Newton's theorem of revolving orbits does not go to infinity. However, this conclusion holds only when two bodies are present (the two-body problem); the motion of three bodies or more acting under their mutual gravitation (the "n"-body problem) remained unsolved for centuries after Newton, although solutions to a few special cases were discovered. Newton proposed that the orbits of planets about the Sun are largely elliptical because the Sun's gravitation is dominant; to first approximation, the presence of the other planets can be ignored. By analogy, the elliptical orbit of the Moon about the Earth was dominated by the Earth's gravity; to first approximation, the
Elements of the Philosophy of Newton mutual Action of Bodies upon Light. Of the Resemblance between the seven Primitive Colours and the seven Notes in Musick. Introductory Ideas concerning Gravity and the Laws of Attraction: That the Opinion of a subtil Matter, Vortices, and a Plenitude, ought to be rejected (But not that subtile Aether which Sir Isaac makes the Cause of Attraction, Refraction, Animal Motion, &c. which pervades the Universe). That the Vortices and Plenitude of Descartes are impossible, and consequently that there is some other Cause of Gravity. What is meant by Vacuity and Space, without which there could be neither Gravity nor Motion.