CHAP. XI. also a pea, on a circle of 430 feet; Mars a rather large pin's head, on a circle of 654 feet; Juno, Ceres, Vesta, and Pallas, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter a moderate-sized orange, in a circle nearly half a mile across; Saturn a small orange, on a circle of four-fifths of a mile; and Uranus a full-sized cherry, or small plum, upon the circumference of a circle more than a mile and a half in diameter. As to getting correct notions on this subject by drawing circles on paper, or, still worse, from those very childish toys called orreries, it is out of the question. To imitate the motions of the planets in the View of above-mentioned orbits, Mercury must describe its own diameter in 41 the planetary seconds; Venus, in 4 m. 14 s.; the earth, in 7 minutes; Mars, in 4 m. motions. 48 s.; Jupiter, in 2 h. 56 m.; Saturn, in 3 h. 13 m.; and Uranus, in 2h. 16 m."-Herschel's Astronomy. CHAPTER XII. · CHAR XII. ON COMETS. (147.) BESIDES the planets, and their satellites, there are Comets great numbers of other bodies, which gradually come into formerly in- view, increasing in brightness and velocity, until they attain a maximum, and then as gradually diminish, pass off, and are lost in the distance. spired ror. ter Knowledge banishes. dread. "These bodies are comets. From their singular and unusual appearance, they were for a long time objects of terror to mankind, and were regarded as harbingers of some great calamity. "The luminous train which accompanied them was particularly alarming, and the more so in proportion to its length. It is but little more than half a century since these superstitious fears were dissipated by a sound philosophy; and comets, being now better understood, excite only the curiosity of astronomers and of mankind in general. These discoveries which give fortitude to the human mind are not among the least useful. “It was formerly doubted whether comets belonged to the class of heavenly bodies, or were only meteors engendered fortuitously in the air by the inflammation of certain vapors. Before the invention of the telescope, there were no means of observing the progressive increase and diminution of their light. They were seen but for a short time, and their appearance and disappearance took place suddenly. Their light and vapory tails, through which the stars were visible, and their whiteness often intense, seemed to give them a strong resemblance to those transient fires, which we call shooting stars. Apparently, they differed from these only in duration. They might be only composed of a more compact substance capable of retarding for a longer time CHAP. XII. their dissolution. But these opinions are no longer maintained; more accurate observations have led to a different theory. "All the comets hitherto observed have a small parallax,* which places Parallax of them far beyond the orbit of the moon; they are not, therefore, formed comets. in our atmosphere. Moreover, their apparent motion among the stars is subject to regular laws, which enable us to predict their whole course from a small number of observations. This regularity and constancy evidently indicate durable bodies; and it is natural to conclude that comets are as permanent as the planets, but subject to a different kind of movement. Comets are mere masses of vapor. "When we observe these bodies with a telescope, they resemble a mass of vapor, at the center of which is commonly seen a nucleus more or apparently less distinctly terminated. Some, however, have appeared to consist of merely a light vapor, without a sensible nucleus, since the stars are visible through it. During their revolution, they experience progressive variations in their brightness, which appear to depend upon their distance from the sun, either because the sun inflames them by its heat, or simply on account of a stronger illumination. When their brightness is greatest, we may conclude from this very circumstance that they are near their perihelion. Their light is at first very feeble, but becomes gradually more vivid, until it sometimes surpasses that of the brightest planets; after which it declines by the same degrees until it becomes imperceptible, We are hence led to the conclusion that comets, coming from the remote regions of the heavens, approach, in many instances, much nearer the sun than the planets, and then recede to much greater distances. Orbits of "Since comets are bodies which seem to belong to our planetary system, it is natural to suppose that they move about the sun like comets. planets, but in orbits extremely elongated. These orbits must, therefore, still be ellipses, having their foci at the center of the sun, but having their major axes almost infinite, especially with respect to us, who observe only a small portion of the orbit, namely, that in which the comet becomes visible as it approaches the sun. Accordingly the orbits of comets must take the form of a parabola, for we thus designate the curve into which the ellipse passes, when indefinitely elongated. "If we introduce this modification into the laws of Kepler, which * The parallaxes of comets are known to be small, by two observers, at distant stations on the earth, comparing their observations taken ⚫ on the same comet at near the same time. At the times the observations are made, neither observer can know how great the parallax is. It is only afterward, when comparisons are made, that judgment, in this particular, can be formed; and it is not common that any more definite conclusion can be drawn, than that the parallax is small, and, of course, the body distant. CHAP. XII. relate to the elliptical motion, we obtain those of the parabolic motion of comets. Comets des "Hence it follows that the areas described by the same comet, in its cribe equal parabolic orbit, are proportional to the times. The areas described by in e different comets in the same time, are proportional to the square roote of their perihelion distances. areas qual times. Three obser "Lastly, if we suppose a planet moving in a circular orbit, whose radius is equal to the perihelion distance of a comet, the areas described by these two bodies in the same time, will be to each other as 1 to 2. Thus are the motions of comets and planets connected. 66 "By means of these laws we can determine the area described by a comet in a given time after passing the perihelion, and fix its position in the parabola. It only remains then to bring this theory to the test of observation. Now we have a rigorous method of verifying it. by causing a parabola to pass through several observed places of a comet, and then ascertaining whether all the others are contained in it "For this purpose three observations are requisite. If we observe vations suffi- the right ascension and declination of a comet at three different cient to find times, and thence deduce its geocentric longitude and latitude, we the orbit of a shall have the direction of three visual rays drawn at these times from the earth to the comet, and in the prolongation of which it must necessarily be found. The corresponding places of the sun are also known; it remains then to construct a parabola, having its focus at the center of the sun, and cutting the visual rays in points, the intervals of which correspond to the number of days between the observations. comet. The orbit of a Fig. 33. T T" "Or if we suppose the earth in motion and the sun at rest, let T, T", T", represent three successive positions of the earth, and TC, T'C', T"C", three visual rays drawn to the comet. The question is to find a parabola CC'C", having its focus in S at the center of the sun, and cutting the three visual rays conformably to the conditions required. "These conditions are more than sufficient to determine completely comet found the elements of the parabolic motion, that is, the perihelion distance by three ob- of the comet, the position of the perihelion, the instant of passing this servations. point, the inclination of the orbit to the ecliptic, and the position of its nodes. These five elements being known, we can assign the position of the comet for any time whatever, and compare it with the results of observation. But the calculation of the elements is very difficult, and can be performed only by a very delicate analysis, which cannot here be made known. Inclinations "About 120 comets have been calculated upon the theory of the CHAP. XII. parabolic motion, and the observed places are found to answer to such a supposition. We can have no doubt, therefore, that this is conformable to the law of nature. We have thus obtained precise knowledge of their or of the motions of these bodies, and are enabled to follow them in space. bits. This discovery has given additional confirmation to the laws of Kepler, and led to several other important results. "Comets do not all move from west to east like the planets. Some have a direct, and some a retrograde motion. "Their orbits are not comprehended within a narrow zone of the heavens, like those of the principal planets. They vary through all degrees of inclination. There are some whose plane is nearly coincident with that of the ecliptic, and others have their planes perpendicular to it. "It is farther to be observed that the tails of comets begin to appear, as the bodies approach near the sun; their length increases with this proximity, and they do not acquire their greatest extent, until after passing the perihelion. The direction is generally opposite to the sun, forming a curve slightly concave, the sun on the concave side. "The portion of the comet nearest to the sun must move more rapidly than its remoter parts, and this will account for the lengthening of the tail. Some com. "The tail is, however, by no means an invariable appendage of comets. Many of the brightest have been observed to have short and ets have no feeble tails, and not a few have been entirely without them.. Those tails. of 1585 and 1763 offered no vestige of a tail; and Cassini describes the comet of 1682 as being as round and as bright as Jupiter. On the other hand, instances are not wanting of comets furnished with many tails, or streams of diverging light. That of 1744 had no less than six, spread out like an immense fan, extending to a distance of nearly 30 degrees in length. "The smaller comets, such as are visible only in telescopes, or with difficulty by the naked eye, and which are by far the most numerous, offer very frequently no appearance of a tail, and appear only as round or somewhat oval vaporous masses, more dense toward the center; where, however, they appear to have no distinct nucleus, or anything which seems entitled to be considered as a solid body. "The tail of the comet of 1456 was 60 degrees long. That of 1618, Others have 100 degrees, so that its tail had not all risen when its head reached the several tails. middle of the heavens. The comet of 1680 was so great, that though its head set soon after the sun, its tail, 70 degrees long, continued visible all night. The comet of 1689 had a tail 68 degrees long. That of 1769 had a tail more than 90 degrees in length. That of 1811 had a tail 23 degrees long. The recent comet of 1843 had a tail 60 degrees in length." The following figure gives a telescopic view of the comet of 1811. CHAP. XII. of "When we have determined the elements of a comet's orbit, we compare them with those of comets before observed, and see whether there Elements is an agreement with respect to any of them. If there is a perfect how mined. comets deter- identity as to the elements, we should have no hesitation in concluding that they belonged to different appearances of the same comet. But this condition is not rigorously necessary; for the elements of the orbit may, like those of other heavenly bodies, have undergone changes from the perturbations of the planets or their mutual attractions. Consequently, we have only to see whether the actual elements are nearly the same with those of any comet before observed, and then, by the doctrine of chances, we can judge what reliance is to be placed upon this resemblance." Comet of 1811. Dr. Halley's prediction verified. "Dr. Halley remarked that the comets observed in 1531, 1607, 1682, had nearly the same elements; and he hence concluded that they belonged to the same comet, which, in 151 years, made two revolutions, its period being about 76 years. It actually appeared in 1759, agreeably to the prediction of this great astronomer; and again in 1832, by the computation of several eminent astronomers. According to Kepler's third law, if we take for unity half the major axis of the earth's Particulars orbit, the mean distance of this comet must be equal to the cube root of the square of 76, that is, to 17.95. The major axis of its orbit must, therefore, be 35.9; and as its observed perihelion distance is found to be 0.58, it follows that its aphelion distance is equal to 35.32. It of comets. |