A complete acquaintance with physical astronomy can be attained by those only who are well versed in the higher branches of mathematical and mechanical science ([N. 2]), and they alone can appreciate the extreme beauty of the results, and of the means by which these results are obtained. It is nevertheless true, that a sufficient skill in analysis ([N. 3]) to follow the general outline—to see the mutual dependence of the different parts of the system, and to comprehend by what means the most extraordinary conclusions have been arrived at,—is within the reach of many who shrink from the task, appalled by difficulties, not more formidable than those incident to the study of the elements of every branch of knowledge. There is a wide distinction between the degree of mathematical acquirement necessary for making discoveries, and that which is requisite for understanding what others have done.
Our knowledge of external objects is founded upon experience, which furnishes facts; the comparison of these facts establishes relations, from which the belief that like causes will produce like effects leads to general laws. Thus, experience teaches that bodies fall at the surface of the earth with an accelerated velocity, and with a force proportional to their masses. By comparison, Newton proved that the force which occasions the fall of bodies at the earth’s surface is identical with that which retains the moon in her orbit; and he concluded, that, as the moon is kept in her orbit by the attraction of the earth, so the planets might be retained in their orbits by the attraction of the sun. By such steps he was led to the discovery of one of those powers with which the Creator has ordained that matter should reciprocally act upon matter.
Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens: and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations ([N. 4]) of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter experience—changes which require millions of years for their accomplishment.
The accumulated efforts of astronomers, from the earliest dawn of civilization, have been necessary to establish the mechanical theory of astronomy. The courses of the planets have been observed for ages, with a degree of perseverance that is astonishing, if we consider the imperfection and even the want of instruments. The real motions of the earth have been separated from the apparent motions of the planets; the laws of the planetary revolutions have been discovered; and the discovery of these laws has led to the knowledge of the gravitation ([N. 5]) of matter. On the other hand, descending from the principle of gravitation, every motion in the solar system has been so completely explained, that the laws of any astronomical phenomena that may hereafter occur are already determined.
SECTION I.
Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation retains the Moon in her Orbit—The Heavenly Bodies move in Conic Sections—Gravitation Proportional to Mass—Gravitation of the Particles of Matter—Figure of the Planets—How it affects the Motions of their Satellites—Rotation and Translation impressed by the same Impulse—Motion of the Sun and Solar System.
It has been proved by Newton, that a particle of matter ([N. 6]) placed without the surface of a hollow sphere ([N. 7]) is attracted by it in the same manner as if the mass of the hollow sphere, or the whole matter it contains, were collected into one dense particle in its centre. The same is therefore true of a solid sphere, which may be supposed to consist of an infinite number of concentric hollow spheres ([N. 8]). This, however, is not the case with a spheroid ([N. 9]); but the celestial bodies are so nearly spherical, and at such remote distances from one another, that they attract and are attracted as if each were condensed into a single particle situate in its centre of gravity ([N. 10])—a circumstance which greatly facilitates the investigation of their motions.
Newton has shown that the force which retains the moon in her orbit is the same with that which causes heavy substances to fall at the surface of the earth. If the earth were a sphere, and at rest, a body would be equally attracted, that is, it would have the same weight at every point of its surface, because the surface of a sphere is everywhere equally distant from its centre. But, as our planet is flattened at the poles ([N. 11]), and bulges at the equator, the weight of the same body gradually decreases from the poles, where it is greatest, to the equator, where it is least. There is, however, a certain mean ([N. 12]) latitude ([N. 13]), or part of the earth intermediate between the pole and the equator, where the attraction of the earth on bodies at its surface is the same as if it were a sphere; and experience shows that bodies there fall through 16·0697 feet in a second. The mean distance ([N. 14]) of the moon from the earth is about sixty times the mean radius ([N. 15]) of the earth. When the number 16·0697 is diminished in the ratio ([N. 16]) of 1 to 3600, which is the square of the moon’s distance ([N. 17]) from the earth’s centre, estimated in terrestrial radii, it is found to be exactly the space the moon would fall through in the first second of her descent to the earth, were she not prevented by the centrifugal force ([N. 18]) arising from the velocity with which she moves in her orbit. The moon is thus retained in her orbit by a force having the same origin, and regulated by the same law, with that which causes a stone to fall at the earth’s surface. The earth may, therefore, be regarded as the centre of a force which extends to the moon; and, as experience shows that the action and reaction of matter are equal and contrary ([N. 19]), the moon must attract the earth with an equal and contrary force.
Newton also ascertained that a body projected ([N. 20]) in space ([N. 21]) will move in a conic section ([N. 22]), if attracted by a force proceeding from a fixed point, with an intensity inversely as the square of the distance ([N. 23]); but that any deviation from that law will cause it to move in a curve of a different nature. Kepler found, by direct observation, that the planets describe ellipses ([N. 24]), or oval paths, round the sun. Later observations show that comets also move in conic sections. It consequently follows that the sun attracts all the planets and comets inversely as the square of their distances from its centre; the sun, therefore, is the centre of a force extending indefinitely in space, and including all the bodies of the system in its action.
Kepler also deduced from observation that the squares of the periodic times ([N. 25]) of the planets, or the times of their revolutions round the sun, are proportional to the cubes of their mean distances from its centre ([N. 26]). Hence the intensity of gravitation of all the bodies towards the sun is the same at equal distances. Consequently, gravitation is proportional to the masses ([N. 27]); for, if the planets and comets were at equal distances from the sun, and left to the effects of gravity, they would arrive at his surface at the same time ([N. 28]). The satellites also gravitate to their primaries ([N. 29]) according to the same law that their primaries do to the sun. Thus, by the law of action and reaction, each body is itself the centre of an attractive force extending indefinitely in space, causing all the mutual disturbances which render the celestial motions so complicated, and their investigation so difficult.