On the Connexion of the Physical Sciences

by Mary Somerville

Comets traverse all parts of the heavens; their paths have every possible inclination to the plane of the ecliptic, and, unlike the planets, the motion of more than half of those that have appeared has been retrograde, that is, from east to west. They are only visible when near their perihelia; then their velocity is such, that its square is twice as great as that of a body moving in a circle at the same distance: they consequently remain but a very short time within the planetary orbits. And, as all the conic sections of the same focal distance sensibly coincide, through a small arc, on each side of the extremity of their axis, it is difficult to ascertain in which of these curves the comets move, from observations made, as they necessarily must be, near their perihelia ([N. 227]). Probably they all move in extremely excentric ellipses; although, in most cases, the parabolic curve coincides most nearly with their observed motions. Some few seem to describe hyperbolas; such, being once visible to us, would vanish for ever, to wander through boundless space, to the remote systems of the universe. If a planet be supposed to revolve in a circular orbit, whose radius is equal to the perihelion distance of a comet moving in a parabola, the areas described by these two bodies in the same time will be as unity to the square root of two, which forms such a connexion between the motion of comets and planets, that, by Kepler’s law, the ratio of the areas described during the same time by the comet and the earth may be found; so that the place of a comet may be computed at any time in its parabolic orbit, estimated from the instant of its passage at the perihelion. It is a problem of very great difficulty to determine all the other elements of parabolic motion—namely, the comet’s perihelion distance, or shortest distance from the sun, estimated in parts of the mean distance of the earth from the sun; the longitude of the perihelion; the inclination of the orbit on the plane of the ecliptic; and the longitude of the ascending node. Three observed longitudes and latitudes of a comet are sufficient for computing the approximate values of these quantities; but an accurate estimation of them can only be obtained by successive corrections, from a number of observations, distant from one another. When the motion of a comet is retrograde, the place of the ascending node is exactly opposite to what it is when the motion is direct. Hence the place of the ascending node, together with the direction of the comet’s motion, show whether the inclination of the orbit is on the north or south side of the plane of the ecliptic. If the motion be direct, the inclination is on the north side; if retrograde, it is on the south side.

The identity of the elements is the only proof of the return of a comet to our system. Should the elements of a new comet be the same, or nearly the same, with those of any one previously known, the probability of the identity of the two bodies is very great, since the similarity extends to no less than four elements, every one of which is capable of an infinity of variations. But, even if the orbit be determined with all the accuracy the case admits of, it may be difficult, or even impossible, to recognize a comet on its return, because its orbit would be very much changed if it passed near any of the large planets of this or of any other system, in consequence of their disturbing energy, which would be very great on bodies of so rare a nature.

By far the most curious and interesting instance of the disturbing action of the great bodies of our system is found in the comet of 1770. The elements of its orbit, determined by Messier, did not agree with those of any comet that had hitherto been computed, yet Lexel ascertained that it described an ellipse about the sun, whose major axis was only equal to three times the length of the diameter of the terrestrial orbit, and consequently that it must return to the sun at intervals of five years and a half. This result was confirmed by numerous observations, as the comet was visible through an arc of 170°; yet this comet had never been observed before the year 1770, nor has it ever again been seen till 1843, though very brilliant. The disturbing action of the larger planets affords a solution of this anomaly, as Lexel ascertained that in 1767 the comet must have passed Jupiter at a distance less than the fifty-eighth part of its distance from the sun, and that in 1779 it would be 500 times nearer Jupiter than the sun; consequently the action of the sun on the comet would not be the fiftieth part of what it would experience from Jupiter, so that Jupiter became the primum mobile. Assuming the orbit to be such as Lexel had determined in 1770, La Place found that the action of Jupiter, previous to the year 1770, had so completely changed the form of it, that the comet which had been invisible to us before 1770 was then brought into view, and that the action of the same planet, producing a contrary effect, has subsequently to that year removed it from our sight, since it was computed to be revolving in an orbit whose perihelion was beyond the orbit of Ceres. However, the action of Jupiter during the summer of 1840 must have been so great, from his proximity to that singular body, that he seems to have brought it back to its former path as he had done in 1767, for the elements of the orbit of a comet which was discovered in November 1843, by M. Faye, agree so nearly with those of the orbit of Lexel’s comet that the two bodies were supposed to be identical; by the subsequent computation of M. le Verrier, it appears, however, that they are not the same, that they were both brought to our system by Jupiter’s attraction, and that they have been in it more than a century, and have frequently come near the earth without having been seen. From the smallness of the excentricity of Lexel’s comet, the orbit resembles those of the planets, but this comet is liable to greater perturbations than any other body in the system, because it comes very near the orbit of Mars when in perihelion, and very near that of Jupiter when in aphelion; besides, it passes within a comparatively small distance of the orbits of the minor planets; and as it will continue to cross the orbit of Jupiter at each revolution till the two bodies meet, its periodic time, now about seven years, will again be changed, but in the mean time it ought to have returned to its perihelion in the year 1851. This comet might have been seen from the earth in 1776, had its light not been eclipsed by that of the sun. There is still so much doubt with regard to Lexel’s comet that during the present year, 1858, M. le Verrier has constructed a table of all the orbits in which the comet may have moved after leaving Jupiter in 1770, which will enable astronomers to recognise the comet even should the elements of its orbit be much altered. He thinks it possible that its path may have become hyperbolic, but that it is more likely an augmentation of its periodic time may have taken place. It is quite possible that comets frequenting our system may be turned away, or others brought to the sun, by the attraction of planets revolving beyond the orbit of Neptune, or by bodies still farther removed from the solar influence.

Other comets, liable to less disturbance, return to the sun at stated intervals. Halley computed the elements of the orbit of a comet that appeared in the year 1682, which agreed so nearly with those of the comets of 1607 and 1531, that he concluded it to be the same body returning to the sun at intervals of about seventy-five years. He consequently predicted its reappearance in the year 1758, or in the beginning of 1759. Science was not sufficiently advanced in the time of Halley to enable him to determine the perturbations this comet might experience; but Clairaut computed that, in consequence of the attraction of Jupiter and Saturn, its periodic time would be so much shorter than during its revolution between 1607 and 1682, that it would pass its perihelion on the 18th of April, 1759. The comet did arrive at that point of its orbit on the 12th of March, which was thirty-seven days before the time assigned. Clairaut subsequently reduced the error to twenty-three days; and La Place has since shown that it would only have been thirteen days if the mass of Saturn had been as well known as it is now. It appears, from this, that the path of the comet was not quite known at that period; and, although many observations were then made, they were far from attaining the accuracy of those of the present day. Besides, since the year 1759, the orbit of the comet has been altered by the attraction of Jupiter in one direction, and that of Saturn, Uranus, and Neptune in the other; yet, notwithstanding these sources of uncertainty, and our ignorance of all the possible causes of derangement from unknown bodies on the confines of our system, or in the regions beyond it, the comet appeared exactly at the time, and not far from the place assigned to it by astronomers; and its actual arrival at its perihelion a little before noon on the 16th of November, 1835, only differed from the computed time by a very few days, which was probably owing to the attraction of Neptune.

The fulfilment of this astronomical prediction is truly wonderful, if it be considered that the comet is seen only for a few weeks during its passage through our system, and that it wanders from the sun for seventy-five years to twice the distance of Uranus. This enormous orbit is four times longer than it is broad; its length is about 3420 millions of miles, or about thirty-six times the mean distance of the earth from the sun. At its perihelion the comet comes within nearly fifty-seven millions of miles of the sun, and at its aphelion it is sixty times more distant. On account of this extensive range it must experience 3600 times more light and heat when nearest to the sun than in the most remote point of its orbit. In the one position the sun will seem to be four times larger than he appears to us, and at the other he will not be apparently larger than a star ([N. 228].)

On the first appearance of Halley’s comet, early in August 1835, it seemed to be merely a globular mass of dim vapour, without a tail. A concentration of light, a little on one side of the centre, increased as the comet approached the sun and earth, and latterly looked so like the disc of a small planet, that it might have been mistaken for a solid nucleus. M. Struve, however, saw a central occultation of a star of the ninth magnitude by the comet, at Dorpat, on the 29th of September. The star remained constantly visible, without any considerable diminution of light; and, instead of being eclipsed, the nucleus of the comet disappeared at the moment of conjunction from the brilliancy of the star. The tail increased as the comet approached its perihelion, and shortly before it was lost in the sun’s rays it was between thirty and forty degrees in length.

According to the observations of M. Valz, the nebulosity increased in magnitude as it approached the sun; but no other comet on record has exhibited such sudden and unaccountable changes of aspect. It was invisible for two months when near its perihelion passage, and when it reappeared on the 24th of January, 1836, its aspect was completely changed; it had no tail, and to the naked eye was like a hazy star; but with a powerful telescope it presented a small, round, planetary-looking nucleus 2ʺ in diameter, surrounded by an extensive coma, and in the centre it had a small, bright, solid part. The nucleus, clear and well defined, like the disc of a planet, was observed on one occasion to become obscure and enlarged in the course of a few hours. But by far the most remarkable circumstance was the sudden appearance of certain luminous brushes or sectors, diverging from the centre of the nucleus through the nebulosity. M. Struve describes the nucleus of the comet, in the beginning of October, as elliptical, and like a burning coal, out of which there issued, in a direction nearly opposite to the tail, a divergent flame, varying in intensity, form, and direction, appearing occasionally even double, and suggesting the idea of luminous gas bursting from the nucleus. On one occasion M. Arago saw three of these divergent flames on the side opposite the tail, rising through the nebulosity, which they greatly exceeded in brilliancy: after the comet had passed its perihelion, it acquired another of these luminous fans, which was observed by Sir John Herschel at the Cape of Good Hope. Hevelius describes an appearance precisely similar, which he had witnessed in this comet at its approach to the sun in the year 1682, and something of the kind seems to have been noticed in the comet of 1744. Possibly the second tail of the comet of 1724, which was directed towards the sun, may have been of this nature.

The influence of the ethereal medium on the motions of Halley’s comet will be known after another revolution, and future astronomers will learn, by the accuracy of its returns, whether it has met with any unknown cause of disturbance in its distant journey. Undiscovered planets, beyond the visible boundary of our system, may change its path and the period of its revolution, and thus may indirectly reveal to us their existence, and even their physical nature and orbit. The secrets of the yet more distant heavens may be disclosed to future generations by comets which penetrate still farther into space, such as that of 1763, which, if any faith may be placed in the computation, goes nearly forty-three times farther from the sun than Halley’s does, and shows that the sun’s attraction is powerful enough, at the enormous distance of 15,500 millions of miles, to recall the comet to its perihelion. The periods of some comets are said to be of many thousand years, and even the average time of the revolution of comets generally is about a thousand years; which proves that the sun’s gravitating force extends very far. La Place estimates that the solar attraction is felt throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun.

Authentic records of Halley’s comet do not extend beyond the year 1456, yet it may be traced, with some degree of probability, even to a period preceding the Christian era. But as the evidence only rests upon coincidences of its periodic time, which may vary as much as eighteen months from the disturbing action of the planets, its identity with comets of such remote times must be regarded as extremely doubtful.

This is the first comet whose periodicity has been established. It is also the first whose elements have been determined from observations made in Europe; for, although the comets which appeared in the years 240, 539, 565, and 837, are the most ancient of those whose orbits have been traced, their elements were computed from Chinese observations.