ON COMETS
By R. d'E. ATKINSON
DURING the past sixty-five years only one really bright comet, "comet r9ioa," has followed a path which gave observers in northern lands a thoroughly satisfactory view ; and even that one was not visible for long. The comet which has recently attracted so much attention has already faded so rapidly that it is clear it will not break this run, and it is safe to say that relatively few people now living in this country have ever had a good view of a first-class comet. The interval of a lifetime is not particularly unusual ; " 1947n " is, as the letter " n " indicates, the fourteenth comet discovered during the year, but all the others were faint, as generally happens. The really bright ones have always been rare enough to excuse those who regarded them as portents.
Of course, educated people no longer succumb to this temptation ; but the fact that the bright comets are almost always unpredicted has encouraged a widespread belief (even in cultivated circles) that comets do not obey the ordinary rules, as though the precision 'which we have come to associate with the idea of astronomy were lacking, even in theory, from this particular branch of it. This view is incorrect ; and indeed many even of those who incautiously express it will hastily reconsider if one reminds them of the name of Halley. For Halley did, in fact, apply the ordinary rules of dynamical astronomy to the cometary problem, and did for the first time predict a comet's return. In principle, he might perhaps have done this merely on the basis of the observation that the interval of seventy-five or seventy-six years had separated the appearances of a number of bright comets ; 1531, 1607 and 1682 had had such comets, and 1758 could be expected to also. What he actually achieved was, however, much more notable than this kind of hit-or- miss guesswork. At a time when the necessary mathematical apparatus was still in a cumbrous and imperfect form, he worked out what the real orbits of a number of old comets must have been, so far as these could be determined from the rough and fragmentary observations available, and on studying his results he found that three of the orbits were very similar to each other in size, shape and position. Several comets might, of course (and sometimes do), follow each other in nearly identical orbits ; even though the intervals between them had been equal, there would be no guarantee that seventy-five years after the last one still anothe.• would appear ; but Halley also showed that the period appropriate to an orbit of this size is in fact about seventy-five years, so that it must have been the same comet each time. This is not to say that he was able to calculate the periods with great precision ; the observational data , were not nearly good enough to make that possible. But there is no -weakness in the theory as such ; the longest diameter of the orbit ' is intimately related to the period, and the relationship is exactly the same whether the body in question be a planet or a comet, and whetherethe orbit be almost a circle or so elongated an ellipse that it becomes difficult to say where the far end really is. In all cases, as the period increases the longest diameter increases too, though less rapidly.
Halley's comet, with a period of about seventy-six years, has an orbit whose far end lies a little beyond the orbit of Neptune. Most comets, however, and in particular all other bright ones, go much 'further away than this, and have periods very much longer. How long, it is really impossible to say ; we are fairly sure that the typical .,,,;.period (if there is such a thing) is greater than io,000 years, but there' simply is no way of estimating actual values in most cases. For all we know, many of the comets we have observtil may have periods of io,000poo years, or even more than that. Miturally, even if the lower figure is correct, we shall usually have no record at all of the last apparition, and when such a comet arrives again it is necessarily unpredicted, just for lack of data. But it is one thing to lack all relevant observations, and another to be unable to evaluate those that we have ; how is our uncertainty about the periods and sizes of the orbits which have been observed reconcilable with the proverbial accuracy of astronomy? There are two reasons. In the first place comets are difficult objects to locate with real precision at any time, and surprisingly hard to see at all unless they are near the sun, i.e., close to one end of their orbits ; and in the second place, all these very long orbits are almost exactly identical in relative shape, if one considers only a small region near one end.
A full discussion of this latter point would, of course, become rather technical. But we may indicate the kind of difficulty by con- sidering the speed of the comet at its nearest approach to the sun, where it moves fastest. If a comet with a period of 8,000 years came about as close to the sun as the earth is, and if at this point its speed were suddenly increased by only one part in Boo, the orbit would become a parabola ; the comet would just succeed in escaping from the sun's control altogether, and would never return. A very slightly smaller increase would convert the period into some hundreds of thousands of years, or some millions. Thus there is a range of speeds, all very much alike, which corresponds to a range of periods differing enormously ; the same is true of the shapes of those parts of the orbits which are close to the sun. It is•clear that, if we are to dis- tinguish between these very similar speeds and orbits, we must be able to make fairly accurate measurements over a reasonably extended range. It is just this which is difficult in the case of comets. The head of a comet is usually rather hazy and ill-defined ; even if there is a " nucleus " in the head, the unsymmetrical surroundings, running off into the tail (or tails), make the normal accuracy of astronomical measurement unattainable. In addition, as we have said, only a small fraction of the orbit is observable at all. A comet's light is due to the sun, even though it is not all simply reflected or scattered as in the case of the planets, and with increasing distance from the sun the amount of energy received falls off rapidly.
Also, of course, with increasing distance from the earth the fraction of the light that gets back to us falls off equally rapidly ; and a furthea factor of importance is that the comet itself usually varies in its effective " size." The head probably is an extremely loose assembly of rocks, stones, dust and gas, and when it gets close to the sun there is a tendency for dust and gas to be ejected from the centre of this assembly, though the exact mechanism is not fully known. Radia- tion-pressure forces some of this matter off in the direction away from the sun, to form the tail, and both the tail and the diffused outer parts of the head are less dense (or less large) at large distances from the sun than at small ; there is less comet to be lit up, as well as less radiation to do the lighting-up, and a more distant observer to see it, so that a comet which looks quite bright when it is close to the sun is already extremely faint by the time it is as far away as Jupiter. Jupiter is only about five times as far from the sun as we are, while a long-period comet will easily go to Soo times ; thus the observable portion of the orbit is only a very small fraction of the total, and a number of very different orbits would all fit the observations about equally well.
In the case of Halley's comet, even though the orbit is compara- tively small, and about thirty appearances have been recorded, we have stated the period only as " about seventy-six years." But the vagueness here does not imply either inadequate observations or imperfect theory ; on the contrary. Comets have orbits which are arranged much less systematically than those of the planets. The planets all keep well out of each other's way, but a comet may some- times pass fairly close to a planet, and the gravitational attraction of a heavy planet, such as Saturn or (especially) Jupiter can appreciably change its orbit. These perturbations are worked out in detail for all the important periodic comets, and such work is one of the crowning achievements of the Newtonian theory of gravitation. It sometimes happens that a long-period comet does in fact, in this way, obtain the small addition to its energy which suffices to let it escape altogether. Halley's comet has suffered small changes in its period, but nothing more, during its observed life.
The fact that the orbits were clearly unlike those of the planets, and, even more, the fact that a comet seemed an ephemeral and " mortal " thing, led the ancients to believe that they were not " heavenly " bodies at all. It was confidently declared that they were within the earth's atmosphere, below even the moon, since that was the only appropriate place, and indeed the only conceivable one, for such manifestly imperfect creatures. Tycho Brahe, the great Danish observer, showed that the comet of 1577 was in fact many times further away than the moon, just as he had, previously shown it for the " new " star of 1572. In so doing, he dealt one of the hardest blows that has ever been aimed at the classical attitude to Nature. His observations were followed, some decades later, by Kepler's rather similar discovery that even the heavenly and " perfect" planets do not move in orbits compounded of circles (the only " perfect " figure), but rather in ellipses with speeds that are not constant. Here again preconceived notions had to be abandoned. But the first major breach in the old system (though it *as not widely recognised as such at the time) was made by Tycho's cometary discovery. The process has continued without a break to this day. More and more we have had to admit that our intui- tions are not reliable guides to the Creator's thoughts ; we no longer venture to say on a priori grounds what is or is not " appropriate " at all, but confine ourselves to what is observed, or can be rigorously inferred from observation. In this field, comets still provide variety, excitement and opportunities for analytical skill.
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