Centripetal force

“ If the body L, by a radius drawn to the other body T, describes areas, which compared with the times, are very unequal; and that other body T be either at rest or moves uniformly forward in a right line: the action of the centripetal force tending to that other body T, is either none at all, or it is mix'd and compounded with very powerful actions of other forces: and the whole force compounded of them all, if they are many, is directed to another (immovable or moveable) centre. The same thing obtains, when the other body is moved by any motion whatsoever ”

“ Therefore if the medium in which any body moves be acted on either by its own gravity, or by any other centripetal force, and the body be urged more powerfully by the same force; the difference of the forces is that very motive force, which, in the foregoing Propositions, I have considered as a centripetal force. But if the body be more lightly urged by that force, the difference of the forces becomes a centrifugal force, and is to be considered as such. ”

“ In each and every case, wherever the centripetal or centrifugal force acts, the action is direct, because it is caused by a physical medium, which physical medium is in direct contact with each body acted upon, and also fills the space between those bodies. With this view of the centripetal force of Gravitation, our Philosophy is made to agree definitely with our experience, which teaches us beyond contradiction, that no body moves, unless it is either pushed or pulled by a physical medium. ”

“ The case of the 6th Corollary obtains in the celestial bodies (as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed) ; and therefore in what follows, I intend to treat more at large of those things which relate to centripetal force decreasing in a duplicate ratio of the distances from the centres. ”

“ Centrifugal force must always be balanced by centripetal force. The difficulty is to understand what force counterbalances the centrifugal force of the rotating material of the vortex-atom. It is not because the centrifugal tendency of the rotating material is controlled by the exterior incompressible fluid, for it offers no resistance whatever to the passage of the atom through it—in short, in so far as the motion of the atom is concerned, this fluid is a perfect void. ”

“ It is well known, that the centripetal force, whereby any body is made to revolve in the circumference of a circle, is such, as is sufficient to generate all the motion in the body, in a time equal to that, wherein the body describes an arch of the circumference, equal in length to the radius. ”

“ The doctrine that the heavenly bodies were moved by vortices was successively modified, so that it came to coincide in its results with the doctrine of an inverse-quadratic centripetal force.... When this point was reached, the vortex was merely a machinery, well or ill devised, for producing such a centripetal force, and therefore did not contradict the doctrine of a centripetal force. Newton himself does not appear to have been averse to explaining gravity by impulse. So little is it true that if one theory be true the other must be false. ”

“ Therefore a homogeneous and perfect globe will not retain several distinct motions, but will unite all those that are irnpressed on it, and reduce them into one; revolving, as far as in it lies, always with a simple and uniform motion about one single given axis with an inclination perpetually invariable. And the inclination of the axis, or the velocity of the rotation will not be changed by centripetal force. ”