Asimov's New Guide to Science

by Isaac Asimov

  With the naked eye, we can see about 6,000 stars. The invention of the telescope at once made plain that these were only a fragment of the universe. When Galileo raised his telescope to the heavens in 1609, he not only found new stars previously invisible but, on turning to the Milky Way, received all even more profound shock. To the naked eye, the Milky Way is merely a luminous band of foggy light. Galileo’s telescope broke down this foggy light into myriads of stars, as numerous as the grains in talcum powder.

  The first man to try to make sense out of this was the German-born English astronomer William Herschel. In 1785, Herschel suggested that the stars of the heavens were arranged in a lens shape. If we look toward the Milky Way, we see a vast number of stars, but when we look out to the sky at right angles to this wheel, we see relatively few stars. Herschel deduced that the heavenly bodies formed a flattened system, with the long axis in the direction of the Milky Way. We now know that, within limits, this picture is correct, and we call our star system the galaxy, which is actually another term for Milky Way. because galaxy comes from the Greek word for milk.

  Herschel tried to estimate the size of the galaxy. He assumed that all the stars had about the same intrinsic brightness, so that one could tell the relative distance of a star by its brightness. (By a well-known law brightness decreases as the square of the distance, so if star A is one-ninth the brightness of star B, it should be three times as far as star B.)

  By counting samples of stars in various spots of the Milky Way, Herschel estimated that there were about 100 million stars in the galaxy altogether. From the levels of their brightness, he decided that the diameter of the galaxy was 850 times the distance to the bright star Sirius, and that the galaxy’s thickness was 155 times that distance.

  We now know that the distance to Sirius is 8.8 light-years, so Herschel’s estimate was equivalent to a galaxy about 7,500 light-years in diameter and 1,300 light-years thick. This estimate turned out to be far too conservative. But like Aristarchus’ overconservative measure of the distance to the sun, it was a step in the right direction.

  It was easy to believe that the stars in the galaxy move about (as I said before) like bees in a swarm, and Herschel showed that the sun itself also moves in this manner.

  By 1805, after he had spent twenty years determining the proper motions of as many stars as possible, he found that, in one part of the sky, the stars generally seemed to be moving outward from a particular center (the apex). In a place in the sky directly opposite to the first, the stars generally seemed to be moving inward toward a particular center (the anti-apex).

  The easiest way of explaining this phenomenon was to suppose that the sun was moving away from the anti-apex and toward the apex, and that the clustered stars seemed to be moving apart as the sun approached, and to be closing in behind. (This is a common effect of perspective. We would see it if we were walking through a grove of trees, and would be so accustomed to the effect that we would scarcely notice it.)

  The sun is not, therefore, the immovable center of the universe as Copernicus had thought, but moves—yet not in the way the Greeks had thought. It does not move about the earth but carries the earth and all the planets along with it as it moves through the galaxy. Modern measurements show that the sun is moving (relative to the nearer stars) toward a point in the constellation of Lyra at a speed of 12 miles a second.

  Beginning in 1906, the Dutch astronomer Jacobus Cornelis Kapteyn conducted another survey of the Milky Way. As he had photography at his disposal and knew the true distance of the nearer stars, he was able to make a better estimate than Herschel had. Kapteyn decided that the dimensions of the galaxy were 23,000 light-years by 6,000. Thus Kapteyn’s model of the galaxy was four times as wide and five times as thick as Herschel’s; but it was still overconservative.

  To sum up, by 1900 the situation with respect to stellar distances was the same as that with respect to planetary distances in 1700. In 1700, the moon’s distance was known, but the distance of the farther planets could only be guessed. In 1900, the distance of the nearer stars was known, but that of the more distant stars could only be guessed.

  MEASURING A STAR’S BRIGHTNESS

  The next major step forward was the discovery of a new measuring rod—certain variable stars that fluctuate in brightness. This part of the story begins with a fairly bright star called Delta Cephei, in the constellation Cepheus. On close study, the star was found to have a cycle of varying brightness: from its dimmest stage, it rather quickly doubled in brightness, then slowly faded to its dim point again. It did this over and over with great regularity. Astronomers found a number of other stars that varied in the same regular way; and in honor of Delta Cephei, all were named cepheid variables or, simply, cepheids.

  The cepheids’ periods (the time from dim point to dim point) vary from less than a day to as long as nearly two months. Those nearest our sun seem to have a period in the neighborhood of a week. The period of Delta Cephei itself is 5.3 days, while the nearest cepheid of all (the Pole Star, no less) has a period of 4 days. (The Pole Star, however, varies only slightly in luminosity—not enough to be noticeable to the unaided eye.)

  The importance of the cepheids to astronomers involves their brightness a subject that requires a small digression.

  Ever since Hipparchus, the brightness of stars has been measured by the term magnitude according to a system he invented. The brighter the star, the lower the magnitude. The twenty brightest stars he called first magnitude. Somewhat dimmer stars are second magnitude. Then, third, fourth, and fifth, until the dimmest, those just barely visible, are of the sixth magnitude.

  In modern times—1856, to be exact—Hipparchus’ notion was made quantitative by the English astronomer Norman Robert Pogson. He showed that the average first-magnitude star was about 100 times brighter than the average sixth-magnitude star. Allowing this interval of five magnitudes to represent a ratio of 100 in brightness, the ratio for 1 magnitude must be 2.512. A star of magnitude 4 is 2.512 times as bright as a star of magnitude 5, and 2.512 × 2.512, or about 6.3 times as bright as a star of magnitude 6.

  Among the stars, 61 Cygni is a dim star with a magnitude of 5.0 (modern astronomical methods allow magnitudes to be fixed to the nearest tenth and even to the nearest hundredth in some cases). Capella is a bright star, with a magnitude of 0.9; Alpha Centauri still brighter, with a magnitude of 0.1. And the measure goes on to still greater brightnesses which are designated by magnitude 0 and beyond this by negative numbers. Sirius, the brightest star in the sky, has a magnitude of −1.42. The planet Venus attains a magnitude of −4.2; the full moon, −12.7; the sun, −26.9.

  These are the apparent magnitudes of the stars as we see them—not their absolute luminosities independent of distance. But if we know the distance of a star and its apparent magnitude, we can calculate its actual luminosity. Astronomers base the scale of absolute magnitudes on the brightness at a standard distance, which has been established at ten parsecs, or 32.6 light years. (The parsec is the distance at which a star would show a parallax of 1 second of arc; it is equal to a little more than 19 trillion miles, or 3.26 light-years.)

  Although Capella looks dimmer than Alpha Centauri arid Sirius, actually it is a far more powerful emitter of light than either of them. It merely happens to be a great deal farther away. If all were at the standard distance, Capella would be much the brightest of the three. Capella has an absolute magnitude of −0.1; Sirius, 1.3; and Alpha Centauri, 4.8. Our own sun is just about as bright as Alpha Centauri, with an absolute magnitude of 4.86. It is an ordinary, medium-sized star.

  Now to get back to the cepheids. In 1912, Henrietta Leavitt, an astronomer at the Harvard Observatory, was studying the smaller of the Magellanic Clouds—two huge star systems in the Southern Hemisphere named after Ferdinand Magellan, because they were first observed during his voyage around the globe. Among the stars of the Small Magellanic Cloud, Miss Leavitt detected twenty-five cepheids. She recorded the period of variation of eac
h and, to her surprise, found that the longer the period, the brighter the star.

  As this is not true of the cepheid variables in our own neighborhood, why should it be true of the small Magellanic Cloud? In our own neighborhood, we know only the apparent magnitudes of the cepheids; not knowing their distances or absolute brightnesses, we have no scale for relating the period of a star to its brightness. But in the Small Magellanic Cloud, all the stars are effectively at about the same distance from us, because the cloud itself is so far away. It is as though a man in New York were trying to calculate his distance from each person in Chicago. He would conclude that all the Chicagoans were about equally distant from himself—what is a difference of a few miles in a total distance of a thousand? Similarly, a star at the far end of the Cloud is not significantly farther away than one at the near end.

  With the stars in the Small Magellanic Cloud at about the same distance from us, their apparent magnitude could be taken as a measure of their comparative absolute magnitude. So Leavitt could consider the relationship she saw a true one: that is, the period of the cepheid variables increases smoothly with the absolute magnitude. She was thus able to establish a period-luminosity curve—a graph that shows what period a cepheid of any absolute magnitude must have; and, conversely, what absolute magnitude a cepeid of a given period must have.

  If cepheids everywhere in the universe behaved as they did in the Small Magellanic Cloud (a reasonable assumption), then astronomers had a relative scale for measuring distances, as far out as cepheids could be detected in telescopes. If they spotted two cepheids with equal periods, they could assume that both were equal in absolute magnitude. If cepheid A seemed four times as bright as cepheid B, cepheid B must be twice as distant from us. In this way, the relative distances of all the observable cepheids could be plotted on a scale map. Now if the actual distance of just one of the cepheids could I be determined, so could the distances of all the rest.

  Unfortunately, even the nearest cepheid, the Pole Star, is hundreds of light-years away, much too far to measure its distance by parallax. Astronomers had to use less direct methods. One usable clue was proper motion: on the average, the more distant a star is, the smaller its proper motion. (Recall that Bessel decided 61 Cygni was relatively close because it had a large proper motion.) A number of devices were used to determine the proper motions of groups of stars, and statistical methods were brought to bear. The procedure was complicated, but the results gave the approximate distances of various groups of stars which contained cepheids. From the distances and the apparent magnitudes of those cepheids, their absolute magnitudes could be determined, and these could be compared with the periods.

  In 1913, the Danish astronomer Einar Hertzsprung found that a cepheid of absolute magnitude −2.3 had a period of 6.6 days. From that finding, and using Leavitt’s period-luminosity curve, he could determine the absolute magnitude of any cepheid. (It turned out, incidentally, that cepheids generally are large, bright stars, much more luminous than our sun. Their variations in brightness are probably the result of pulsations. The stars seem to expand and contract steadily, as though they are ponderously breathing in and out.)

  A few years later, the American astronomer Harlow Shapley repeated the work and decided that a cepheid of absolute magnitude 2.3 had a period of 5.96 days. The agreement was close enough to allow astronomers to go ahead. They had their yardstick.

  DETERMINING THE GALAXY’S SIZE

  In 1918, Shapley began observing the cepheids of our own galaxy in an attempt to determine the galaxy’s size by this new method. He concentrated on the cepheids found in groups of stars called globular clusters—densely packed spherical aggregates of tens of thousands to tens of millions of stars, with diameters of the order of 100 light-years.

  These clusters (whose nature had first been observed by Herschel a century earlier) present an astronomical environment quite different from that prevailing in our own neighborhood in space. At the center of the larger clusters, stars are packed together with a density of 500 per 10 cubic parsecs, as compared with 1 star per 10 cubic parsecs in our own neighborhood. Starlight under such conditions would be far brighter than moonlight on Earth, and a hypothetical planet situated near the center of such a cluster would know no true night.

  There are about 100 known globular clusters in our galaxy and probably as many again that have not yet been detected. Shapley calculated the distance of the various globular clusters at from 20,000 to 200,000 light-years from us (The nearest cluster, like the nearest star, is in the constellation Centaurus and is visible to the naked eye as a starlike object, Omega Centauri. The most distant, NGC 2419, is so far off as scarcely to be considered a member of the galaxy.) Shapley found the clusters to be distributed in a large sphere that the plane of the Milky Way cuts in half, and to surround a portion of the main body of the galaxy like a halo. Shapley made the natural assumption that they encircle the center of the galaxy. His calculations placed the central point of this halo of globular clusters within the Milky Way in the direction of the constellation Sagittarius and about 50,000 light-years from us. The implication was that our solar system, far from being at the center of the galaxy, as Herschel and Kapteyn had thought, is far out toward one edge.

  Shapley’s model pictured the galaxy as a giant lens about 300,000 light-years in diameter. This time its size was overestimated, as another method of measurement soon showed. From the fact that the galaxy had a disk shape, astronomers from William Herschel on assumed it had to be rotating in space. In 1926, the Dutch astronomer Jan Oort set out to measure this rotation. Since the galaxy is not a solid object, but is composed of numerous individual stars, it is not to be expected to rotate in one piece, as a wheel does. Instead, stars close to the gravitational center of the disk must revolve around it faster than those farther away (just as the planets closest to the sun travel fastest in their orbits). Hence, the stars toward the center of the galaxy (that is, in the direction of Sagittarius) should tend to drift ahead of our sun, whereas those farther from the center (in the direction of the constellation Gemini) should tend to lag behind us in their revolution. And the farther a star is from us, the greater this difference in speed should be.

  On these assumptions, it became possible to calculate, from the relative motions of the stars, the rate of rotation around the galactic center. The sun and nearby stars, it turned out, travel at about 150 miles a second relative to the galactic center and make a complete revolution around the center in approximately 200 million years. (The sun travels in a nearly circular orbit, but the orbit of some stars, such as Arcturus, are quite elliptical. The fact that the various stars do not rotate in perfectly parallel orbits accounts for the sun’s relative motion toward the constellation Lyra.)

  Having estimated a value for the rate of rotation, astronomers were then able to calculate the strength of the gravitational field of the galactic center and, therefore, its mass. The galactic center (which contains most of the mass of the galaxy) turns out to be well over 100 billion times as massive as our sun. Since our sun is a star of greater than average mass, our galaxy therefore contains perhaps 200 to 300 billion stars—up to 3,000 times the number estimated by Herschel.

  From the curve of the orbits of the revolving stars, it is also possible to locate the center around which they are revolving. The center of the galaxy in this way has been confirmed to be in the direction of Sagittarius, as Shapley found, but only 27,000 light-years from us, and the total diameter of the galaxy comes to 100,000 light-years, instead of 300,000. In this new model, now believed to be correct, the thickness of the disk is some 20,000 light-years at the center and falls off toward the edge: at the location of our sun, which is two-thirds of the way out toward the extreme edge, the disk is perhaps 3,000 light-years thick (figure 2.3). But these are only rough figures, because the galaxy has no sharply definite boundaries.

  If the sun is so close to the edge of the galaxy, why is not the Milky Way much brighter in the direction toward the
center than in the opposite direction, where we look toward the edge? Looking toward Sagittarius, we face the main body of the galaxy with some 200 billion stars, whereas out toward the edge there is only a scattering of some millions. Yet in each direction the band of the Milky Way seems of about the same brightness. The answer appears to be that huge clouds of obscuring dust hide much of the center of the galaxy from us. As much as half the mass of the galactic outskirts may be composed of such clouds of dust and gas. Probably we see no more than 1/10,000 (at most) of the light of the galactic center.

  Figure 2.3. A model of our galaxy seen edgewise. Globular clusters are arrayed around the central portion of the galaxy. The position of our sun is indicated by +.

  Thus it is that Herschel and other early students of the galaxy thought our solar system was at the center; and also, it seems, that Shapley originally overestimated the size of the galaxy. Some of the clusters he studied were dimmed by the intervening dust, so that the cepheids in them seemed dimmer and therefore more distant than they really were.

  ENLARGING THE UNIVERSE

  Even before the size and mass of the galaxy itself had been determined, the cepheid variables of the Magellanic Clouds (where Leavitt had made the crucial discovery of the period-luminosity curve) were used to determine the distance of the Clouds, which proved to be more than 100,000 light-years away. The best modern figures place the Large Magellanic Cloud at about 150,000 light-years from us and the Small Magellanic Cloud at 170,000 light-years. The Large Cloud is no more than half the size of our galaxy in diameter; the Small Cloud, no more than one-fifth. Besides, they seem to be less densely packed with stars. The Large Magellanic Cloud contains 5 billion stars (only 1/20 or less the number in our galaxy), while the Small Magellanic Cloud has only 1.5 billion.