Gauss calculated the orbit of Piazzi's new planet, and when it was in observable range once more there was Olbers and his telescope watching the place where Gauss's calcula tions said it would be. Gauss was right and, on January 1, 1802, Olbers found it.
To be sure, the new planet (named "Ceres") was a peculiar one, for it turned out to be less than 500 miles in diameter. It was far smaller than any other known planet and smaller than at least six of the satellites known at that time.
Could Ceres be all that existed between Mars and Jupiter? The German astronomers continued looking (it would be a shame to waste all that preparation) and sure enough, three more planets between Mars and Jupiter were soon discovered. Two of them, Pallas and Vesta, were dis covered by Olbers. (In later years many more were discovered.)
But, of course, the big payoff isn't for second place. All Olbers got out of it was the name of a planetoid. The thou sandth planetoid between Mars and Jupiter was named "Piazzia," the thousand and first "Gaussia," and the thou sand and second (hold your breath, now) "Olberia."
Nor was Olbers much luckier in his other observations.
He specialized in comets and discovered five of them, but practically anyone can do that. There is a comet called "Olbers' Comet" in consequence, but that is a minor dis tinction.
Shall we now dismiss Olbers? By no means.
It is hard to tell just what will win you a place in the annals of science. Sometimes it is a piece of interesting reverie that does it. In 1826 Olbers indulged himself in an idle speculation concerning the black of night and dredged out of it an'apparently ridiculous conclusion.
Yet that speculation became "Olbers' paradox," which has come to have profound significance a century after ward. In fact, we can begin with Olbers' paradox and end with the conclusion that the only reason life exists any where in the universe is that the distant galaxies are reced ing from us.
What possible effect can the distant galaxies have on us?
Be patient now and we'll work it out.
In ancient times, if any astronomer had been asked why the night sky was black, he would have answered-quite reasonably-that it was because the light of the Sun was absent. If one had then gone on to question him why the stars did not take the place of the Sun, he would have answered-again reasonably-that the stars were limited in number and individually dim. In fact, all the stars we can see would, if lumped together, be only a half-birionth as bright as the Sun. Their influence on the blackness of the night sky is therefore insignificant.
By the nineteenth century, however, this last argument had lost its force. The number of stars was tremendous.
Large telescopes revealed them by the countless millions.
Of course, one might argue that those countless millions of stars were of no importance for they were not visible to the naked eye and therefore did not contribute to the light in the night sky. This, too, is a useless argument. The stars of the Milky Way are, individually, too faint to be made out, but en masse they make a dimly luminous belt about the sky. The Andromeda galaxy is much farther away than the stars of the Milky Way and the individual stars that make it up are not individually visible except (just barely) in a very large telescope. Yet, en masse, the Andromeda galaxy is faintly visible to the naked eye. (It'is, in fact, the farthest object visible to the unaided eye; so if anyone ever asks you how far you can see; tell him 2,000,000 light years.)
In short distant stars-no matter how distant and no matter how dim, individually-must contribute to the light of the night sky, and this contribution can even become detectable without the aid of instruments if these dim distant stars exist in sufficient density.
Olbers, who didn't know about the Andromeda galaxy, but did know about the Milky Way, therefore set about asking himself how much light ought to be expected from the distant stars altogether. He began by making several assumptions:
1. That the universe is infinite in extent.
2. That the stars are infinite in number and evenly spread throughout the universe.
3. That the stars are of uniform average brightness through all of space.
Now let's imagine space divided up into shells (like those of an onion) centering about us, comparatively thin. shells compared with the vastness of space, but large enough to contain stars within them.
Remember that the amount of light that reaches us from individual stars of equal luminosity varies inversely as the square of the distance from us. In other words, if Star A and Star B are equally bright but Star A is three times as far as Star B, Star A delivers only % the light. If Star A were five times as far as Star B, Star A would deliver 1/2r, the light, and so on.
This holds for our shells. The average star in a shell 2000 light-years from us would be only 1/4 as bright in appearance as the average star in a shell only 1000 light years from us. (Assumption 3 tells us, of course, that the intrinsic brightness of the average star in both shells is the same, so that distance is the only factor we need consider.)
Again, the average star in a shell 3000 light-years from us would be only % as bright in appearance as the average star in the 10004ight-year shell, and so on.
But as you work your way outward, each succeeding shell is more voluminous than the one before. Since each shell is thin enough to be considered, without appreciable error, to be the surface of the sphere made up of all the shells within, we can see that the volume of the shells in creases as the surface of the spheres would-that is, as the square of the radius. The 2000-light-year shell would have four times the volume of the 1000-light-year shell.
The 3000-light-year shell would have nine times the volume of the 1000-light-year shell, and so on.
If we consider the stars to be evenly distributed through space (Assumption 2), then the number of stars in any given shell is proportional to the volume of the shell. If the 2000-light-year shell is four times as voluminous as the 1000-light-year shell, it contains four times as many stars.
If the 3000-light-year shell is nine times as voluminous as the 1000-light-year shell, it contains nine times as many stars, and so on.
Well, then, if the 2000-light-year shell contains four ,times as many stars as the IOOG-light-year shell, and if each star in the former is % as bright (on the average) as each star of the latter, then the total light delivered by the 20GO-light-year shell is 4 times Y4 that of the 1000 fight-year shell. In other words, the 2000-light-year shell delivers just as much total light as the 1000-light-year shell. The total brightness of the 3000-light-year shell is 9 times % that of the 1000-light-year shell, and the bright ness of the two shells is equal again.
In summary, if we divide the universe into successive shells, each shell delivers as much light, in toto, as do any of the others. And if the universe is infinite in extent (As sumption 1) and therefore consists of an finate number of shells, the stars of the universe, however dim they may be individually, ought to deliver an infinite amount of light to the Earth.
The one catch, of course, is that the nearer stars may block the light of the more distant stars.
To take this into account, let's look at the problem in another way. In no matter which direction one looks, the eye will eventually encounter a star, if it is true they are infinite in number and evenly distributed in space (As sumption 2). The star may be individually invisible, but it will contribute its bit of light and will be immediately adjoined in all directions by other bits of light.
The night sky would then not be black at all but would be I an absolutely solid smear of starlight. So would the day sky be an absolutely solid smear of starlight, with the Sun itself invisible against the luminous background.