The intensity of gravitation is said in mathematical parlance "to vary inversely with the square of the distance." This means that at twice the distance the pull will become only one-quarter as strong, and not one-half as otherwise might be expected. At four times the distance, therefore, it will be one-sixteenth as strong. At the earth's surface a body is pulled by the earth's gravitation, or "falls," as we ordinarily term it, through 16 feet in one second of time; whereas at the distance of the moon the attraction of the earth is so very much weakened that a body would take as long as one minute to fall through the same space.
Newton's investigations showed that if a body were to be placed at rest in space entirely away from the attraction of any other body it would remain always in a motionless condition, because there would plainly be no reason why it should move in any one direction rather than in another. And, similarly, if a body were to be projected in a certain direction and at a certain speed, it would move always in the same direction and at the same speed so long as it did not come within the gravitational attraction of any other body.
The possibility of an interaction between the celestial orbs had occurred to astronomers before the time of Newton; for instance, in the ninth century to the Arabian Musa-ben-Shakir, to Camillus Agrippa in 1553, and to Kepler, who suspected its existence from observation of the tides. Horrox also, writing in 1635, spoke of the moon as moved by an emanation from the earth. But no one prior to Newton attempted to examine the question from a mathematical standpoint.
Notwithstanding the acknowledged truth and far-reaching scope of the law of gravitation—for we find its effects exemplified in every portion of the universe—there are yet some minor movements which it does not account for. For instance, there are small irregularities in the movement of Mercury which cannot be explained by the influence of possible intra-Mercurial planets, and similarly there are slight unaccountable deviations in the motions of our neighbour the Moon.
CHAPTER V
CELESTIAL DISTANCES
Up to this we have merely taken a general view of the solar system—a bird's-eye view, so to speak, from space.
In the course of our inquiry we noted in a rough way the relative distances at which the various planets move around the sun. But we have not yet stated what these distances actually are, and it were therefore well now to turn our attention to this important matter.