Science Fiction Today and Tomorrow

by Reginald Bretnor

  Sorry. Because they burn at such a prodigal rate, these great stars are short-lived. Once they have condensed from interstellar dust and gas, Type O suns spend a bare few million years on the main sequence; then they apparently go out in the supernal violence of supernova explosions. Their ultimate fate, and the precise death throes of their somewhat lesser brethren, are too complicated to discuss here. But even an AQ star like Sirius is good for no more than about four hundred million years of steady shining—not much in terms of geology and evolution.

  Furthermore, the evidence is that giants don't have planets in the first place. There is a most suggestive sharp drop in the rotation rate, just about when one gets to the earlier Type Fs. From then on, down through Type M, suns appear to spin so slowly that it is quite reasonable to suppose the "extra" has gone into planets.

  Giants are rare, anyway. They are far outnumbered by the less showy yellow dwarfs like Sol—which, in turn, are outnumbered by the inconspicuous red dwarfs. (There are about ten times as many M as G stars.) And this great majority also has the longevity we need. For instance, an F5 spends a total of six billion years on the main sequence before it begins to swell, redden, and die. Sol, G2, has a ten-billion-

  year life expectancy, and is about halfway through it at the present day, making a comfortingly long future. The K stars live for several times that figure, the weakest M stars for hundreds of billions of years. Even if life, in the biological sense, is slow to get generated and slow to evolve on a planet so feebly irradiated, it will have—or will have had—a vast time in which to develop. That may or may not make a significant difference; and thereby hangs many a tale.

  So let's take a star of Type F or later. If we want to give it a planet habitable to man, probably it must be somewhere between, say, F5 and K5. Earlier in the sequence, the system will presumably be too young for photosynthesis to have started, releasing oxygen into the air. Later, the sun will be too cool, too dull, too niggardly with ultraviolet, to support the kind of ecology on which humans depend.

  Granted, a planet of a red dwarf may bear life of another sort than ours. Or it may orbit close enough that the total radiation it gets is sufficient for us. In the latter case, the chances are that it would rotate quite slowly, having been braked by tidal friction. The sun would appear huge and reddish, or even crimson, in the sky; one might be able to gaze straight at it, seeing spots and flares with the naked eye. Colors would look different, and shadows would have blurrier outlines than on Earth. Already, then, we see how many touches of strangeness we can get by changing a single parameter. In the superficially dry data of astronomy and physics is the potential of endless adventure.

  But for our concrete example of planet-building, let's go toward the other end of the scale, i.e., choosing a star brighter than Sol. The main reason for doing so is to avoid the kind of complications we have just noticed in connection with a weaker sun. We will have quite enough to think about as is!

  The hypothetical planet is one that I recently had occasion to work up for a book to be edited by Roger Elwood, and is used with his kind permission. I named it Cleopatra. While tracing out the course of its construction, we'll look at a few conceivable variations, out of infinitely many.

  First, where in the universe is the star? It won't be anywhere in our immediate neighborhood, because those most closely resembling Sol within quite a few light-years are somewhat dimmer—ours being, in fact, rather more luminous than average. (True, Alpha Centauri A is almost a twin, and its closer companion is not much different. However, this is a multiple system. That does not necessarily rule out its having planets; but the possibility of this is controversial, and in any event it would complicate things too much for the present essay if we had more than one sun.)

  Rather than picking a real star out of an astronomical catalogue, though that is frequently a good idea,

  I made mine up, and arbitrarily put it about four hundred light-years off in the direction of Ursa Major. This is unspecific enough—it defines such a huge volume of space—that something corresponding is bound to be out there someplace. Seen from that location, the boreal constellations are considerably changed, though most remain recognizable. The austral constellations have suffered the least alteration, the equatorial ones are intermediately affected. But who says the celestial hemispheres of Cleopatra must be identical with those of Earth? For all we know, its axis could be at right angles to ours. Thus a writer can invent picturesque descriptions of the night sky and of the images which people see there.

  Arbitrary also is the stellar type, F?. This means it has 1.2 times the mass of Sol, twenty percent more. As we shall see, the diameter is little greater; but it has 2.05 times the total luminosity.

  Numbers this precise cannot be taken off a graph. I computed them on the basis of formulas. But you can get values close enough for most purposes from Figure 2. It charts the relevant part of the main sequence on a larger scale than Figure 1, and has no need to depict any numbers logarithmically. In other words, with the help of a ruler you can find approximately what mass corresponds to what brightness. Nor is this kind of estimating dishonest. After all, as said before, there is considerable variation in reality. If, say, you guessed that a mass of 1.1 Sol meant an energy output of 1.5, the odds are that some examples of this actually exist. You could go ahead with reasonable confidence. Anyway, it's unlikely that the actual values you picked would get into the story text. But indirectly, by making the writer understand his own creation in detail, they can have an enormous influence for the better.

  Returning to Cleopatra: an F? is hotter and whiter than Sol. Probably it has more spots, prominences, flares, and winds of charged particles sweeping from it. Certainly the proportion of ultraviolet to visible light is higher, though not extremely so.

  It is natural to suppose that it has an entire family of planets; and a writer may well exercise his imagination on various members of the system. Here we shall just be dealing with the habitable one. Bear in mind, however, that its nearer sisters will doubtless from time to time be conspicuous in its heavens, even as Venus, Mars, and others shine upon Earth. What names do they have—what poetic or mystical significance in the minds of natives or of long-established colonists?

  For man to find it livable, a planet must be neither too near nor too far from its sun. The total amount of energy it receives in a given time is proportional to the output of that sun and inversely proportional to the square of the distance between. Figure 3 diagrams this for the inner Solar System in terms of the astronomical unit, the average separation of Sol and Earth. Thus we see that Venus, at 0.77 a.u., gets about 1.7 times the energy we do, while Mars, at 1.5 a u., gets only about 0.45 the irradiation. The same curve will work for any other star if you multiply its absolute brightness. For example, at its distance of 1.0 a.u., Earth gets 1.0 unit of irradiation from Sol; but at this remove from a sun half as bright, it would only get half as much, while at this same distance from our hypothetical sun, it would get 2.05 times as much.

  That could turn it into an oven—by human standards, at any rate. We want our planet in a more comfortable orbit. What should that be? If we set it about 1.4 a.u. out, it would get almost exactly the same total energy that Earth does. No one can say this is impossible. We don't know what laws govern the spacing of orbits in a planetary system. There does appear to be a harmonic rule (associated with the names of Bode and Titius) and there are reasons to suppose this is not coincidental. Otherwise we are ignorant. Yet it would be remarkable if many stars had planets at precisely the distances most convenient for man.

  Seeking to vary the parameters as much as reasonable, and assuming that the attendants of larger stars will tend to swing in larger paths, I finally put Cleopatra 1.24 a.u. out. This means that it gets 1.33 times the total irradiation of Earth—a third again as much.

  Now that is an average distance. Planets and moons have elliptical orbits. We know of none which travel in perfect circles. However, some, like Venus, come clos
e to doing so; and few have courses which are very eccentric. For present purposes, we can use a fixed value of separation between star and planet, while bearing in mind that it is only an average. The variations due to a moderate eccentricity will affect the seasons somewhat, but not much compared to other factors.

  If you do want to play with an oddball orbit, as I have done once or twice, you had better explain how it got to be that way; and to follow the cycle of the year, you will have to use Kepler's equal-areas law, either by means of the calculus or by counting squares on graph paper. In the present exposition, we will assume that Cleopatra has a near-circular track.

  Is not an added thirty-three percent of irradiation enough to make it uninhabitable?

  This is another of those questions that cannot be answered for sure in the current state of knowledge. But we can make an educated guess. The theoretical ("black body") temperature of an object is proportional to the fourth root—the square root of the square root—of the rate at which it receives energy. Therefore it changes more slowly than one might think. At the same time, the actual mean temperature at the surface of Earth is considerably greater than such calculations make it out to be, largely because the atmosphere maintains a vast reservoir of heat in the well-known greenhouse effect. And air and water together protect us from such day-night extremes as Luna suffers.

  The simple fourth-root principle says that our imaginary planet should be about 20°C, or roughly 40° F., warmer on the average than Earth is. That's not too bad. The tropics might not be usable by men, but the higher latitudes and uplands ought to be pretty good. Remember, though, that this bit of arithmetic has taken no account of atmosphere or hydrosphere. I think they would smooth things out considerably. On the one hand, they do trap heat; on the other hand, clouds reflect back a great deal of light, which thus never has a chance to reach the surface; and both gases and liquids blot up, or redistribute, what does get through.

  My best guess is, therefore, that while Cleopatra will generally be somewhat warmer than Earth, the difference will be less than an oversimplified calculation suggests. The tropics will usually be hot, but nowhere unendurable; and parts of them, cooled by altitude or sea breezes, may well be quite balmy. There will probably be no polar ice caps, but tall mountains ought to have their eternal snows.

  Pleasant climates should prevail through higher latitudes than is the case on Earth.

  You may disagree, in which case you have quite another story to tell. By all means, go ahead. Varying opinions make science fiction yarns as well as horse races.

  Meanwhile, though, let's finish up the astronomy. How long is the planet's year? Alas for ease, this involves two factors, the mass of the sun and the size of the orbit. The year-length is inversely proportional to the square root of the former, and directly proportional to the square root of the cube of the semi-major axis. Horrors.

  So here we need two graphs. Figure 4 shows the relationship of period to distance from the sun within our solar system. (The "distance" is actually the semi-major axis; but for purposes of calculations as rough as these, where orbits are supposed to be approximately circular, we can identify it with the mean separation between star and planet.) We see, for instance, that a body twice as far out as Earth is takes almost three times as long to complete a circuit. At a remove of 1.24 a.u., which we have assigned to Cleopatra, its period would equal 1.38 years.

  But our imaginary sun is more massive than Sol. Therefore its gravitational grip is stronger and, other things being equal, it swings its children around faster. Figure 5 charts inverse square roots. For a mass of 1.2 Sol, this quantity is 0.915.

  —I—I—1-»—I. . I.—l i__l

  06 O.B 1.0 1.2 14 1,6 1 6 2 0

  FIG. 5 Inverse square root

  If we multiply together the figures taken off these two graphs —1.38 times 0.915—we come up with the number we want, 1.26. That is, our planet takes 1.26 times as long to go around its sun as Earth does to go around Sol. Its year lasts about fifteen of our months.

  Again, the diagrams aren't really that exact. I used a slide rule. But for those not inclined to do likewise, the diagrams will furnish numbers which can be used to get at least a general idea of how some fictional planet will behave.

  Let me point out afresh that these are nevertheless important numbers, a part of the pseudo-reality the writer hopes to create. Only imagine: a year a fourth again as long as Earth's. What does this do to the seasons, the calendar, the entire rhythm of life? We shall need more information before we can

  Although more massive than Sol, the sun of Cleopatra is not much bigger. Not only is volume a cube function of radius, which would make the diameter just six percent greater if densities were equal, but densities are not equal. The heavier stars must be more compressed by their own weight than are the lighter ones. Hence we can say that all suns which more or less resemble Sol have more or less the same size.

  Now our imaginary planet and its luminary are further apart than our real ones. Therefore the sun must look smaller in the Cleopatran than in the terrestrial sky. As long as angular diameters are small (and Sol's, seen from Earth, is a mere half a degree) they are closely enough proportional to the linear diameters and inversely proportional to the distance between object and observer. That is, in the present case we have a star whose breadth, in terms of Sol, is 1, while its distance is 1.24 a.u. Therefore the apparent width is 1 /1.24, or 0.87 what Sol shows to us. In other words, our imaginary sun looks a bit smaller in the heavens than does our real one.

  This might be noticeable, even striking, when it was near the horizon, the common optical illusion at such times exaggerating its size. (What might the psychological effects of that be?) Otherwise it would make no particular difference—since no one could safely look near so brilliant a thing without heavy eye protection—except that shadows would tend to be more sharp-edged than on Earth. Those shadows ought also to have a more marked bluish tinge, especially on white surfaces. Indeed, all color values are subtly changed by the light upon Cleopatra. I suspect men would quickly get used to that; but perhaps not.

  Most likely, so active a sun produces some auroras that put the terrestrial kind to shame, as well as occasional severe interference with radio, power lines, and the like. (By the time humans can travel that far, they may well be using apparatus that isn't affected. But there is still a possible story or two in this point.) An oxygen-containing atmosphere automatically develops an ozone layer which screens out most of the ultraviolet. Nevertheless, humans would have to be more careful about sunburn than on Earth, especially in the lower latitudes or on the seas.

  Now what about the planet itself? If we have been a long time in coming to that, it simply emphasizes the fact that no body— and nobody—exists in isolation from the whole universe.

  Were the globe otherwise identical with Earth, we would already have innumerable divergences. Therefore let us play with some further variations. For instance, how big or small can it be? Too small, and it won't be able to hold an adequate atmosphere. Too big, and it will keep most of its primordial hydrogen and helium, as our great outer planets have done; it will be even more alien than are Mars or Luna. On the other hand, Venus—with a mass similar to Earth's—is wrapped in gas whose pressure at the surface approaches a hundred times what we are used to. We don't know why. In such an area of mystery, the science fiction writer is free to guess.

  But let us go at the problem from another angle. How much gravity—or how little—can mankind tolerate for an extended period of time? We know that both high weight, such as is experienced in a centrifuge, and zero weight, such as is experienced in an orbiting spacecraft, have harmful effects. We don't know exactly what the limits are, and no doubt they depend on how long one is exposed.

  However, it seems reasonable to assume that men and women can adjust to some such range as 0.75 to 1.25 Earth gravity. That is, a person who weighs 150 pounds on Earth can safely live where he weighs as little as 110 or as much as 190. Of course,
he will undergo somatic changes, for instance in the muscles; but we can suppose these are adaptive, not pathological.

  (The reference to women is not there as a concession to militant liberationists. It takes both sexes to keep humanity going. The Spaniards failed to colonize the Peruvian altiplano for the simple reason that, while both they and their wives could learn to breathe the thin air, the wives could not bring babies to term. So the local Indians, with untold generations of natural selection behind them, still dominate that region, racially if not politically. This is one example of the significance of changing a parameter. Science fiction writers should be able to invent many more.)

  The pull of a planet at its surface depends on its mass and its size. These two quantities are not independent. Though solid bodies are much less compressible than gaseous ones like stars, still, the larger one of them is, the more it tends to squeeze itself, forming denser allotropes in its interior. Within the man-habitable range, this isn't too important, especially in view of the fact that the mean density is determined by other factors as well. If we assume the planet is perfectly spherical—it won't be, but the difference isn't enough to worry about except under the most extreme conditions—then weight is proportional to the diameter of the globe and to its overall density.

  Suppose it has 0.78 the (average) Terrestrial diameter, or about 6,150 miles; and suppose it has 1.10 the (mean) Terrestrial density, or about 6.1 times that of water. Then, although its total mass is only 0.52 that of Earth, about half, its surface gravity is 0.78 times 1.10, or 0.86 that which we are accustomed to here at home. Our person who weighed 150 pounds here, weighs about 130 there.

  I use these particular figures because they are the ones I chose for Cleopatra. Considering Mars, it seems most implausible that any world that small could retain a decent atmosphere; but considering Venus, it seems as if many worlds of rather less mass than it or Earth may do so. At least, nobody today can disprove the idea.