To describe a parabola, the projectile velocity must be equal to that which would be produced by a body in falling through the distance of the planet from the focus : a less projectile velocity would cause the planet to describe an ellipse; while a greater would cause it to describe an hyperbola. On the other hand, were the attractive force to gain the ascendency, the planet would whirl round in a series of curves, gradually decreasing in magnitude till it rushed into the sun. But so accurately have, they been adjusted, that from the first moment of creation till the present time, no confusion, no interference has disturbed, or ever will disturb the beautiful equilibrium. In this general view of the planetary orbits, many points of the highest importance have been omitted. To enter into them fully would require great nicety of mathematical calculation; to pass over them entirely would dismiss from our consideration some of the most wonderful instances of the accuracy of modern science, and of the beauty of the arrangement of the forces which regulate the solar system. 187. We are not to suppose that the sun remains stationary in the focus of the planetary orbits: strictly speaking, there is only one stationary point in the whole system, and that is the centre of gravity of the whole. A few words on this subject will explain what we mean. If we unite two balls of different weights by a wire, and suspend them by a string attached to it, the point of suspension, when the balls exactly balance each other, will be their centre of gravity. Give them a whirling motion, and they will both describe circles round this centre of gravity, which alone will remain fixed: the heavier ball will describe a circle smaller in inverse proportion to its weight, compared with the circle described by the lighter body, for the distance of the body A (fig. 42) from the centre of gravity c bears the same A B Fig. 42. proportion to the distance of B as the mass or weight of B does to that of A; that is, AC CBB A. Now, provided the whole solar system was only one planet revolving round the sun, these two balls would not inaptly represent it, for the bodies are as closely united to each other by gravity as these are by the wire A B. 188. If we add other bodies to these two, the centre of gravity will change its position, but will still be the point where, when the system is supported, there will be stable equilibrium. In the case of the sun and planets, from their constant change of position with respect to each other, it is plain that they must constantly vary their position with respect to the centre of gravity; the sun being sometimes on one side (so to speak) of the centre of gravity, and sometimes on the other, according as the planets are distributed; the mass of the sun, however, so much surpasses that of all the members of the solar system besides, that his distance from the centre of gravity is never very great, as we shall have occasion again to remark. 189. Now, not the slightest movement is made by the smallest planet without disturbing the equilibrium of the whole system, and a corresponding motion of all the rest must take place to restore it. If the attraction of the sun on a planet diminishes in the way we have seen in § 185, and the planet therefore recedes from him, and consequently from the common centre of gravity, the attraction of the planet on the sun decreases also (from Law V.), and he recedes so far from the centre of gravity as to restore the equilibrium. Nor is this the case with one planet only, but with every planet; at all times they are changing their position with respect to each other and the sun; not one instant therefore is the sun stationary, for every one of their movements must be accompanied by a corresponding change of position, however small, on his part. Now the extreme difficulty of calculating, so accurately as has been done, the places of the heavenly bodies, will be easily imagined when, in addition to this circumstance, we consider that not only is there this reciprocity of attraction between the sun and planets, but that the planets mutually attract each other; so that no planet describes, during any two revolutions, exactly the same curve. If, for instance, the earth should approach very near the planet Jupiter one year, its orbit would be elongated towards him: perhaps the next year at the same period, Jupiter's attraction would draw the earth in an opposite direction; that part of the earth's orbit would then, so to speak, be flattened. Moreover, such of the planets as are provided with satellites are disturbed by them; for the regular curve of the orbit is not described by the planet itself, but by the centre of gravity of the primary and satellites. Again, the plane of the orbit will also suffer disturbance in its inclination; for if we suppose Jupiter to lie above the earth's orbit, the line of attraction will cause the earth, when passing him, to ascend somewhat towards him; perhaps in another part of the earth's orbit she may meet with Saturn, whose orbit we will imagine to lie on the opposite side; the consequence will be, that the earth will advance somewhat in a contrary direction to meet him. To these effects are given the name of PERTURBATIONS: in calculating them the aid of the most refined mathematical analysis must be called in-the motions, the masses, and the distances of all the planets at every instant of time must be perfectly known; and yet so completely has this branch of astronomy been mastered, that, for years in advance, the exact spot in the heavens which will be occupied by the most insignificant body of our system can be predicted with undoubted and astonishing accuracy. 190. Even if at any time all the planets were on one side of the centre of gravity and the sun on the other, the mass of the sun so far exceeds that of the planets collectively, that the centre of gravity would still fall within the surface, or nearly so, of the sun. Again, should it so happen that the planets are so distributed that those on one side of the sun exactly balance those on the other, the centre of gravity will coincide with the centre of the sun. In any case the centre of gravity of the system and that of the sun so nearly coincide, that we are justified in using the popular expression and speaking of the sun as the centre of the solar system. 191. It may be asked, how can any human contrivance, as that of the two balls before called in to our aid, of which the centre of gravity is of necessity supported, bear any resemblance to the planetary system? What supports the centre of gravity of the sun and planets ? To this it may be sufficient to reply, that, in any contrivance to illustrate the solar system, we are obliged to counteract, by some support, the attraction of the earth, which would cause it to fall to the ground. But the solar system is so disunited from any bodies extraneous to itself, that there is nothing to disturb or draw from its position the centre of gravity of the whole; which retains, as far as we have the means of judging, the exact situation, in the particular point of infinite space, which was originally assigned to it by the Almighty Creator: unless, indeed, the whole has a motion round the centre of the universe, of which the later discoveries of science seem to give a distant intimation. 192. Amidst all the variations, then, which we have enumerated, is there nothing stable? Has the Great Author of nature launched those bodies into space with any probability of collision? subject to disturbances which sooner or later will bring about the destruction of the whole system, or so change the character of the orbits of the planets that their adaptation to present circumstances will no longer continue? that variations, minute individually, will so accumulate as at last to involve all nature in confusion? |