The distances to which different comets recede from the sun are equally various. While Encke's comet performs its entire revolution within the orbit of Jupiter, Halley's comet recedes from the sun to twice the distance of Uranus; or nearly thirty-six hundred millions of miles. Some comets, indeed, are thought to go a much greater distance from the sun than this, while some are supposed to pass into curves which do not, like the ellipse, return into themselves; and in this case they never come back to the sun. (See Fig. 34, page 153.)
Comets shine by reflecting the light of the sun. In one or two instances, they have been thought to exhibit distinct phases, like the moon, although the nebulous matter with which the nucleus is surrounded would commonly prevent such phases from being distinctly visible, even when they would otherwise be apparent. Moreover, certain qualities of polarized light,—an affection by which a ray of light seems to have different properties on different sides,—enable opticians to decide whether the light of a given body is direct or reflected; and M. Arago, of Paris, by experiments of this kind on the light of the comet of 1819, ascertained it to be reflected light.
The tail of a comet usually increases very much as it approaches the sun; and it frequently does not reach its maximum until after the perihelion passage. In receding from the sun, the tail again contracts, and nearly or quite disappears before the body of the comet is entirely out of sight. The tail is frequently divided into two portions, the central parts, in the direction of the axis, being less bright than the marginal parts. In 1744 a comet appeared which had six tails spread out like a fan.
The tails of comets extend in a direct line from the sun, although more or less curved, like a long quill or feather, being convex on the side next to the direction in which they are moving,—a figure which may result from the less velocity of the portion most remote from the sun. Expansions of the envelope have also been at times observed on the side next the sun; but these seldom attain any considerable length.
The quantity of matter in comets is exceedingly small. Their tails consist of matter of such tenuity, that the smallest stars are visible through them. They can only be regarded as masses of thin vapor, susceptible of being penetrated through their whole substance by the sunbeams, and reflecting them alike from their interior parts and from their surfaces. It appears perhaps incredible, that so thin a substance should be visible by reflected light, and some astronomers have held that the matter of comets is self-luminous; but it requires but very little light to render an object visible in the night, and a light vapor may be visible when illuminated throughout an immense stratum, which could not be seen if spread over the face of the sky like a thin cloud. "The highest clouds that float in our atmosphere," says Sir John Herschel, "must be looked upon as dense and massive bodies, compared with the filmy and all but spiritual texture of a comet."
The small quantity of matter in comets is proved by the fact, that they have at times passed very near to some of the planets, without disturbing their motions in any appreciable degree. Thus the comet of 1770, in its way to the sun, got entangled among the satellites of Jupiter, and remained near them four months; yet it did not perceptibly change their motions. The same comet, also, came very near the earth; so that, had its quantity of matter been equal to that of the earth, it would, by its attraction, have caused the earth to revolve in an orbit so much larger than at present, as to have increased the length of the year two hours and forty-seven minutes. Yet it produced no sensible effect on the length of the year, and therefore its mass, as is shown by La Place, could not have exceeded 1/5000 of that of the earth, and might have been less than this to any extent. It may indeed be asked, what proof we have that comets have any matter, and are not mere reflections of light. The answer is, that, although they are not able by their own force of attraction to disturb the motions of the planets, yet they are themselves exceedingly disturbed by the action of the planets, and in exact conformity with the laws of universal gravitation. A delicate compass may be greatly agitated by the vicinity of a mass of iron, while the iron is not sensibly affected by the attraction of the needle.
By approaching very near to a large planet, a comet may have its orbit entirely changed. This fact is strikingly exemplified in the history of the comet of 1770. At its appearance in 1770, its orbit was found to be an ellipse, requiring for a complete revolution only five and a half years; and the wonder was, that it had not been seen before, since it was a very large and bright comet. Astronomers suspected that its path had been changed, and that it had been recently compelled to move in this short ellipse, by the disturbing force of Jupiter and his satellites. The French Institute, therefore, offered a high prize for the most complete investigation of the elements of this comet, taking into account any circumstances which could possibly have produced an alteration in its course. By tracing back the movements of this comet, for some years previous to 1770, it was found that, at the beginning of 1767, it had entered considerably within the sphere of Jupiter's attraction. Calculating the amount of this attraction from the known proximity of the two bodies, it was found what must have been its orbit previous to the time when it became subject to the disturbing action of Jupiter. It was therefore evident why, as long as it continued to circulate in an orbit so far from the centre of the system, it was never visible from the earth. In January, 1767, Jupiter and the comet happened to be very near to one another, and as both were moving in the same direction, and nearly in the same plane, they remained in the neighborhood of each other for several months, the planet being between the comet and the sun. The consequence was, that the comet's orbit was changed into a smaller ellipse, in which its revolution was accomplished in five and a half years. But as it approached the sun, in 1779, it happened again to fall in with Jupiter. It was in the month of June that the attraction of the planet began to have a sensible effect; and it was not until the month of October following, that they were finally separated.
At the time of their nearest approach, in August, Jupiter was distant from the comet only 1/491 of its distance from the sun, and exerted an attraction upon it two hundred and twenty-five times greater than that of the sun. By reason of this powerful attraction, Jupiter being further from the sun than the comet, the latter was drawn out into a new orbit, which even at it's perihelion came no nearer to the sun than the planet Ceres. In this third orbit, the comet requires about twenty years to accomplish it's revolution; and being at so great a distance from the earth, it is invisible, and will for ever remain so unless, in the course of ages, it may undergo new perturbations, and move again in some smaller orbit, as before.
With the foregoing leading facts respecting comets in view, I will now explain to you a few things equally remarkable respecting their motions.
The paths of the planets around the sun being nearly circular, we are able to see a planet in every part of it's orbit. But the case is very different with comets. For the greater part of their course, they are wholly out of sight, and come into view only while just in the neighborhood of the sun. This you will readily see must be the case, by inspecting the frontispiece, which represents the orbit of Biela's comet, in 1832. Sometimes, the orbit is so eccentric, that the place of the focus occupied by the sun appears almost at the extremity of the orbit. This was the case with the orbit of the comet of 1680. Indeed, this comet, at it's perihelion, came in fact nearer to the sun than the sixth part of the sun's diameter, being only one hundred and forty-six thousand miles from the surface of the sun, which, you will remark, is only a little more than half the distance of the moon from the earth; while, at it's aphelion, it was estimated to be thirteen thousand millions of miles from the sun,—more than eleven thousand millions of miles beyond the planet Uranus. Its velocity, when nearest the sun, exceeded a million of miles an hour. To describe such an orbit as was assigned to it by Sir Isaac Newton, would require five hundred and seventy-five years. During all this period, it was entirely out of view to the inhabitants of the earth, except the few months, while it was running down to the sun from such a distance as the orbit of Jupiter and back. The velocity of bodies moving in such eccentric orbits differs widely in different parts of their orbits. In the remotest parts it is so slow, that years would be required to pass over a space equal to that which it would run over in a single day, when near the sun.