Gravitational acceleration

“ Zero gravity or decreased gravity occurs during freefall, in parabolic trajectory, or during orbit around the Earth. Gravitational force decreases by the square of the distance away from the Earth's center. It is reduced about 5 percent at about 200 nautical miles' altitude. Gravitational force greater than 1 g can be obtained by acceleration, deceleration, or impact. It also can be increased by using a centrifuge which adds a radial acceleration vector to the 1 g of Earth. ”

“ In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. 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. ”

“ The energy of these oscillations, which can be very substantial, would (as long as the atoms remain unchanged) emerge in no other way than through inertia, by which it opposes to a translational acceleration of the oscillating system, and by the gravitational effect which is apparently in close connection to it. However, the views based on the kinetic theory of gases, which assume the inertial mass as something primarily given and the chemical atoms as rigid bodies or as simple material points, are insufficient for a further development of those ideas ”

“ The actual strain is in space. It is space that takes the strain, but in normal cases, unless the masses are very large, no considerable acceleration is produced over any great distance. That law operates in the case of the pulled body; it pulls the gravitational field as a normal field, the inverse-square law applying.
"But on the other hand, the gravity-beam pulls with a constant force.
"It might be likened to the light-pressure effects of a spotlight and a star. The spotlight would push the sun with a force that was constant ”

“ So long as forces are confined to the thrusts and tensions of elementary mechanics, where there is supposed to be direct contact of material, there is good ground for this distinction; we can visualise the active hammering of the molecules on the body, causing it to change its motion. But when force is extended to include the gravitational field the distinction is not so clear.
For our part we deny the distinction in this last case. Gravitational force is not an active agent working against the passive tendency of inertia. Gravitation and inertia are one. ”

“ Inertia says a body will move once started, but it doesn't say why or how. How does that particle once started gain the knowledge to continue without some direct control over its spatial framework? That it will continue, we know. That in the presence of a gravitic field or a magnetic field or other attractive force at right angles to its motion, we can create an acceleration which will maintain it in an exactly circular path called an orbit. ”

“ A luminous impulse emanating from the sun requires about 8 1⁄4 minutes to reach the earth. Were the gravitative influence supposed to be so much swifter than light as to require but a single minute to pass through this distance, there would still be a corresponding gravity "aberration" of 2.4" of angle. The effect of this slight obliquity of traction would be an acceleration of the earth's orbital velocity which would become measurable in a single year. ”

“ Every particle of matter in the universe is found in fact to attract every other particle. The moon, for instance, attracts the earth also, but the controlling force is on the side of the much greater mass of the earth. This force of gravity or attraction of gravitation, as it is also called, is perfectly regular in its action. Its power depends first of all exactly upon the mass of the body which exerts it. The gravitational pull of the sun, for instance, reaches out to an enormous distance, controlling perhaps, in their courses, unseen planets circling far beyond the orbit of Neptune. ”

“ Nothing forbids one to assume that the man-meteorite might grow, as an acorn does, absorbing light, heat, electricity,—or thought; for, in recent times, such transference of energy has become a familiar idea; but the simplest figure, at first, is that of a perfect comet,—say that of 1843,—which drops from space, in a straight line, at the regular acceleration of speed, directly into the sun, and after wheeling sharply about it, in heat that ought to dissipate any known substance, turns back unharmed, in defiance of law, by the path on which it came. ”

“ Primarily it is an acceleration relative to the earth ; but then that can equally well be described as an acceleration of the earth relative to , and it is not fair to regard it as something located with . Its importance in Newtonian philosophy is that it is an acceleration relative to what we have called the super-observer. ”

“ Hence it appears that mass (inertia) and energy are essentially the same thing, or, at the most, two aspects of the same thing. It must be remembered that on this view the greater part of the mass of matter is due to concealed energy, which is not as yet releasable.
The question whether electrical energy not bound to electric charges has mass, is answered in the affirmative in the case of light. Light has mass. Presumably also gravitational energy has mass; or, if not, mass will be created when, as often happens, gravitational energy is converted into kinetic energy. ”

“ Suppose all the stars were to be annihilated at a given instant of our earth frame. The gravitational disturbance produced by this annihilation would require a number of years to reach us, since gravitational disturbances travel with the speed of light. Hence, the metrical field, or space-time structure, round the earth would persist for a considerable time. For a number of years, therefore, centrifugal force would still continue to manifest itself. ”

“ Newton noticed that this power extended at any rate to the tops of mountains, and it occurred to him that it might possibly extend as far as the moon and so give rise to the required acceleration. Although, however, the acceleration of falling bodies, as far as was known at the time, was the same for terrestrial bodies wherever situated, it was probable that at such a distance as that of the moon the acceleration caused by the earth would be much less. ”

“ For smaller or hotter bodies, radiation repulsion overpowers mutual gravitation; and it increases with the fourth power of their absolute temperature. The gravitational attractive force between particles is exceedingly small; and that between two atoms or two electrons is negligibly small, even though they be within molecular distance of each other. ”

“ When we choose the non-rotating observer the centrifugal force disappears completely and everywhere. When we choose the occupant of the falling projectile, gravitation disappears in his immediate neighbourhood; but he would notice that, although unsupported objects round him experienced no acceleration relative to him, objects on the other side of the earth would fall towards him. So far from getting rid of the field of force, he has merely removed it from his own surroundings, and piled it up elsewhere. Thus gravitation is removable locally, but centrifugal force can be removed everywhere. ”

“ This will be of great advantage to us," he continued, "for if a projectile could move away from the earth with no more rapid acceleration than that with which it approaches, it would take too long to reach the nearest planet, but the maximum repulsion being at the start by reason of its proximity to the earth--for apergy, being the counterpart of gravitation, is subject to Newton's and Kepler's laws--the acceleration of a body apergetically charged will be greatest at first. ”

“ If so, the maintenance of the field of strain about an atom as it moves presents no greater difficulty than the maintenance of the field of light about a moving candle, or of the field of sound about a moving bell. The propagation of such ether strains as occur in light, electricity and magnetism is very greatly influenced by the material substances present in the strained medium. It is not probable that the gravitational strain differs from others in this respect, and we may reasonably hope to find some inductive phenomena in connection with gravitation. ”

“ The law of gravitation is not a law in the sense that it restricts the possible behaviour of the substratum of the world; it is merely the definition of a vacuum. We need not regard matter as a foreign entity causing a disturbance in the gravitational field ”

“ Newton assumed as a working hypothesis that the acceleration diminished according to the same law which he had previously arrived at in the case of the sun's action on the planets, that is that the acceleration produced by the earth on any body is inversely proportional to the square of the distance of the body from the centre of the earth. ”

“ If a stone rests on the hand, the force with which the stone presses the hand downwards is equal to that with which the hand presses the stone upwards; if the earth attracts a stone downwards with a certain force, then the stone attracts the earth upwards with the same force, and so on. It is to be carefully noted that if, as in the last example, two bodies are acting on one another, the accelerations produced are not the same, but since force is measured by the product of mass and acceleration, the body with the larger mass receives the lesser acceleration. ”

“ To be sure, the accelerated coordinate systems cannot be called upon as real causes for the field, an opinion that a jocular critic saw fit to attribute to me on one occasion. But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field. ”

“ Such a force is able to produce no perceptible effect. The acceleration it causes in the earth and the whole solar system, at its present speed through space, is only able to curve the path with a radius of curvature of length thirty thousand times the distance of the star. ”

“ We may take it as an experimental result, although the best evidence is indirect, that a particle falling freely under gravity experiences a constant acceleration which at the same place is the same for all bodies. This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 32.2 feet per second. It increases somewhat with the latitude, the extreme variation from the equator to the pole being about 1⁄2%. We infer that on our reckoning the force of gravity on a mass m is to be measured by mg, the momentum produced per second when this force acts alone. ”

“ However, the effects of this wave of acceleration, in particular the corresponding loss of energy, are in most cases negligible, that is to say not only in ordinary mechanics and in the motions of the heavenly bodies, but even in the radium rays, where the velocity is very great without the acceleration being so. We may then confine ourselves to applying the laws of mechanics, putting the force equal to the product of acceleration by mass, this mass, however, varying with the velocity according to the laws explained above. ”