George Berkeley
Berkeley argued that forces and gravity, as defined by Newton, constituted "occult qualities" that "expressed nothing distinctly". He held that those who posited "something unknown in a body of which they have no idea and which they call the principle of motion, are in fact simply stating that the principle of motion is unknown." Therefore, those who "affirm that active force, action, and the principle of motion are really in bodies are adopting an opinion not based on experience." Forces and gravity existed nowhere in the phenomenal world. On the other hand, if they resided in the category of "soul" or "incorporeal thing", they "do not properly belong to physics" as a matter. Berkeley thus concluded that forces lay beyond any kind of empirical observation and could not be a part of proper science. He proposed his theory of signs as a means to explain motion and matter without reference to the "occult qualities" of force and gravity.
Newton's theorem of revolving orbits
Isaac Newton derived this theorem in Propositions 43–45 of Book I of his "Philosophiæ Naturalis Principia Mathematica", first published in 1687. In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance "r" between the particle and a point fixed in space (the center). In Proposition 44, he derived a formula for the force, showing that it was an inverse-cube force, one that varies as the inverse cube of "r". In Proposition 45 Newton extended his theorem to arbitrary central forces by assuming that the particle moved in nearly circular orbit.