ORBITS DESCRIBED ABOUT A CENTRE OF FORCE 31. The problem confronting Newton, for which he developed his system of dynamics, was to explain the motion of the heavenly bodies— the paths, or orbits, which they describe in relation to the earth. His explanation is based on the assumption of "universal gravitation"; i.e., of mutual attraction between any two bodies, depending in intensity upon their masses and upon their distance apart.
If an attractive force of this kind acts between two bodies A and B, it will affect the motion of both. We have seen however (§ 23) that their mass centre will move with constant velocity in a straight line, notwithstanding the interaction between them, if momentum as his own explanation of the law indicates. He ex plains this law as follows : "If a force generate any motion, a double force will generate a double motion, a triple force, a triple motion, whether they be applied simultaneously and at once, or gradually and successively. This motion, if the body were already moving, is either added to the previous motion, if in the same direction, or subtracted from it, if directly opposed, or com pounded with it if the two motions are inclined at an angle."
37. According to Newton's second law of motion, the possession by a mass M of an acceleration F in any direction implies that a force P, given by is acting in that direction. As a deduction from this law, it was shown (§ 16) that forces can be resolved or compounded ac cording to the vector law. Combining these results, we observe that a body can remain at rest (that is, it can have zero accelera tion), either because it is entirely free from the action of force (§ 14), or because the forces which act upon it have no resultant, i.e., neutralize one another when combined by the vector law. The former condition cannot be contemplated in a universe char acterized by universal gravitation : the second is the concern of statics—the science of forces in balance, or equilibrium.