Gravitation

Gravitation. It is a matter of common experience that all unsupported bodies near the surface of the earth fall to the ground, the direction of their motion being towards the earth's centre. The modern explanation of this phenomenon is that it is due to an attractive force termed gravitation or gravity, which exists between any such body and the earth, in virtue of which they tend to move towards one another. The motion of the earth and other planets round the sun, and of the various satellites round their primaries, may be explained on the same ground. The mode of action of this force is given in the following generalisation, first explicitly given by Newton, and known as the Law of Gravitation: Every particle of matter in the universe attracts every other particle with a force whose direction is that of the straight line joining the two, and whose magnitude is proportional directly as the product of their masses, and inversely as the square of their mutual distance.

Previous to Newton's investigations, Kepler, by a truly prodigious amount of labour, had deduced from the observations of Tycho Brahé the following kinematical laws of planetary motion: (1) The path of each planet is an ellipse, of which the sun occupies one focus; (2) the radius-vector (i.e. the straight line which joins the centre of the sun to that of the planet) of each planet describes equal areas in equal times; (3) the square of the periodic time (i.e. the time during which a planet makes one complete revolution round the sun) of each planet is proportional to the cube of the major axis of its elliptic orbit. From the second of these deductions Newton showed that if the sun attracts the earth or other planet, the direction of this attractive force must be in the line joining their centres; from the first and third he proved that its intensity must be inversely proportional to the square of their mutual distance (so that at double that distance the intensity of attraction would be one-fourth; at three times the distance, one-ninth; and so on). Lastly, the proof that the attraction is proportional to the product of the masses is found in the fact that the weight of any body is under all circumstances proportional to its mass. To test the truth of his deductions, Newton studied the motion of the moon round the earth, and found that this satellite is retained in its orbit by an attraction which is exactly the same as that which causes a body near the earth's surface to fall with an acceleration of (about) 32·2 feet per second.

It must, however, be remembered that Kepler's laws are themselves only approximately true, owing to the attraction of one planet on another interfering with what might be termed the ideal state of things, and thus producing those small superposed motions of a planet which astronomers have termed perturbations. But it is just in this that the confirmatory proofs of the law of gravitation are found; for not only are all these perturbations completely explained by its means, but they have also been discovered and measured by it.

The action of gravitation is independent of the nature of matter, thus differing from magnetic attraction, which is only found in a restricted class of bodies. At the same time the manner in which magnetic and also electric attraction depends upon distance is the same as gravitation. Gravitation is not affected by the presence of other matter; in other words, the weight of a body is the sum of the weights of its parts.

The intensity of gravity at the earth's surface is measured by the acceleration of a body falling freely under its influence; it is usually denoted by $g$. It is found, from pendulum experiments, to vary slightly with the latitude, and also with the height above sea-level of the observing station. For any locality in the British Islands it is, however, little different from 32·2 feet per second. The following table gives the value of $g$ for several places in the northern hemisphere:

From these figures it will be seen that a body apparently gains weight as it is carried from the equator to higher latitudes. This is due to two causes. First, owing to the ellipsoidal shape of the earth, gravitational attraction at the poles is $\backslash frac\{1\}\{289\}$ greater than at the equator; (2) owing to the 'centrifugal force' of the earth's axial rotation, bodies at the equator are $\backslash frac\{1\}\{289\}$ lighter than at the poles, where this cause does not affect their weight. These two fractions together make up the difference, $\backslash frac\{1\}\{289\}$, between equatorial and polar gravity. The fraction denoting diminution of weight due to the centrifugal force of the earth's rotation, may be employed to find at what speed the earth would need to revolve in order that gravity would just be balanced by 'centrifugal force.' It is found that, to fulfil this condition, the earth would require to revolve at seventeen times its present speed; when revolving at this rate bodies would not have any tendency to remain on the earth's surface, and with an increased speed they would be projected into space. Taking also into consideration the diminution of gravity with increase of height, the value of terrestrial gravity is expressed by the formula $g\; =\; 32·173\; -\; 0·82\; \backslash cos\; 2\backslash lambda\; -\; 0·00003\; h$ where $\backslash lambda$ is the latitude, and $h$ the height, in feet, above sea-level. It must be remembered that this value of $g$ is different from that which would be obtained were there no axial rotation of the earth; under the latter circumstances, the value of gravitational attraction alone would be $g\; =\; 32·525\; -\; 0·26\; \backslash cos\; 2\backslash lambda$.

To account for the phenomenon of gravitational attraction several theories have been advanced; but in spite of the best efforts of mathematicians and physicists, the real cause remains undiscovered. Nor is there any physical reason in evidence of the truth of the several assumptions upon which these theories have been based. As Clerk-Maxwell has pointed out, their chief value lies in their suggestiveness, and in there being an incentive to the deeper and more prolonged research after possible causes for gravitation. The earliest speculations on the subject were, of course, almost wholly metaphysical, and therefore misleading, if not absolutely erroneous. To begin with, the assignment of an attraction between the earth and sun as the cause of the earth's motion was set down as being impossible, on the plea that a body could not act in the place where it was not. Again it was urged that such a cause would be simply 'action at a distance,' and hence impossible. Newton's only speculation on the subject showed that he looked to some intervening medium as the agent by means of which attraction between bodies was exerted; that if bodies rarefied this medium round them at a rate lessening as the distance increased, gravitational attraction might thus be accounted for. Another hypothesis, and one of an entirely novel kind, was put forward in 1818 by Le Sage. He presupposed that space contains an exceedingly large number of small bodies moving rapidly in all directions. To these bodies he gave the name of ultramundane corpuscles. They would impinge upon any single isolated body in space in all directions, the result being that the body would not be moved, the impacts being equal on both its sides. But with two bodies in space, one would screen the other from a certain number of blows, so that on their opposed faces there would be a fewer number than on their distant faces; in consequence of this excess of impacts on one side over those on the other, each body would tend to move towards the other. The attraction between the two would be inversely as the square of their distance, and proportional to the surface of the bodies resolved normally to the line joining their centres. So that if mass be proportional to surface, there should be coincidence between the results of the hypothesis and the observed law. The chief objection to this hypothesis is that it would require not only that the corpuscles be infinitely small compared with the molecular distances in ordinary matter, but that they move at a speed enormous compared with anything we are acquainted with. Moreover the amount of energy required to maintain the gravitational attraction of a comparatively small body near the earth's surface would, if converted into heat, be sufficient to raise the earth to the temperature of incandescence. Sir William Thomson has shown that gravitation might be explained by the assumption of the existence of an incompressible fluid filling all space, being either created in each particle at a rate proportional to its mass, and flowing off everywhere to an infinite distance; or by each particle absorbing a quantity proportional to its mass, the supply coming in all directions from an infinite distance. Another method of accounting for gravitation is that of

Clerk-Maxwell, who showed that if in a medium, such as that of the luminiferous ether, there be pressure along, and tension at right angles to the lines of force, the effect would be an attraction such as that of gravitation. The main objection to all these proffered hypotheses is that they presupposed the existence of quantities of energy in the universe which are absolutely enormous compared with the effects they produce; or, at all events, postulate some cause working not in accordance with the known laws of energy.