The Story of the Heavens

Comets contrasted with Planets in Nature as well as in their Movements—Coggia's Comet—Periodic Returns—The Law of Gravitation—Parabolic and Elliptic Orbits—Theory in Advance of Observations—Most Cometary Orbits are sensibly Parabolic—The Labours of Halley—The Comet of 1682—Halley's Memorable Prediction—The Retardation produced by Disturbance—Successive Returns of Halley's Comet—Encke's Comet—Effect of Perturbations—Orbit of Encke's Comet—Attraction of Mercury and of Jupiter—How the Identity of the Comet is secured—How to weigh Mercury—Distance from the Earth to the Sun found by Encke's Comet—The Disturbing Medium—Remarkable Comets—Spectrum of a Comet—Passage of a Comet between the Earth and the Stars—Can the Comet be weighed?—Evidence of the Small Mass of the Comet derived from the Theory of Perturbation—The Tail of the Comet—Its Changes—Views as to its Nature—Carbon present in Comets—Origin of Periodic Comets. In our previous chapters, which treated of the sun and the moon, the planets and their satellites, we found in all cases that the celestial bodies with which we were concerned were nearly globular in form, and many are undoubtedly of solid substance. All these objects possess a density which, even if in some cases it be much less than that of the earth, is still hundreds of times greater than the density of merely gaseous materials. We now, however, approach the consideration of a class of objects of a widely different character. We have no longer to deal with globular objects possessing considerable mass. Comets are of altogether irregular shape; they are in large part, at all events, formed of materials in the utmost state of tenuity, and their masses are so small that no means we possess have enabled them to be measured. Not only are comets different in constitution from planets or from the other more solid bodies of our system, but the movements of[Pg 337] such bodies are quite distinct from the orderly return of the planets at their appointed seasons. The comets appear sometimes with almost startling unexpectedness; they rapidly swell in size to an extent that in superstitious ages called forth the utmost terror; presently they disappear, in many cases never again to return. Modern science has, no doubt, removed a great deal of the mystery which once invested the whole subject of comets. Their movements are now to a large extent explained, and some additions have been made to our knowledge of their nature, though we must still confess that what we do know bears but a very small proportion to what remains unknown. Let me first describe in general terms the nature of a comet, in so far as its structure is disclosed by the aid of a powerful refracting telescope. We represent in Plate XII. two interesting sketches made at Harvard College Observatory of the great comet of 1874, distinguished by the name of its discoverer Coggia. We see here the head of the comet, containing as its brightest spot what is called the nucleus, and in which the material of the comet seems to be much denser than elsewhere. Surrounding the nucleus we find certain definite layers of luminous material, the coma, or head, from 20,000 to 1,000,000 miles in diameter, from which the tail seems to stream away. This view may be regarded as that of a typical object of this class, but the varieties of structure presented by different comets are almost innumerable. In some cases we find the nucleus absent; in other cases we find the tail to be wanting. The tail is, no doubt, a conspicuous feature in those great comets which receive universal attention; but in the small telescopic objects, of which a few are generally found every year, this feature is usually absent. Not only do comets present great varieties in appearance, but even the aspect of a single object undergoes great change. The comet will sometimes increase enormously in bulk; sometimes it will diminish; sometimes it will have a large tail, or sometimes no tail at all. Measurements of a comet's size are almost futile; they may cease to be true even during the few hours[Pg 338] in which a comet is observed in the course of a night. It is, in fact, impossible to identify a comet by any description of its personal appearance. Yet the question as to identity of a comet is often of very great consequence. We must provide means by which it can be established, entirely apart from what the comet may look like. It is now well known that several of these bodies make periodic returns. After having been invisible for a certain number of years, a comet comes into view, and again retreats into space to perform another revolution. The question then arises as to how we are to recognise the body when it does come back? The personal features of its size or brightness, the presence or absence of a tail, large or small, are fleeting characters of no value for such a purpose. Fortunately, however, the law of elliptic motion established by Kepler has suggested the means of defining the identity of a comet with absolute precision. After Newton had made his discovery of the law of gravitation, and succeeded in demonstrating that the elliptic paths of the planets around the sun were necessary consequences of that law, he was naturally tempted to apply the same reasoning to explain the movements of comets. Here, again, he met with marvellous success, and illustrated his theory by completely explaining the movements of the remarkable body which was visible from December, 1680, to March, 1681. [Pg 339] Fig. 69.—The Parabolic Path of a Comet. There is a certain beautiful curve known to geometricians by the name of the parabola. Its form is shown in the adjoining figure; it is a curved line which bends in towards and around a certain point known as the focus. This would not be the occasion for any allusion to the geometrical properties of this curve; they should be sought in works on mathematics. It will here be only necessary to point to the connection which exists between the parabola and the ellipse. In a former chapter we have explained the construction of the latter curve, and we have shown how it possesses two foci. Let us suppose that a series of ellipses are drawn, each of which has a greater distance between its foci than the preceding one. Imagine the process carried on until at length the distance between the foci became enormously great in comparison with the distance from each focus to the curve, then each end of this long ellipse will practically have the same form as a parabola. We may thus look on the latter curve represented in Fig. 69 as being one end of an ellipse of which the other end is at an indefinitely great distance. In 1681 Doerfel, a clergyman of Saxony, proved that the great comet then recently observed moved in a parabola, in the focus of which the sun was situated. Newton showed that the law of gravitation would permit a body to move in an ellipse of this very extreme type no less than in one of the more ordinary proportions. An object revolving in a parabolic orbit about the sun at the focus moves in gradually towards the sun, sweeps around the great luminary, and then begins to retreat. There is a necessary distinction between parabolic and elliptic motion. In the latter case the body, after its retreat to[Pg 340] a certain distance, will turn round and again draw in towards the sun; in fact, it must make periodic circuits of its orbit, as the planets are found to do. But in the case of the true parabola the body can never return; to do so it would have to double the distant focus, and as that is infinitely remote, it could not be reached except in the lapse of infinite time. The characteristic feature of the movement in a parabola may be thus described. The body draws in gradually towards the focus from an indefinitely remote distance on one side, and after passing round the focus gradually recedes to an indefinitely remote distance on the other side, never again to return. When Newton had perceived that parabolic motion of this type could arise from the law of gravitation, it at once occurred to him (independently of Doerfel's discovery, of which he was not aware) that by its means the movements of a comet might be explained. He knew that comets must be attracted by the sun; he saw that the usual course of a comet was to appear suddenly, to sweep around the sun and then retreat, never again to return. Was this really a case of parabolic motion? Fortunately, the materials for the trial of this important suggestion were ready to his hand. He was able to avail himself of the known movements of the comet of 1680, and of observations of several other bodies of the same nature which had been collected by the diligence of astronomers. With his usual sagacity, Newton devised a method by which, from the known facts, the path which the comet pursues could be determined. He found that it was a parabola, and that the velocity of the comet was governed by the law that the straight line from the sun to the comet swept over equal areas in equal times. Here was another confirmation of the law of universal gravitation. In this case, indeed, the theory may be said to have been actually in advance of calculation. Kepler had determined from observation that the paths of the planets were ellipses, and Newton had shown how this fact was a consequence of the law of gravitation. But in the case of the comets their highly erratic orbits had never been reduced to geometrical form until the theory of Newton showed him that they were parabolic, and then he invoked observation to verify the anticipations of his theory. PLATE XII. COGGIA'S COMET. (AS SEEN ON JUNE 10TH AND JULY 9TH, 1874.) [Pg 341] The great majority of comets move in orbits which cannot be sensibly discriminated from parabolæ, and any body whose orbit is of this character can only be seen at a single apparition. The theory of gravitation, though it admits the parabola as a possible orbit for a comet, does not assert that the path must necessarily be of this type. We have pointed out that this curve is only a very extreme type of ellipse, and it would still be in perfect accordance with the law of gravitation for a comet to pursue a path of any elliptical form, provided that the sun was placed at the focus, and that the comet obeyed the rule of describing equal areas in equal times. If a body move in an elliptic path, then it will return to the sun again, and consequently we shall have periodical visits from the same object. An interesting field of enquiry was here presented to the astronomer. Nor was it long before the discovery of a periodic comet was made which illustrated, in a striking manner, the soundness of the anticipation just expressed. The name of the celebrated astronomer Halley is, perhaps, best known from its association with the great comet whose periodicity was discovered by his calculations. When Halley learned from the Newtonian theory the possibility that a comet might move in an elliptic orbit, he undertook a most laborious investigation; he collected from various records of observed comets all the reliable particulars that could be obtained, and thus he was enabled to ascertain, with tolerable accuracy, the nature of the paths pursued by about twenty-four large comets. One of these was the great body of 1682, which Halley himself observed, and whose path he computed in accordance with the principles of Newton. Halley then proceeded to investigate whether this comet of 1682 could have visited our system at any previous epoch. To answer this question he turned to the list