Newton's law of universal gravitation

“ Newton himself, as we have seen, had no theory of gravitation, or at least was extremely careful not to publish it if he ever had one. Later disciples, however, have been less cautious, and the Newtonian view has been erected into something of a theory. This assumes that all matter attracts all matter, and this quite independently of its state of excitation. The intensity of the attraction has been formulated in the well-known law that gravity is proportional to the mass and inversely proportional to the square of the distance. ”

“ The planets likewise act upon each other; and as their relative distances are perpetually varying, certain perturbations are caused in the system, which, though minute in each particular case, become considerable by accumulation, and yet are ultimately corrected and repaired by the same cause that produces them. Newton left to posterity the task of thoroughly investigating these inequalities, of showing them to be a result of the law of gravitation, and establishing the permanence of the system, notwithstanding the accumulating influence of its internal disturbances. ”

“ This brought about the strange view that inertial and gravitational phenomena, which are probably not less intimately connected with one another than electric and magnetic phenomena, have nothing to do with one another. The phenomenon of inertia is placed at the base of classical mechanics as the fundamental property of matter, whereas gravitation is only, as it were, introduced by Newton's law as one of the many possible forces of nature. The remarkable fact of the equality of the inertial and gravitational mass of bodies only appears as an accidental coincidence. ”

“ As a matter of fact, it is little short of a miracle, in view of the insignificance of our mathematical ability, that theoretical physics should have been possible at all. Had our solar system contained two suns such as are present in the double-star systems, or had one of the planets been comparable in size to the sun, it is safe to say that Newton, in spite of his genius, would never have discovered his law of gravitation ”

“ Newton himself regarded this “action at a distance” as impossible, and believed that there was some hitherto undiscovered mechanism by which the sun’s influence was transmitted to the planets. However, no such mechanism was discovered, and gravitation remained a puzzle. The fact is that the whole conception of “force” is a mistake. The sun does not exert any force on the planets; in Einstein’s law of gravitation, the planet only pays attention to what it finds in its own neighborhood. ”

“ This solution, however, would be scarcely permissible. Thus, we have shown that the space-time theory, independently of any empirical study of nature, suggests the existence of permanent entities surrounded by fields of force. In actual practice, we identify the undetermined constant with the “mass” of the central particle; and since mass is always positive in the world of our experience, the constant is always a positive number, and attraction is the outcome. In this way the integrated form of Einstein’s law of gravitation is obtained. ”

“ For inasmuch as we know practically nothing about the intra-atomic occurrences responsible for radiation, we may postulate anything we please with impunity, and as a result make the theory predict any shift we wish, be it vanishing or great. But the purpose of a scientific theory is to give us the power to predict phenomena as yet unknown, and not merely to account for what we already know. It was for this reason that Newton’s law of gravitation was so great an advance over Kepler’s laws of planetary motion or Ptolemy’s crystal spheres. ”

“ To say, therefore, that a rotation of the firmament round a test-body would affect the field of force surrounding the body is equivalent to stating that a rotation of the stars would be capable of affecting the distribution of the metrical field round the body and of dragging the geodesics along. There is no reason to be surprised at some such effect taking place, seeing that the phenomenon of gravitation connotes that matter, whether at rest or in motion, must affect the curvature of space-time, hence the lay of the metrical field. ”

“ For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo) , when they start off from rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a different form in the light of the following consideration.
According to Newton's law of motion, we have [Pg 64] where the "inertial mass" is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have where the "gravitational mass" is likewise a characteristic constant for the body. ”

“ Newton's law of gravitation is said to furnish the principle which is involved in Kepler's formula of details; because once Newton's law is admitted as governing planetary motion, what Kepler observed of the movements of the planets, can be deduced by calculation. It would be perhaps more philosophical, in the present state of our knowledge, to regard even the most apparently elementary and fundamental law as only empirical, and the ultimate principle as lying deeper than any known law. ”

“ In classical science, laws were always tensor equations in separate space and time; but the relativity theory, by compelling us to substitute space-time for space, narrows down our choice of laws in a remarkable manner. Thus, in classical science, the law of gravitation might have been practically anything ”

“ If the attraction of M is unequal, then that body which is most strongly attracted will move fastest, and this will increase it’s distance from the other body. Therefore, by the law of gravitation, M will attract H more strongly than it does O, by which, the distance between H and O will be increased: and a spectator on O will perceive H rising higher toward Z. In like manner, O being more strongly attracted than D, it will move farther towards M than D does: consequently, the distance between O and D will be increased ”

“ We can only say that astronomers have as yet but stepped upon the threshold of the universe, and fixed the telescope’s great eye upon that which is within.
Let us then begin by reminding the reader what is meant by that Newtonian law of gravitation. It appears all things possess the remarkable property of attracting or pulling each other. Newton declared that all substances, solid, liquid or even gaseous, from the massive cliff of rock down to the invisible air—all matter can no more help pulling than it can help existing. ”