Emily. How then can you reconcile the motion of the secondary planets to the laws of gravitation; for the sun is much larger than any of the primary planets; and is not the power of gravity proportional to the quantity of matter?
Caroline. Perhaps the sun, though much larger, may be less dense than the planets. Fire you know, is very light, and it may contain but little matter, though of great magnitude.
Mrs. B. We do not know of what kind of matter the sun is made; but we may be certain, that since it is the general centre of attraction of our system of planets, it must be the body which contains the greatest quantity of matter in that system.
You must recollect, that the force of attraction is not only proportional to the quantity of matter, but to the degree of proximity of the attractive body: this power is weakened by being diffused, and diminishes as the distance increases.
Emily. Then if a planet was to lose one-half of its quantity of matter, it would lose one half of its attractive power; and the same effect would be produced by removing it to twice its former distance from the sun; that I understand.
Mrs. B. Not so perfectly as you imagine. You are correct as respects the diminution in size, because the attractive force is in the same proportion as the quantity of matter; but were you to remove a planet to double its former distance, it would retain but one-fourth part of its gravitating force; for attraction decreases not in proportion to the simple increase of the distance, but as the squares of the distances increase.
Caroline. I do not exactly comprehend what is meant by the squares, in this case, although I know very well what is in general intended by a square.
Mrs. B. By the square of a number we mean the product of a number, multiplied by itself; thus two, multiplied by two, is four, which is therefore the square of two; in like manner the square of three, is nine, because three multiplied by three, gives that product.
Emily. Then if one planet is three times more distant from the sun than another, it will be attracted with but one-ninth part of the force; and if at four times the distance, with but one-sixteenth, sixteen being the square of four?
Mrs. B. You are correct; the rule is, that the attractive force is in the inverse proportion of the square of the distance. And it is easily demonstrated by the mathematics, that the same is the case with every power that emanates from a centre; as for example, the light from the sun, or from any other luminous body, decreases in its intensity at the same rate.