Smallpox of Space

Article No. 15 in a study of the Solar System

by John W. Campbell, Jr. (pages 62-67 of August 1937's Astounding Stories)

THE early astronomers had no conception of the complexity of the solar system; perhaps, if they had, the science would never have started. The problems would have appalled them. Normally, we think of the solar system as being composed of the Sun, around which encircle nine large planets, a few small ones, and a few odd moons, making a total of -- oh, thirty members or so.

The total number of individual units composing the solar system, each unit following its own orbit under the influence of solar and planetary gravities, certainly exceeds 100,000,000,000. Astronomers must consider the effects of all those units. Roughly, the divisions are: 1 sun; 9 planets; 26 moons belonging to 6 planets (discovered to date; Neptune and Uranus probably have more); 3,000, or so, planetoids; 1,000, or more, comets; meteors to make the balance.

So far we have considered the arithmetic of the solar system; it has gone in nice, big, round units: 1, 2, 3, 4-9. Arithmetic properly deals with units; now comes the calculus of the system, the mathematics of the infinitesimal.

Of what importance are these infinitesimals, these 30,000 asteroids and planetoids? Calculus depends on multiplying the infinitely minute by infinity; the answer then can be any quantity. No matter how small the quantity, multiplied by something equal almost to infinity, it becomes staggeringly huge.

Consider the problem from this angle. Mathematicians and astronomers since the day of Newton have struggled with the famous problem of 3 bodies; most laymen consider that problem a sort of higher brain teaser, an interestingly difficult trick problem on which mathematicians may spend idle hours. Basically, the problem requires that mathematical formulas be developed such as to describe, fully and completely, the motions of three gravitating bodies. When solved it would permit the astronomer to substitute into standard formulas the quantities representing the masses of the bodies, their distances apart, and their velocities. By certain, specified manipulations the equations could then be solved to find their positions and velocities at any future time, however remote. Its solution, perhaps, seems merely interesting, but not vitally important, since we can solve the problem of 2 bodies, predict the positions and velocities of two gravitating bodies, by the laws originally worked out by Newton.

Actually, the problem of 2 bodies is an unreal fiction, of no practical importance in itself. Nowhere in the solar system does any such problem come up. This is the problem of purely theoretical interest, the toy for mathematicians, because it has no actual parallel in the system. That, not the problem of 3 bodies is the impractical theory.

To fully express the motions of three gravitating bodies is the closest of all astronomical problems. The Earth-Moon-Sun trio constitute exactly such a system, and as Charles Fort pointed out in Lo, astronomers cannot accurately determine the time or place of occurrence of a total, solar eclipse. Neither can the tides be exactly forecasted, nor will they be till the 3 bodies can be solved.

The immense importance of the problem of 2 bodies lies only in its ability to give approximate answers to the three bodies by considering them two at a time, two at a time, time and again, each time nibbling off a tiny bit more of the inevitable inaccuracy. At planetary distances, the Earth-Moon system can be considered one body, acting as a mass concentrated at the center of gravity of the two masses. Thus, until the real problem is solved, quite accurate approximations can be made. Actually, of course, the problem of the solar system represents a problem of an almost infinite number of bodies. We do not, and cannot know the fate of the system in the far future, because we cannot solve that problem.

The 3 bodies can be solved; eventually it will be. Shortly after it was recognized, Lagrange developed some special solutions. That is, if the astronomer is allowed to pick and choose, and place his bodies where he wishes, solutions can be attained for these highly artificial arrangements. Lagrange's original solutions were of two types; in the first, the three bodies so moved as to always form a straight line. In the other, the three form an equilateral triangle, whatever their masses. Both of these systems are eternally stable. The most complete discussion of the problem yet developed is due to Poincare, who developed several other, more complex special solutions.

CURIOUSLY, there is in the solar system an almost perfect example of one of these seemingly impractical, trick solutions. It involves Jupiter, the Sun, and some interesting bodies never mentioned in science-fiction: the Trojan planets, some of the most curious worlds of the entire system. They are unique in this way, too; since they do represent one of the few, rare, solutions to the problem, they are, unlike the Earth-Moon system which will eventually crash, stable. The Trojan planets will wheel about the Sun in perfect stability for long æons after the Moon has crashed to Earth, strange little worlds circling in orbits made rigid and secure by the influences of the mightiest masses of the solar system; the Sun itself, and giant Jupiter.

In a sense, the Trojan planets are members of the general class called planetoids or asteroids. The first of the planetoids was discovered on the first day of the first month of the first year of the nineteenth century, January 1, 1804 [ed 1801]. Piazzi, on that night, discovered Ceres*, and calculations developed by the German mathematician Gauss soon showed that it was in an orbit between Mars and Jupiter.

By 1807 Pallis [ed Pallas], Juno and Vesta had been added to the list of planets in orbits between Mars and Jupiter. In 1845 another was discovered. Since 1847 they have discovered at least one every year. The thing had evidently gotten somewhat out of hand. One was all right but at present about 1,200 planetoids are known, circling in and about that region ranging in size from Ceres, the largest of them and only 485 miles in diameter, down to mere cosmic boulders 5 miles or so across, things not even round enough to merit the term diameter.

So out of hand id it get, in fact, that astronomers began to feel that there must be thousands, if not tens of thousands of worlds there. The best guess as to the total number at present seems to be about 30,000 of all sizes, shapes and types. At first, astronomers had thrilled to the new discoveries, but the sheer number soon become [ed. became] boring, and labor-saving devices were invented.

At present, asteroid discoveries are made by mass-production machinery. Two general methods are used, each based on the same idea. In the earlier method, a telescopic camera is mounted on a clockwork drive and adjusted so that it moves exactly fast enough to offset the Earth's rotation on its axis. The stars then appear to stand still. They form sharp, pin-point images on the exposed plate. The planetoids, however, are members of the solar system, and move relative to Earth; Earth's motion in its orbit shifts them across the background of stars. The finished plate, after hours of exposure, will show the rich, star-strewn background of stars. The finished plate, after hours of exposure, will show the rich, star-strewn background of points, marred by a few, short, stubby lines -- smears produced by moving asteroids. Planetoids discovered by the dozen while you wait.

The second method is even more sensitive. Since all the asteroids are almost equally distant from Earth, revolving as they do in approximately equal orbits, they must all move in just about the same manner, shift across the plate at about the same rate. Fine. Then move the plate by means of the clockwork at a rate such as to exactly offset the motion of the average planetoid. Now our plate will show the stars blurred and smeared by motion, while the asteroids will appear as nice, clean points, in general with only a tiny bit of blurring in one direction or the other, dependent on whether one was a bit nearer or more distant than average. The advantage is that all the light reaching the plate from one tiny asteroid builds up, hour after hour, on one small point of the plate, and bodies so dim as to be unable to mark the plate when moved across, leave a firm impression. This method, however, may miss asteroids in highly eccentric orbits at such distances as to make them move almost as slowly as the stars.

THIS WORK is done largely by amateurs, but what amateurs! To find a new planetoid means that you must first show that it is not an old one. Almost 1,200 are known and recorded. If the amateur suspects he has discovered a new one, he must determine its orbit, then compare it with known orbits, and thus show that it is not an old one. They have simplified orbital calculations to the utmost, but it remains inevitably a mathematical problem not to be lightly undertaken by grammar-school arithmeticians. Further, the orbits cannot be determined just more or less, roughly, because of the immense complexity and the close parallelism of those already known.

If the asteroid system were modeled, each body and its orbit being shown by a bead on a loop of wire, it would be impossible to remove one of the intertwining, interwoven, tangled orbits without pulling out almost all the rest. The model would resemble a steel-wool scouring pad.

Some of the planetoids follow orbits almost exactly circular, some have orbits so elliptical and elongated they actually are more eccentric than those of many comets.

Most of them lie almost exactly in the plane of the orbits of the large planets, some cut out at weird angles, as much as 30° out of the plane. Further, those that slant out at this angle usually have very eccentric orbits as well. The orbits are neither concentric nor evenly spaced. Although most of them lie always between Mars and Jupiter, some cross over to distances less than that of Mars, one, at least, approaching nearer the Sun than does Earth. On the other hand, many loop out far beyond Jupiter, one, again, going on out to the depths of space beyond Saturn.

The orbits are not by any means evenly distributed, and, furthermore, there are sharp and definite breaks; concentric rings about the Sun where no asteroid can have its orbit, just as there are breaks in the rings of Saturn, and for similar reason. At any given distance from the Sun, a fixed orbital period is required for stability, the period being determined rigidly by the characteristics of solar gravity.

At those distances which require an orbital period of 5.94 years, 3.95 years or 8.795 years there are no planetoids. If there were -- they would be in phase with the orbit of Jupiter; periodically the enormous mass of the Jovian System would lay violent strains on them, twisting their orbits aside viciously, for Jupiter's period is twice 5.94 years, three times 3.95 years, and 4/3 of 8.795 years; commensurable periods cannot be stable.

In this action, not only the mass of Jupiter would act, but the combined mass of 5 worlds, each planetary size in its own right: Jupiter, Io, Europa, Ganymede and Callisto. This enormous mass combines to act as a mighty whip to force every body in the solar system to avoid synchronization. Saturn itself would not dare to approach close synchronization with that overwhelming mass.

The asteroids themselves vary as widely as their orbits, in size, character and every other particular. Only the largest have been investigated as individuals: Ceres, 485 miles in diameter; Pallas, 304 miles; Vesta, 243 miles; and Juno, 118 miles through. The reflecting power of the surfaces are our only clue to their nature, for, being so small, they have very little mass, and hence no noticeable perturbing power.

The mass of Venus can be deduced from the way it affects Mercury and Earth; the mass of Mars can be accurately determined from the motions of its satellites. Ceres and the other planetoids are too small for perturbation work, and although they may well have satellites in a region so richly populated with small bodies moving at almost the same speed, we cannot detect any. Since they are so small it is practically certain that they have no atmospheres; the light reflected from them does not pass through a gaseous medium other than Earth's own atmosphere, and hence the spectroscope is useless. A mirror can show equally well the spectrum of a sodium flame or that of the Sun, but in neither case does the reflected light say much of the mirror's composition.

HOWEVER, the reflection intensity, the "albedo" does indicate some things of interest. Ceres reflects light to about the same degree as does our Moon. From that we might reasonably deduce that, like the moon, its surface was a cragged, mountainous region of colossal heights and fearsome gorges, with great plains limited by sharp-dropping horizons. They are, no doubt, scarred by the millions of meteors that have pounded into its unweathered surface. Juno is a bit more reflective than Mars, Pallas about equally. Their surfaces may be made up of less-cragged rocks, or perhaps a coating of rock dust, broken by the spalling action of sudden, furious blasts of solar heat alternating with interplanetary cold.

But Vesta is as reflective as the silvery, cloud-wrapped surface of Venus or Jupiter! It is impossible that so tiny a body has either atmosphere or cloud; even ice would be impossible in space, for ice has a low, but distinct vapor pressure, and during the æons would dissipate into space. Nothing more volatile than mercury metal (it throws off distinct traces of vapor, which become visible when viewed under a mercury-vapor arc light) could survive astronomic time on Vesta. Yet its reflective power equals that of the planets wrapped with the most dense and cloud-filled atmosphere. What the solution is we do not know. A guess might suggest that it was composed largely of quartz crystals, or masses of white rock such as calcium sulphate, or aluminium oxides.

The oldest theory of the origin of the planetoids is the suspicion that they may represent the remains of an exploded primal planet, whose parts, though blasted by some colossal violence, still follow the ancient orbit. If so, then all the orbits should cross at one point, were it not that during the ages Jupiter's attraction, the cross haul and tug of Saturn and Mars, have served to distort those orbits beyond recognition. However, certain other properties of the orbits would remain forever, sufficiently stable to show, even to-day, that they had once started from a common point.

Laborious investigation has been undertaken, and this has shown that the orbits cross -- some few of them. But not in one point -- in several, as a matter of fact. There are families of planetoids that had a common origin somewhere in space, but not one common origin -- many. And there is one property that throws even graver doubt on this question. Many of the asteroids rotate on their axes, and the direction of this rotation can be determined in those cases (which are numerous) where there is one bright spot, or a brighter side of the planetoid. All those investigated rotate in the same direction, in the direction that those bodies created in the original creation turn. Would the flying fragments of a broken planet rotate all in the same direction?

Let us return for a moment to the effects of Jupiter's mass on the planetoid orbits. He would, evidently, make an orbit of half his period unstable, one of 2/3, or 3/4. Bodies in such orbits would be driven outward, or forced inward. Saturn, too, would have a lesser effect, stirring and wavering the orbits. Forced back and forth, changing and shifting, the harassed planetoids would seem some measure of stability, an orbit that would not be disturbed in any way, incommeasurable with all perturbing bodies.

But, there is one, and only one: Jupiter's own orbit. Nothing dares to get in step with that mighty mass. Unless it gets exactly in step, for Jupiter cannot perturb a body rotating in its own orbit, at exactly the same rate, so that it never comes nearer or gets farther away from the planet. Remember that one of the special solutions requires that the three bodies, whatever their mass, form the vertices of an equilateral triangle. The Sun is one mass, Jupiter the second -- and, of course, to be an equal distance from the Sun, the third point must lie in Jupiter's orbit. Further, there are 2 possible points in that orbit, one a distance ahead of Jupiter equal to the distance from Jupiter to the Sun, one an equal distance behind.

The Trojan planets illustrate this solution neatly; 5 of these bodies oscillate about the point ahead of Jupiter, and 4 about the second point behind him. Their orbit is perfectly stable, it being one of the 3-body solutions, and defended by the combined masses of Jupiter and his 4, planet-sized satellites. Probably once planetoids were harassed and whipped about by the cross tugs of planetary reactions; they were driven out, till, at last, they found the most stable situations in the entire solar system; the 3-body solution involving the 2 greatest masses of the system: Jupiter and the Sun itself.

WHAT VALUE can the asteroids have to man? When space travel is established, the asteroids will be useless, but their economic importance will, unfortunately, be undeniable. They will, so to speak, rate with disease: valueless things that cause all sorts of trouble.

First, the only use that has been proposed for them involves mining them for precious metals, or hauling them off bodily for their content of nickel iron. There is no doubt that they do, many of them, consist of pure masses of nickel-steel armor piercing projectiles. That inextricable tangle of orbits makes it impossible to work with even reasonable safety among them; they were all revolving in neat, concentric orbits, the danger of collision would be small, because the space ship bent on mining could match the speed of the local asteroid field, and so be in no danger of high-velocity collisions. The asteroids are the anarchists of the system; they don't behave that way; all those looped, eccentric orbits would come crashing through at high velocity, making it impossible to match the speed of all those in the neighborhood.

Furthermore, in discussing interplanetary dividends it was pointed out that Pittsburgh could compete successfully with pure, free iron on the surface of the Moon. If free iron could not pay its way from the Moon, it certainly has no chance of paying its way from the deadly asteroid belt. Asteroid mining is not likely to pay very early in space travel, that is certain. Imagine the danger of prospecting, and developing. Living on Ceres, for instance, would be like establishing a mining camp in No Man's Land during the Battle of the Somme.

Most of that cosmic scrap, such as meteors and, probably, the asteroids contains platinum, silver and other precious metals. Perhaps they would pay for the work. The man who attempts that must treat the nickel-steel alloy containing the platinum solely as a peculiar kind of platinum ore. And, man, it's a honey! You can't crush it. Only the toughest tools will cut it up. It's a notoriously stubborn alloy (armor plate) and it is dense, heavy stuff. Before separation can be affected, it must be dissolved in acid, or some similar reagent.

The iron and nickel, at any rate, are merely annoyances, not secondary sources of profit. The best illustration of that trouble is on our own Earth: Monel metal. That is an alloy of copper and nickel. The nickel ores contain definite, recoverable amounts of platinum, iridium, gold, silver, and a host of other precious metals. However, so does the finished Monel metal. It doesn't pay to go to the trouble of extracting them.

And no one can doubt that the asteroids promise to be the space pilot's nightmare. That they will for a moment consider battering through the asteroid belt is insane; naturally, they will dodge it by the simple process of going north or south* out of the plane of the ecliptic, and dodging over the belt before returning to the plane. But since some of the asteroids follow orbits inclined more than 30° to the plane, that dodge will be a detour of hundreds of millions of miles, and days of travel. And a nice, judicial balance between "How close to the plane can I go without getting ruined?" and "How many days is this blasted detour going to take?"

No, nobody is likely to become fond of these smallpox of space.


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