If a sphere at rest in space receive an impulse passing through its centre of gravity, all its parts will move with an equal velocity in a straight line; but, if the impulse does not pass through the centre of gravity, its particles, having unequal velocities, will have a rotatory or revolving motion, at the same time that it is translated (N. 36) in space. These motions are independent of one another; so that a contrary impulse, passing through its centre of gravity, will impede its progress, without interfering with its rotation. The sun rotates about an axis, and modern observations show that an impulse in a contrary direction has not been given to his centre of gravity, for he moves in space, accompanied by all those bodies which compose the solar system—a circumstance which in no way interferes with their relative motions; for, in consequence of the principle that force is proportional to velocity (N. 37), the reciprocal attractions of a system remain the same whether its centre of gravity be at rest, or moving uniformly in space. It is computed that, had the earth received its motion from a single impulse, that impulse must have passed through a point about twenty-five miles from its centre.
Since the motions of rotation and translation of the planets are independent of each other, though probably communicated by the same impulse, they form separate subjects of investigation.
Elliptical Motion—Mean and True Motion—Equinoctial—Ecliptic—Equinoxes—Mean and True Longitude—Equation of Centre—Inclination of the Orbits of Planets—Celestial Latitude—Nodes—Elements of an Orbit—Undisturbed or Elliptical Orbits—Great Inclination of the Orbits of the New Planets—Universal Gravitation the Cause of Perturbations in the Motions of the Heavenly Bodies—Problem of the Three Bodies—Stability of Solar System depends upon the Primitive Momentum of the Bodies.
A PLANET moves in its elliptical orbit with a velocity varying every instant, in consequence of two forces, one tending to the centre of the sun, and the other in the direction of a tangent (N. 38) to its orbit, arising from the primitive impulse given at the time when it was launched into space. Should the force in the tangent cease, the planet would fall to the sun by its gravity. Were the sun not to attract it, the planet would fly off in the tangent. Thus, when the planet is at the point of its orbit farthest from the sun, his action overcomes the planet’s velocity, and brings it towards him with such an accelerated motion, that at last it overcomes the sun’s attraction, and, shooting past him, gradually decreases in velocity until it arrives at the most distant point, where the sun’s attraction again prevails (N. 39). In this motion the _radii vectores_ (N. 40), or imaginary lines joining the centres of the sun and the planets, pass over equal areas or spaces in equal times (N. 41).