WHEN Herschel first observed Uranus, you will remember, he discovered it was a member of the solar system, and reported it to the Royal Society as a comet. That planets unknown to the scientists of the ancient world could exist, and did exist, was a theory held by the sound thinkers of the day. They had no legitimate reason to think so, no basis for such a belief. Those who did consider that planets beyond Saturn really existed were not "ahead of their day"; they were wishers. They hoped there were planets, but had no reason whatever to believe there were.
Since Herschel's day, Neptune and Pluto have been discovered. The discovery of Uranus had opened to the scientific world a new field of endeavor; the discovery of new planets. For, having found one, it gave logical reason to believe that there might be still more undiscovered. The discovery of further worlds ceased to be the vain daydreams of a night-prowling astronomer; it now had scientific, orderly thought behind it.
Two more have been discovered? Are there yet more worlds beyond these worlds? Can we, will we, in the next decade or so discover another world, lost now in the blazing sheet of stars the heavens display?
It is impossible to say with absolute assurance that we won't, because any searcher of the skies may stumble on one. That planets more distant than Pluto may exist is unquestionable; the Sun's gravitational control rules space rigidly for a distance certainly ten times greater than the radius of Pluto's orbit. Probably it could maintain effective control at a distance one hundred times as great. Some of the long-period comets must retire to those immense distances, perhaps wavering in the farthest, uncertain fringes of the Sun's "sphere of influence," where cross pulls of Proxima Centaura and the more distant stars make the orbits hesitate.
There is room there for a hundred unknown worlds. They could be there. But are they? Have we any reason, not mere guess, to believe they are?
It is in connection with these questions, perhaps, that the seemingly similar, but actually widely differing stories of the discoveries of the two outermost known planets are most interesting. Both these planets were found by intention, not blundering fate, or obvious brilliance in the skies, and in this they are unique. Yet, though both were found by logic, each case typified one of the two possible means of planetary search: mathematical research, and planned, patient, persistent mapping of the heavens.
Uranus was, in more sense than one, the key to the question of further planets. Primarily, it gave reason to believe they existed, and, secondarily, it gave proof that Neptune existed even before it was found. Herschel's original announcement of the discovery of a "comet" was proven wrong, because, on continuing observations of the new body, it was soon evident that the slow movement of the object did not correspond with the motion a comet must display; it was typically planetary. By their orbits shall ye know them, so to speak. Herschel's original, scanty observations had sufficed to show that it moved, but not how it moved.
Theoretically, of course, three points determine a circle -- any three points. It is possible to determine the approximate orbit of a body moving about the Sun by three observations (really cheating a bit to say three, because if it revolves about the Sun, then the Sun is a fourth relevant point), but, despite theory, in practice, any three points will not serve; they must be sufficiently separated. That was the reason it was not until some time had passed the Uranus was recognized as a planet.
URANUS makes one revolution about the Sun in approximately 85 years, so that three points determined at intervals of a year, even, show only a minute fraction of the total, vast arc, and determine it inadequately. Decades of observation were needed to fix the exact motions of the planet. Even to-day we have known and followed the planet for less than 2 full years since it was discovered in 1781, 156 years ago. What, then, was the situation of the astronomers in 1791, when Uranus had been followed for the Uranian equivalent of about a month and a half?
Evidently their data would have been highly erratic, but for one thing: Many astronomers before Herschel had seen that telescopically brilliant body, but had always recorded it as a star, in drawing up their star maps. They located this "star," and carefully put a small point on their maps (all done laboriously by hand) for the benefit of future researchers. There were no photo-engraving processes in those days, and copying those delicately drawn maps was far beyond the ordinary printer. They had a very, very limited circulation, else Uranus would have been found before.
But, once found, those maps were immediately consulted. "Why didn't old So-and-so record this planet? He examined that area --" Knowing the approximate orbit, it was easy to say that it should have been just about there in 1720, for example, and examine the maps of 1720. When they did find it, and on another map of, say, 1760, they had three points in its orbit covering more than a whole revolution. That should fix the orbit accurately.
But now a new factor enters into the problem. Neptune, as yet undiscovered, was out there in space, more massive and larger than Uranus itself. (Neptune is 31,000 miles in diameter -- 17.16 times as massive as Earth; Uranus is 30,000 miles in diameter and 14.7 times as massive as Earth.) Those old observations and the observations made in the 1780s were used to draw up tables of the planet's motions. But observations made through the years, in 1780--1790--1800, began to disagree with the predicted values. The blamed planet "warn't whar it orter bin," so to speak. By 1820 there was no question about the discrepancies; they were, to astronomers, huge. Their existence could not be denied.
Three things were possible: first, that the old observations made when Uranus was thought to be a star, were in error. They were made years ago, when the telescopes were less perfect (thought the astronomers of 1820) and, further, they didn't know the old records were made carefully, while they knew very well that they had worked hard over the observations they themselves had made. Furthermore this hypothesis was attractive, because it was the old observations (since they gave the greatest separation of points, and hence fixed the orbit more rigidly) which had the greatest influence on the calculations. Dropping them eliminated the errors fairly well. But to do so meant accusing the old observers of brutal error.
The second possibility was even more distasteful: Newton's law might be wrong. Gravity had never been proven at such immense distances. It had been know that Saturn was not quite obeying the law for many years (due to the then undiscovered Uranus) and the though this had been accounted for now, for the most part, there still remained some irregularity, and there was this new and greater irregularity of Uranus.
Was Newton wrong? His formula read F=GMm/d2, but suppose he were wrong to this extent, that the exponent should have been not 2 but 2.0000001 or 1.999999, for instance. Those minute differences would become mighty when applied to billions of miles. Perhaps values that had not been suspected lay in that. The possibility made it even more vitally necessary that the irregularity be accounted for, lest they find that their whole structure was at fault at the very root.*
The third explanation conceivable was the possibility of a new and undiscovered planet. This idea was by far the most interesting and pleasing, but it was not without its thorny side. By 1820 it was a very much sought-for world, and various people had suggested trying to find it by calculation, working back from observed effects produced on Uranus.
Sir George Airy, astronomer royal of England, and a man who should have known if any one should, declared later than 1840 that the mathematical problem of predicting the unknown planet's position could not be solved. But the errors in Uranus' position by 1840 were intolerable. (They amounted actually to an angular distance about 2/3 as great as the smallest angle detectable to the unaided eye.)
WHAT CHANCES had they for locating that (or, for that matter, have we for locating any other) unknown planet? There are two available methods: the Adams-Leverrier method and the Columbus method. The latter is the hunt-and-discover system, and while it worked for Uranus, the problem was different with Neptune and, of course, Pluto.
Neptune is entirely beyond the range of human vision -- much too faint. Today, it would be possible to discover it fairly readily by photographic star mapping, which makes it possible to map a whole region of the heavens accurately, beyond question, in a single evening. At that time every star had to be marked by human eye and human hand.
Furthermore, since it was so faint, a large magnification was needed to see it. Say you needed a tenfold magnification. Then, in the first place, there would be ten times as great an area to map -- because you have magnified not only Neptune but all the heavens as well. And, worse yet, the magnification that brings Neptune into view, brings also an immense number of stars which must all be mapped. And here the factor is not 10, but an even greater number. There are approximately 2,000 stars of the 6th magnitude, the brightness of Uranus. But there are 27,000 stars visible when 10 times the optical power is used. Pluto needs about all the optical power available for any real observation. By that time 890,000,000 stars are visible. The thing gets out of control.
To find Neptune by direct search would have required 2 complete mappings, each showing every body within reach of the maximum optical power. 2 were needed, made at different times, in order that motion of the planet during the interval might be detected. Each of the tens of thousands of bodies would have to be observed and pointed on the finished work by laborious manual operation, in that day before photography.
Finally, if the entire, immense labor were done, the 2 maps would have to be searched with utmost accuracy, each of the thousands of points being separately compared. If, even after this, no body were found that indicated a planetary motion, that would be negative proof; it would mean only that no planet detectable in their optical apparatus existed. It would not mean that no planet existed.
That left the mathematical analysis as the only practicable hope. But -- was it practicable? Sir George Airy said was not. He had reason to. In solving a geometrical problem the proposition usually starts off something like this: A equals B, and Angle C equals B; to find -- or to prove --- But always, Given: ---- But -- nature wasn't giving a thing. Probably the planet was in the plane of the ecliptic, the same plane that all the other planetary orbits lay in. But -- how far out? Was the orbit circular, like the profile of an egg, or like the profile of a dirigible? Was it an unsuspected giant, like Jupiter, 300 or more times as massive as Earth, and very distant, or a light planet, perhaps no larger than Earth, and comparatively close? Both might have the same effects. Not quite, because the big, massive planet, very distant, would have a longer year than the smaller, nearer planet. But -- to detect this a period of something like 200 Earth years would be needed.
That greater time had really been needed was indicated by the final, brilliant work of Adams, of Cambridge, England, and of Leverrier, of Paris -- 2 comparatively young men who, independently, solved the problem with sufficient accuracy to locate the planet. (Their results agreed to within one part in 300, and the planet was within one part in 300 of their results.) Leverrier assumed the new planet to be more massive than Neptune actually is, and that it was at a greater average distance from the Sun. But -- his mathematics was very sound; the errors canceled somewhat, because he also assumed an egg-shaped orbit, and that Neptune, was, at the time of the work -- 1846 -- at or near perihelion, and hence actually nearer the Sun than his average distance. The result was that his distance-at-the-time and actual distance came out pretty close. Had he had observations of Uranus extending over 200 years, he would have seen at once that the average distance of Neptune was less than he had assumed.
NOW, about further planets? Pluto is an excellent answer, for though the story of the discovery of Pluto and the history of Neptune's discovery seem very similar on the surface, they are not. Neptune was definitely discovered by mathematical reasoning based on known facts and a sprinkling of assumptions. There certainly was no question about the vagaries of Uranus' motion.
But Pluto was not discovered as a result of mathematical calculations. It was obvious that, as Neptune had been discovered by mathematical research, others would attempt to similarly locate trans-Neptunian planets. Of all those who tried, Percival Lowell made the most thorough investigation of all pertinent data.
Remember this, however, in considering the problem; in general, the planets taper off at both ends, so to speak. From Mercury to Jupiter they increase in size fairly regularly, the one exception being Mars; and from Jupiter out they dwindle, Saturn smaller than Jupiter, Uranus and Neptune smaller than Saturn, and about equal in size, Pluto smaller yet. But Jupiter is 340,000,000 miles beyond Mars, Saturn 400,000,000 miles beyond Jupiter. And then, suddenly, 800,000,000 miles more to Uranus, a round billion to Neptune, and nearly another billion to Pluto. Pluto is farther from its nearest known neighbor, then, than Saturn, the most distant of the anciently known planets, is from the Sun. The distances have become swollen, bloated figures, beyond our comprehension. Gravity, meanwhile, weakens as the square of the distance increases (and a billion squared is 1,000,000,000,000,000,000), while the planets are growing lighter. The effects to be detected are growing rapidly fainter.
Further, century on century must elapse before Neptune and Pluto are twice in conjunction at their nearest approaches. With infinite slowness, Neptune creeps ahead of Pluto in its vast sweep. 164 years elapse before Neptune makes one sweep. 250 years pass before Pluto makes one, and then Neptune is only about half a lap ahead of Pluto. It must make another complete lap before conjunction occurs once more, and maximum effects are visible. Meanwhile, Uranus and Saturn have several times tugged on Neptune as they rushed past.
Actually, with only about 80 years (half a Neptunian year) of observations on which to base his calculations, Lowell's figures could not be accurate. They were not, and his mathematical planning was a work of genius, frustrated by a lack of data. But he laid another plan. Lowell discovered Pluto, even after his own death, by the plan he had laid. Wide-angle telescopic pictures mapped the whole region of the sky where the planet might be. Stars do not move; but even Pluto must move slowly. Between two photographs of the same region taken at different times, motion existed. By projecting the two plates alternately in rapid succession, the same effect that makes the movie projector possible came to the aid of the searchers. The motionless stars remained unchanged, whether viewed singly, or in this flicker projector. Pluto, however jumped and wavered. It was the effect of super-super-high-speed movie. Pluto's creep was amplified a million times to a darting race.
Lowell had calculated the effects produced by a hypothetical planet unsuccessfully. The reasons are obvious: mathematical inquiry breaks down hopelessly without data. There simply are not enough data. Pluto was found not by the logic of mathematics, but by the logic of planned persistence.
THEN, evidently, no trans-Plutonian planet can be found by mathematical logic, for the same reasons. It must be still more remote, its effects still more slow to manifest themselves. It is probably a pretty safe statement to say that no planet will be found beyond Pluto by mathematical prediction until a period of 500 years or so has elapsed, permitting the gravitational disturbances to accumulate, and accurate plots of Neptune and Pluto to be made.
The effects Lowell had calculated on, in assuming his hypothetical planet, had not permitted him to find Pluto, for Pluto did not at all fulfill the specifications he suggested. It was much, much too small to produce the changes in other bodies from which Lowell had worked. It was not exactly where he had said it should be (though this meant less). The great point was that unless the planet is, most improbably, dense, it cannot possibly be the object that Lowell's mathematics referred to. And it is considerably nearer than Lowell's hypothetical planet.
It will be a fearful task to find yet more distant planets. We do not even know that the laborious search would be repaid by a discovery; it may be that Pluto is the last, the ultimate planet of the solar system. There must be a limit somewhere; perhaps Pluto is that limit.
Remember this though: Percival Lowell was no fool. He worked for years gathering and selecting data, calculating, trying to predict the unknown position of an unknown planet. When, years later, Pluto was found, it became evident that, for all his careful study, the data did not apply to the new planet.
To what, then, did they apply?
Article No. 14 in the Study of the Solar System
by John W. Campbell, Jr.
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