The Heavens Above: A Popular Handbook of Astronomy

by J. A. Gillet; W. J. Rolfe

Fig. 323.

Since a comet is visible only while it is near the sun, it is impossible to tell, by the form of the portion of the orbit which it describes during the period of its visibility, whether it is a part of a very elongated ellipse, a parabola, or a hyperbola. Thus in Fig. 323 are shown two orbits, one of which is a very elongated ellipse, and the other a parabola. The part ab, in each case, is the portion of the orbit described by the comet during its visibility. While describing the dotted portions of the orbit, the comet is invisible. Now it is impossible to distinguish the form of the visible portion in the two orbits. The same would be true were one of the orbits a hyperbola.

Whether a comet will describe an ellipse, a parabola, or a hyperbola, can be determined only by its velocity, taken in connection with its distance from the sun. Were a comet ninety-two and a half million miles from the sun, moving away from the sun at the rate of twenty-six miles a second, it would have just the velocity necessary to describe a parabola. Were it moving with a greater velocity, it would necessarily describe a hyperbola, and, with a less velocity, an ellipse. So, at any distance from the sun, there is a certain velocity which would cause a comet to describe a parabola; while a greater velocity would cause it to describe a hyperbola, and a less velocity to describe an ellipse. If the comet is moving in an ellipse, the less its velocity, the less the eccentricity of its orbit: hence, in order to determine the form of the orbit of any comet, it is only necessary to ascertain its distance from the sun, and its velocity at any given time.

Comets move in every direction in their orbits, and these orbits have every conceivable inclination to the ecliptic.

292. Periodic Comets.—There are quite a number of comets which are known to be periodic, returning to the sun at regular intervals in elliptic orbits. Some of these have been observed at several returns, so that their period has been determined with great certainty. In the case of others the periodicity is inferred from the fact that the velocity fell so far short of the parabolic limit that the comet must move in an ellipse. The number of known periodic comets is increasing every year, three having been added to the list in 1881.

The velocity of most comets is so near the parabolic limit that it is not possible to decide, from observations, whether it falls short of it, or exceeds it. In the case of a few comets the observations indicate a minute excess of velocity; but this cannot be confidently asserted. It is not, therefore, absolutely certain that any known comet revolves in a hyperbolic orbit; and thus it is possible that all comets belong to our system, and will ultimately return to it. It is, however, certain, that, in the majority of cases, the return will be delayed for many centuries, and perhaps for many thousand years.

293. Origin of Comets.—It is now generally believed that the original home of the comets is in the stellar spaces outside of our solar system, and that they are drawn towards the sun, one by one, in the long lapse of ages. Were the sun unaccompanied by planets, or were the planets immovable, a comet thus drawn in would whirl around the sun in a parabolic orbit, and leave it again never to return, unless its path were again deflected by its approach to some star. But, when a comet is moving in a parabola, the slightest retardation would change its orbit to an ellipse, and the slightest acceleration into a hyperbola. Owing to the motion of the several planets in their orbits, the velocity of a comet would be changed on passing each of them. Whether its velocity would be accelerated or retarded, would depend upon the way in which it passed. Were the comet accelerated by the action of the planets, on its passage through our system, more than it was retarded by them, it would leave the system with a more than parabolic orbit, and would therefore move in a hyperbola. Were it, on the contrary, retarded more than accelerated by the action of the planets, its velocity would be reduced, so that the comet would move in a more or less elongated ellipse, and thus become a permanent member of the solar system.

In the majority of cases the retardation would be so slight that it could not be detected by the most delicate observation, and the comet would return to the sun only after the expiration of tens or hundreds of thousands of years; but, were the comet to pass very near one of the larger planets, the retardation might be sufficient to cause the comet to revolve in an elliptical orbit of quite a short period. The orbit of a comet thus captured by a planet would have its aphelion point near the orbit of the planet which captured it. Now, it happens that each of the larger planets has a family of comets whose aphelia are about its own distance from the sun. It is therefore probable that these comets have been captured by the action of these planets. As might be expected from the gigantic size of Jupiter, the Jovian family of comets is the largest. The orbits of several of the comets of this group are shown in Fig. 324.

Fig. 324.