Newtonian gravity

“ Our inability to differentiate between a field of inertial forces generated by acceleration and one of gravitation generated by matter is due solely to a miraculous coincidence, that of the equality of the two masses. Again, when, in the elevator falling in the earth’s gravitational field, we experience no feeling of weight, it is not that the gravitational field has vanished; it is solely that the field of gravity has been counteracted by an equal and opposite field of inertia generated by the elevator’s accelerated motion. ”

“ Without describing the successive stages of the existence of this centre, it may be enough here to state, that a part of Newton's world-wide renown arises from his having cashiered this immovable point from the solar system, and sent it on its travels in search of the real centre of gravity of the whole universe. Newton substituted, for the old law of gravitation towards a centre, his law of universal gravitation, namely, that every particle gravitates towards every other. ”

“ According to Sir Isaac Newton's principles of gravity, the particle of matter that happened to be the largest would attract the smaller in its neighbourhood, which would increase the power of attraction in proportion to the increase of matter, until all in the universe would be collected into one vast body in the centre of space, and there remain motionless and at rest forever. ”

“ The gravitational theory, which emerges out of the general theory of relativity, is, in contradistinction to the Newtonian theory, built up, not upon an elementary law of the gravitational forces, but upon an elementary law of the motion of a body in the gravitational field. ”

“ This law holds that every object in the universe attracts every other object with a single gravitational force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Newton had at first accepted the Cartesian system of celestial vortices of aether that swirled the planets and comets around their orbits. He determined that Kepler's law that areas were swept out in equal times implied that gravity acts in the direction of a line between the planet and the sun. ”

“ And if the perpendicular RG cut off the hyperbolic area PIGR, which shall be to the area PIEQ as any arc CD to the arc BC described in the whole descent; the resistance in any place D will be to the force os gravity, as the area (OR/OQ) IEF - IGH to the area PINM.
For since the forces arising from gravity with which the body is urged in the places Z, B, D, a, are as the arcs CZ, CB, CD, Ca, and those arcs are as the areas PINM, PIEQ, PIGR, PITS; let those areas be the exponents both of the arcs and of the forces respectively. Let Dd be a very small space described by the body in its descent ”

“ Before the days of Kepler and of Newton it may have been possible, it may be possible still, to imagine more than one explanation of the fall of a heavy body to the ground and of the action of one inert mass upon another. The law of gravity, as elaborated by Newton, represents what, so far as we know, has viiiinvariably happened and what we believe will invariably happen in space between two or more bodies, namely, that they will, as heretofore, each attract all the other bodies directly as their mass and inversely as the square of their distance. ”

“ Newton is not well understood even in our days. Some dictionaries say that Newton discovered the law of gravity. This law was introduced by Newton to save his theory. The inertia principle states that any material body, which is left free, is moving in a straight line, with constant velocity to infinity. But in the external reality such a phenomenon is not met. The planets are moving on closed trajectories in space. The only solution to save the theory was to invent a new force, which was called "gravity". ”

“ Newton had a radically novel idea that equated instantaneous acceleration to the gravity force which provoked it. He theorized that the same gravity force that pulled an apple down from a tree extended out to the moon hold it in its orbit around the earth. ”

“ It, therefore, one attributes a massive structure to molecules, then, for the explanation of cohesion and chemical affinity, forces must be assumed which, by diminution of distance, increase quicker in intensity than according to the Newtonian gravitation law. On the other hand, the attraction of two cylinders of finite length and infinitely small section becomes infinitely great so soon as they touch each other. ”

“ Isaac Newton has shew'd how to define the Spaces of the Descent of a Body, let fall from any given height, down to the Center, supposing the Gravitation to increase, as in the fifth Property; but considering the smallness of heighth, to which any Project can be made ascend, and over how little an Arch of the Globe it can be cast by any of our Engines, we may well enough suppose the Gravity equal throughout, and the Descents of Projects in parallel Lines, which in Truth are towards the Center, the difference being so small as by no means to be discovered in Practice. ”

“ All that it is meant here to imply is that the physical nature of fields of gravity and of inertia is one and the same. It is not meant to imply that any actual distribution of matter could ever produce a perfectly uniform field of force in the chest’s interior such as existed under the influence of constant acceleration. We know, indeed, that a distribution of matter under the chest would produce a somewhat similar field of force, but the field would be non-uniform, the magnitude of the force being smaller at the top than at the base of the chest. ”

“ But on the other hand, when we consider that the degree or force of Gravity is exactly in proportion to the quantities of matter in those bodies, without any regard to their bulks or quantity of surface, acting as freely on their internal as external parts, it seems to surpass the power of mechanism ”

“ If we confine the application of the theory to the case where the gravitational fields can be regarded as being weak, and in which all masses move with respect to the co-ordinate system with velocities which are small compared with the velocity of light, we then obtain as a first approximation the Newtonian theory. Thus the latter theory is obtained here without any particular assumption, whereas Newton had to introduce the hypothesis that the force of attraction between mutually attracting material points is inversely proportional to the square of the distance between them. ”

“ But if the universe is spatially finite there is a second deviation from the Newtonian theory, which, in the language of the Newtonian theory, may be expressed thus: — The gravitational field is in its nature such as if it were produced, not only by the ponderable masses, but also by a mass-density of negative sign, distributed uniformly throughout space. ”

“ We know that momentum is carried along on the path of a beam of light. Gravity in acting creates momentum in a direction different from that of the path of the ray and so causes it to bend. For the half-effect we have to assume that gravity obeys Newton’s law; for the full effect which has been obtained we must assume that gravity obeys the new law proposed by Einstein. ”

“ This would be the case, though the bodies T and L attract each other mutually with accelerative forces either greater or less than those with which they attract the other bodies in proportion to their distance. Let all the mutual accelerative attractions be to each other as the distances multiplied into the attracting bodies; and from what has gone before it will easily be concluded that all the bodies will describe different ellipses with equal periodical times about their common centre of gravity B, in an immovable plane. ”

“ Since then all bodies, whether upon Earth or in the Heavens, are heavy, so far as we can make any experiments or observations concerning them; we must certainly allow that gravity is found in all bodies universally. And in like manner as we ought not to suppose that any bodies can be otherwise than extended, moveable or impenetrable; so we ought not to conceive that any bodies can be otherwise than heavy. The extension, mobility and impenetrability of bodies become known to us only by experiments ”

“ Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers." [7]
At the conclusion of the third book of his Principia, Newton remarks : " Hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypothesis ; for whatever is not deduced from the phenomena is to be called an hypothesis. . . . To us it is enough that gravity does really exist, and act according to the laws which we have explained." ”

“ Newton’s law of gravitation stated that the attractions exerted between bodies depended solely on their masses and mutual distances; the conditions of relative motion or rest of the bodies being considered irrelevant. But if Mach’s ideas are accepted, we must assume that in addition to the ordinary Newtonian attraction, a supplementary field of attraction, hitherto unsuspected, should arise if the bodies were in a state of relative acceleration, as in the case of the stars rotating round the earth, or the planets moving round the sun. ”

“ If we suppose the gravity of the æther to be very small, and its elasticity or expansive and repulsive force very great, both which must be supposed, if we admit it at all in the manner proposed by Sir Isaac Newton, its density may increase in receding from gross matter, and be much less in the pores of bodies than in open spaces void of gross matter. Thus we may suppose even the air, which remains in the large pores of such bodies as repel its particles, to be rarer than the common external air. ”

“ The most serious objection against the Newtonian law as an exact law was that it had become ambiguous. The law refers to the product of the masses of the two bodies; but the mass depends on the velocity—a fact unknown in Newton's day. Are we to take the variable mass, or the mass reduced to rest? ”

“ Newton’s successful solution of the problem of the planetary movements entirely depended at first upon a great simplification. The law of gravity only applies directly to two infinitely small particles, so that when we deal with vast globes like the earth, Jupiter, and the sun, we have an immense aggregate of separate attractions to deal with, and the law of the aggregate need not coincide with the law of the elementary particles. ”

“ The force of gravity is not cut off or screened off by the interposition of other masses. A recent investigation by Professor Poynting, F.R.S., has shown that so far as all evidence goes all bodies, even the densest, are transparent with respect to gravitational forces. ”

“ Thus in water, bodies which, by their greater or less gravity, descend or ascend, are comparatively and apparently heavy or light, and their compararive and apparent gravity or levity is the excess or defect by which their true gravity either exceeds the gravity of the water or is exceeded by it. But those things which neither by preponderating descend, nor, by yielding to the preponderating fluid, ascend, altho' by their true weight they do increase the weight of the whole, yet comparatively, and in the sense of the vulgar, they do not gravitate in the water. ”

“ Therefore the pressure acting on every superficies, is not as the solid quantity of the incumbent fluid, but as the number of the orbs reaching to the upper surface of the fluid; and is equal to the gravity of the lowest orb multiplied by the number of orbs: that is, to the gravity of a solid whose whose ultimate ratio to the cylinder abovementioned (when the number of the orbs is increased and their thickness diminished ad infinitum, so that the action of gravity from the lowest superficies to the uppermost may become continued) is the ratio of equality. ”