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planet, sun, times, equal, lesser and velocity

PLANETS, motion of the. Each of the primary planets bend their course about the centre of the Sun, and are accelerat ed in their motions as they approach to him, and retarded as they recede from him ; so that a ray, drawn from any one of them to the Sun, always describes equal spaces, or areas, in equal times : whence it follows that the power which bends their way into a curve line, must be directed to the Sun. This power is no other than that of gravitation, which we have already proved to increase, as the square of the planet's distance from the Sun decreases. See GRAVITATION, &c. But the universality of this law still further appears, by comparing the mo tions of the different planets : for the power which acts on a planet near the Sun is manifestly greater than that which acts on a planet more remote ; both because it moves with greater velo city, and because it moves in a lesser or bit, which has more curvature, and sepa rates further from its tangent, in arcs of the same length, than in a greater orbit By comparing the motion of the planets, the velocity of a nearer planet is found to be greater than that of one more remote, in the proportion of the square root of the number which expresses the great er distance, to the square root of that which expresses the lesser distance ; so that if one planet was four times further from the Sun than another, the velocity of the first would be half the velocity of the latter ; and the nearer planet would describe an arc in one minute, equal to the arc described by the other planet in two minutes ; and though the curvature of the orbits were the same, the nearer planet would describe, by its gravity, four times as much space as the other . would describe in the same time ; so 'that, the gravity of the nearer planet would ap: pear to be quadruple, from the consider ation of its greater velocity only. But be

sides this, as the radius of the lesser orbit is supposed to be four times less than the radius of the other, the lesser orbit must be four times more curved ; and the extremity of a small arc of the same length, will be four times further below the tangent, drawn at the other extremi ty, in the lesser orbit than in the greater; so that, though the velocities were equal, the gravity of the nearer planet would, on this account only, be found to be qua. druple. Hence, on both these accounts together, the greater velocity of the near er planet, and the greater curvature of its orbit, its gravity towards the Sun must be supposed sixteen times greater, though its distance from the Sun isonly four times less than that of the other ; that is, when the distances are as 1 to 4, the gravities are reciprocally as the squares of these numbers, or as 16 to 1. And in the same manner as this principle governs the motions of the primary plan. ets of the great solar system, acts at their_ surfaces, and keeps their parts together; so it governs also the motions of the sa tellites, or secondary planets, in the les ser systems of which the greater is com posed, and is extended around them, de• creasing in the same manner as the Squares of the distances increase. The comets are evidently governed by the same law, since they descend with an ac celerated motion, as they approach to wards the Sun, and ascend again with a retarded motion, bending their way about the Sun, and describing equal areas in equal times, by, rays drawn from them to his centre. See ASTRONOMY.