 light-years, or 27,000; the margin of error is, let’s say, about 2,000 light-years in either direction. We wouldn’t want to skip the Earth just because we happen to be a little off on its exact distance from the galactic center.
If the Milky Way galaxy were a spherically symmetric ball of stars, and we had to systematically check each star in a shell 25,000 light-years in radius and 2,000 light-years thick, we would have to cover a volume of about 20 trillion cubic light-years. At that distance—including our local neighborhood of stars—the density of stars is about 1 star every 50 cubic light-years. That would mean we’d have to cover 400 billion stars, at 4 light-years a pop. As we noted above, that would take 16 million years.
Fortunately, the Milky Way is not a ball of stars, but rather a beautiful spiral, a little like a pinwheel. In other words, it’s flattened out—and rather dramatically so. Estimates vary, but a typical figure is that the disc of the Milky Way is about 50 times wider than it is thick. It’s considerably thicker at the center, where there’s a bulge, but we’ve already eliminated those stars from consideration. Since the Milky Way is about 100,000 light-years across, from edge to edge, its thickness is about 2,000 light-years.
That means that we only have to consider a ring of stars, located at a distance of about 25,000 light-years from the center, 4,000 light-years wide and 2,000 light-years thick. That gives us a volume of “only” about a trillion cubic light-years. Again, at a local density of 1 star every 50 cubic light-years, that means 20 billion stars. At 4 light-years a step, that’s about 80 billion light-years, which—at our top speed of 100,000 c—would take us 800,000 years. A lot better than 16 million years, or even 4 million years, but quite obviously not good enough.
The problem is that we don’t know which direction to go from the center of the galaxy. If we knew, even approximately, which way to go, we could eliminate a huge part of the ring of stars we have to examine, and shorten the search time commensurately.
A century ago, there would have been little we could have done. As far as anybody knew, the Milky Way was the entire universe. And we didn’t even know its structure that well, because even though we get to examine it close up—being a part of it ourselves—that very closeness makes it difficult to get a feel for its large-scale structure. What’s more, much of our view of distant parts of the galaxy is blocked by clouds of dark gas. This gas is actually pretty thin, thinner than a good laboratory vacuum, but because the clouds are so large, and we look through such a great thickness of them, they are very effective at obscuring anything behind them. If you don’t know the structure of the Milky Way, it makes it hard to figure out how to get back home from the center—even assuming you know there to be a well-defined center.
To be sure, there are suspicious looking clouds, called nebulae (from the Latin word for “cloud,” naturally enough), some of which had been discovered, by the middle of the 19th century, to display some spiral structure. One of the largest lies in the constellation of Andromeda, and was consequently called the Andromeda Nebula. At the time, these spiral nebulae were thought by most astronomers to be other solar systems in the making; our own Sun was believed to have condensed out of just such a spiraling cloud of gas and dust.
Some believed, however, that they might be other galaxies—”island universes,” they were often called—each containing about as many stars as the Milky Way itself contained—and that the only reason they looked nebular (that is, cloudlike) was that they were so far away that no individual stars in them could be made out. At the end of the 19th century, there was no way to tell for sure which idea, if either, was right. No telescope could resolve the nebulae into component stars, and in smaller telescopes they often resembled comets. The comet hunter Charles Messier (1730-1817) put the Andromeda Nebula in his catalogue of comet-like objects (to be avoided when hunting for comets) as M31. The inability to resolve it and other nebulae seemed to imply that they really were clouds of gas and dust within the Milky Way.
As the 20th century dawned, however, a breed of larger and better telescopes was being put into use. The 100-inch telescope at Mount Wilson Observatory, under the command of the American astronomer Edwin Hubble (1889-1953), was the first to be able to resolve the Andromeda Nebula. The overall dimness of those stars demonstrated that M31 had to be very far away indeed—probably hundreds of thousands of light-years, although it was impossible to tell more precisely just from that. At that great distance, it had to be very large and external to the Milky Way. Naturally, there went any idea of it being a solar system condensing out of gas and dust, and from then on, the Andromeda Nebula was increasingly often referred to as the Andromeda Galaxy.
But just how far away was M31? In 1912, Henrietta Leavitt (1868-1921), then working at Harvard University under Edward Pickering, was studying a class of variable stars called Cepheids, named after their prototype, delta Cephei, in the constellation of Cepheus the King. She discovered, after analyzing the brightness curves of Cepheids in the Large Magellanic Cloud, a satellite galaxy of the Milky Way in the southern hemisphere, that there was a direct correlation between the period of a Cepheid—that is, the time between its brightness “peaks”—and its average intrinsic brightness.