Читать книгу Aether and Gravitation - William George Hooper - Страница 22
ОглавлениеThus the further a body is from its controlling centre, the weaker the Attraction of Gravitation upon it becomes. Taking therefore Mercury and the earth as examples, we find that their mean distances are respectively 35,000,000 miles and 92,000,000, which is a proportion of about 1 to 2–½. So that the intensity of the sun's attraction on the earth is about four-twenty-fifths of what it is on Mercury, that being the inverse square of the relative distances of the two bodies.
Now the intensity of Light and Heat received by the earth is regulated by the same law of inverse squares, so that the earth would receive about four-twenty-fifths the intensity of light and heat which Mercury receives when they are both at their mean distances.
This law of inverse squares is applicable to every body which acts as a gravitating source throughout the whole of the universe, whether that body be small or large, and whether it be in the form of meteor, satellite, planet, sun or star.
Each satellite, planet or sun exerts an attractive influence upon every body that exists, that attractive influence being regulated by the masses of the respective bodies, and decreasing inversely as the square of the distance from the body viewed as the centre of attraction. So that, the further the attracted body is from the attracting body, the less is the intensity of the mutual attracting forces, though that intensity does not vary simply as the distance, but rather as the square of the distance, and that in its inverse ratio. Thus if we take two masses of any kind or sort, and place them at various distances as represented by the numbers 1, 2, 3, 4, 5, 6, the intensity of the attracting forces between the same masses at the relative distances will be represented by the numbers 1,¼, 1/9, 1/16,½5, ⅓6, which are the inverse squares of the respective numbers representing their distances. As we shall see, the same law holds good in relation to heat, light and electricity, and indeed to all forms of energy which radiate out from a centre equally in all directions.
There is no need to apply Newton's Rules of Philosophy to this Attraction of Gravitation, as it has been demonstrated to exist, times without number. Moreover its laws are exactly the same as those governing the phenomena of sound, light, heat, and electricity, so that apart from being proved by actual experiments in relation to the gravity of the earth, we have a wider experience of the application of the same ruling principles of the law in other departments of science.
The Law of Universal Attraction, which is strictly the Centripetal Force of the compound Law of Gravitation, fully satisfies the three governing rules of Newton's Philosophy. Not only is it simple in its conception, but it is borne out by experience, and adequately accounts for the distinctive phenomena which it seeks to explain. By it, astronomical observations can be taken with a precision and certainty that defy error or failure. The motion of a planet in its orbit can be so perfectly calculated, that its position in space in relation to other planets can be foretold years in advance. The theory of the Aether, therefore, which is to be perfected in this work, must philosophically show that the pressures or tensions of that medium, which are postulated as the cause of Gravitation Attraction, must themselves fulfil the laws of inverse squares, which govern light, heat, electricity and the Attraction of Gravitation. I premise that this will be done in the theory of the Aether to be submitted to the reader in the after pages of this work.
Art. 23. Terrestrial Gravity.--Before passing from this phase of the subject, I should like briefly to look at the question of the Attraction of Gravitation from the standpoint of our own earth, as by so doing we shall notice some facts regarding the same, hitherto unnoticed, in the preceding articles.
Terrestrial Gravity is but a phase of Universal Gravitation. One of the most familiar facts and phenomena of everyday life is, that when a body, such as a stone or stick or bullet, is thrown or projected into the air, it always falls to the earth again. This is due to the attraction of the earth and the stone for each other. It has been proved experimentally that if a stone and a weight are let fall from a height of 16 feet, they would reach the earth in one second of time. Again, a feather, or cork, or even a piece of iron would take exactly the same time falling through the same space, provided that the feather or cork could be screened from the resistance of the air.
The distance, however, through which a body falls in one second varies at different parts of the earth's surface, being least at the equator, and greatest at the North and South Poles. This is accounted for by the fact that the polar diameter is only 7899 miles, while the equatorial diameter is 7925 miles, thus the distance from the centre of the earth to either pole is about 3950 miles, or 13 miles less than the equatorial radius of the earth. Now the force of gravity decreases upwards from the earth's surface inversely as the square of the distance from the earth's centre of gravity, but decreases downwards simply as the distance from the centre decreases. Thus if a ball were taken down 2000 miles, that is half the distance to the centre, it would only weigh half-a-pound, while if it were taken to the centre of the earth, it would have no weight at all; while a pound weight at the equator would not weigh one pound at the poles, because it would be nearer the centre of the earth by 13 miles.
Thus a pound weight is not always a pound weight. It varies as we carry it to different parts of the earth's surface, depending upon its relation to the centre of the earth for its exact weight. The point which I wish to make perfectly clear, as it will be necessary for future reference, is, that there is no such thing as weight apart from the gravity of the earth; or, if we apply the principle to the solar system, there is no gravitating force in that system apart from the gravitating force of the central body, the sun, or the planets and other bodies which form the solar system.
Let us look at this matter from another standpoint, in order to prove this truth and make the same perfectly clear. If a pound weight were put in a spring-balance, then at the surface of the earth it would weigh one pound. Now, we will suppose that we have taken the weight to a height of 4000 miles above the surface of the earth, that is exactly double the distance from the centre of the earth, the radius of the earth being approximately 4000 miles. According to the law of inverse squares, the force of Gravitation decreases inversely as the square of the distance. The distance having been doubled, the proportion of the forces at the two places, i.e. the earth's surface and 4000 miles above it, are as 1 to ¼.
Thus at a distance of 4000 miles the weight which weighed one pound at the earth's surface, now only weighs a quarter of a pound. At a distance of 8000 miles, the distance would be trebled, therefore the force of Gravitation is one-ninth, and the weight would weigh one-ninth of a pound. If we could take the pound weight to the moon, the attractive force of the earth would be reduced to 1–3600, as the moon is 240,000 miles distant, that is sixty times the earth's radius. The square of 60 is 3600, and if we invert that we get 1–3600, so that the weight which weighs a pound at the earth's surface, would only weigh 1–3600 part of a pound at the distance of the moon. This again proves, that apart from the Attraction of Gravitation, there is no such thing as weight, and that the weight so called of any body, such as a planet or satellite, increases or decreases as its distance increases or decreases from its central attracting body.
Art. 24. Centrifugal Force.--I have already shown in Art. 10 that the Centripetal Force and Universal Attraction are one and the same; as the Centripetal Force always acts towards the centre, and must therefore be in its operation and influence a gravitating or attractive power.
I have also pointed out in the same article, the necessity of another force, which is to be the complement, and the counter part of Gravitation Attraction. That complement and counter force was conceived by Newton, and called by him the Centrifugal Force. The very nature of the Centripetal Force demands and necessitates a force which in its mode of operation is exactly the opposite of the Centripetal Force. Unless there were such a force, a repellent and repulsive force, then instead of there being that harmonious working of the universe that now exists, there must inevitably be a gradual drawing together of all planets and satellites, of all stars and suns, into one vast, solitary, and ruinous body.
There are also other phenomena which demand a Centrifugal Force in the universe. It is a well-known fact, that there exist between the orbits of Jupiter and Mars, what are called planetoids, about 500 in number, which are supposed to be the remnants of a broken or shattered world. As may be expected from such an accumulation, they present the most extraordinary diversities and eccentricities in the orbits that can possibly be conceived. They are of all shapes and sizes, and besides their orbits round the sun, have orbits among themselves. They are so clustered together that their orbits intersect each other at numerous points, and when in conjunction are said to suffer great perturbations, being pulled great distances this way and that by each other's attractive influence. It is further stated that their orbits so intersect each other, that if they were imagined to be material rings, they would be inseparable, and the whole could be suspended by taking any one of them up at random. Here, then, is presented to us a kind or order of celestial phenomena for whose well-being and effectual working the Centripetal Force or the Attraction of Gravitation cannot possibly account. In their case another force is demanded which shall be the exact complement and counterpart of the Centripetal Force. There needs therefore a force, not an imagined one, simply conceived to fill a want, but a real Force, as real and as plainly to be understood as the Centripetal Force. A force existing in each world just like the Attraction of Gravitation, only the reverse of Gravitation, a repellent, repulsive Force, acting in the reverse mode, and way, to universal attraction. This Force must be governed by the same rules and laws that govern the Centripetal Force, if it is to work in harmony with the same. It must be universal in its character, having a proportion of forces equal to the product of the masses of the two bodies which are concerned, and its path must coincide with the path of gravitational attraction, that is, in the straight line which joins the centres of gravity of the two bodies. Further, and what is perhaps the most important of all, it must act as a repelling or repulsive force which shall be in the same proportion in regard to distance, as the law governing Centripetal Force, that is, inversely as the square of the distance.
Again, and briefly, there are also in existence small bodies called meteors, which are said to exist by myriads, which float in space, and circle round the sun. They are of all shapes and sizes, from one ounce to a ton or even tons, thousands of them coming into contact with our earth's atmosphere every year, especially in August and November. All of these small bodies have orbits among themselves, and gravitate round one another, as they revolve round the sun. Now if the orbits of the planetoids be such an entangled mass, what must be the orbits of these meteors? What an indescribable, unimaginable mass of labyrinthian motions must exist among these myriads of little bodies! How they must intersect, cross and intermingle each other's orbits! What attraction and counter-attraction they must exert upon each other! Let me ask any man to sit down and try to imagine how the present recognized Centripetal and Centrifugal Forces can account for the effectual working of these meteors. As illustrating the necessity of a real and physical Centrifugal Force which is to be the exact counterpart of the Centripetal Force, I would call the attention of the reader to Herschel's view of this matter. In dealing with the phenomena of comets' tails he writes:[1] “Beyond a doubt, the widest and most interesting prospect of future discovery, which this study holds out to us, is, that distinction between gravitating and levitating matter, that positive and irrefutable demonstration in nature of a repulsive force, co-extensive with, but enormously more powerful than the attractive force we call gravity which the phenomena of their tails afford.” I premise that this prophecy of Herschel's will be fully demonstrated and proved in the succeeding pages of this work. For, in the theory of the Aether that is to be afterwards perfected, it will be philosophically proved that the physical medium so conceived will satisfactorily account for a force or motion from the centre of all bodies; which motions fulfil all the conditions required by that Centrifugal Force, which is the complement and counterpart of the Attraction of Gravitation. At the present time, with the conception of a frictionless Aether, it is impossible to harmonize the existence of such a force or motion with our theory of the Aether. Yet Professor Lebedew of Moscow, and Nichols and Hull of America, have incontrovertibly demonstrated by actual experiments the existence of such a force. Therefore it follows, that if our present theory of the Aether fails to agree with experimental evidence, such a theory must be reconstructed in order that our philosophy may be made to agree with our experiments and our experience.
[1]Lectures on Scientific Subjects.
Art. 25. Kepler's Laws.--A long time before Newton had discovered the Law of Gravitation, Kepler had found out that the motions of the planets were governed by certain laws, and these came to be known as Kepler's Laws.
These laws which were given to the world by Kepler, simply represented facts or phenomena which had been discovered by observation, as Kepler was unable to account for them, or to give any mathematical basis for the same.
On the discovery, however, of Universal Gravitation, Newton saw at once that these laws were simply the outcome of the application of the Law of Gravitation to the planets, and that they could be accounted for on a mathematical basis by the Law of Gravitation, as they seemed to flow naturally from that law.
Kepler's Laws are three in number and may be thus stated--
1st Law. Each planet revolves round the sun in an elliptic orbit, with the sun occupying one of the Foci.
2nd Law. In the revolution of a planet round the sun, the Radius Vector describes equal areas in equal times.
3rd Law. The squares of the periodic times of planets are proportional to the cubes of their mean distances.
Now the question arises, whether it is possible to form a theory of the Aether which shall satisfactorily and philosophically account for all the phenomena associated with Kepler's Laws in their relation to the motions of planets, satellites, or other solar bodies? On the present conception of the Aether such a result is an absolute impossibility. With the theory of the Aether, however, to be submitted to the reader in this work, the result is possible and attainable. If, therefore, such a result is philosophically proved, as I submit will be done, then we shall have greater evidence still that the theory so propounded is a more perfect theory than the one at present recognized by scientists generally.
Art. 26. Kepler's First Law.--Each planet revolves round the sun in an elliptic orbit, the sun occupying one of the Foci.
The ancients thought that the paths of the planets around the sun were circular in form, because they held that circular motion was perfect. A system of circular orbits for the paths of the planets round the sun would be very simple in its conception, and would be full of beauty and harmony. But exact calculations reveal to us that the path of a planet is not exactly that of a circle, as the distance of a planet from the sun in various parts of its orbit is sometimes greater, and sometimes less, than its mean distance.
The planet Venus has the nearest approach to a circular orbit, as there are only 500,000 miles between the mean, and greatest and least distances, but both Mercury and Mars show great differences between their greatest and least distances from the sun.
If, therefore, the orbits of a planet are not exactly circular, what is their exact shape? Kepler solved this problem, and proved that the exact path of a planet round its central body the sun was that of an ellipse, or an elongated circle. Thus he gave to the world the first of his famous laws which stated that each planet revolves round the sun in an orbit which has an elliptic form, the sun occupying one of the Foci.
Not only is the orbit of a planet round the sun elliptic in form, but the path of the moon round the earth, or the path of any satellite, as for example a satellite of Mars or Jupiter or Saturn, is also that of an ellipse, the planet round which it revolves occupying one of the Foci.
It has also been found that certain comets have orbits which cannot be distinguished from that of an elongated ellipse, the sun occupying one of the Foci.
Now let us apply the Law of Gravitation to Kepler's First Law, and note carefully its application.
Let A, B, C, D be an ellipse representing the orbit of the earth, and let S represent the sun situated at one of the Foci.
We will suppose that the earth is projected into space at the point A, then according to the First Law of Motion, it would proceed in a straight line in the direction of A E, if there were no other force acting upon the earth. But it is acted upon by the attraction of the sun, that is the Centripetal Force which is exerted along the straight line S A (Art. 20), which continues to act upon it according to the principle already explained in Arts. 21 and 22.
Now, according to the Second Law of Motion and the Parallelogram of Forces, instead of the earth going off at a tangent in the direction of A E, it will take a mean path in the direction of A B, its path being curved instead of being a straight line.
If the sun were stationary in space, then the mean distance, that is, the length of the imaginary straight line joining the sun S A to the earth, would remain unaltered. The Radius Vector S A, or the straight line referred to, would then be perpendicular to the tangent, and the velocity of the earth round the sun would be uniform, its path being that of a circle.
The Radius Vector S A, however, is not always perpendicular to the tangent F E, and therefore the velocity of the earth is not always uniform in its motion in its orbit, as sometimes it travels at a lesser or greater speed than its average speed, which is about 18 miles per second.
It has to be remembered that the sun itself is in motion, having a velocity through space of about 4–½ miles per second, so that, while the earth is travelling from A to B the sun is also travelling in the direction of S B. Thus the orbital velocity of the earth, and the orbital velocity of the sun, together with the Centripetal Force or universal Gravitation Attraction, are all acting in the same direction when the earth is travelling from A to B, that is, in the direction of the orbit situated at B. This point of the orbit is known as the perihelion, and at that point the velocity of the earth is at its greatest, because the earth is then nearest the sun.
According to Newton, the planet when at B would still have a tendency to fly off into space owing to its Centrifugal Force, but it is held in check by the Centripetal Force, so that instead of it flying off into space, it is whirled round and starts off on its journey away from the sun in the direction of B, C. The sun, however, is still continuing its journey in the direction of S, H, so that not only is the increased orbital velocity of the earth, which it obtained at its perihelion, urging the earth away from the sun, but the sun itself in its advance through space is leaving the earth behind it. The combined effect of the two motions, the advancing motion of the sun, and the receding motion of the earth, due to its increased orbital velocity, drives the earth towards the aphelion, where its distance from the sun is greatest, and its orbital velocity is the least.
By the time the planet has arrived at point C, its motion through space has gradually decreased, and the Centripetal Force begins to re-assert itself, with the result that the earth is slowly made to proceed towards the point D of the ellipse, at which point its motion is the slowest in orbital velocity, only travelling about 16 miles per second, while the distance of the earth from the sun is the greatest and has increased from 91,000,000 miles at the perihelion to 94,500,000. This point of the orbit is known as its aphelion.
After rounding this point, the orbital velocity of the earth begins to increase again, owing to the diminishing distance of the earth from the sun, which according to the law of inverse squares (Art. 22) gives an added intensity to the Centripetal Force.
Thus by the combination of the Laws of Motion and the Law of Gravitation discovered by Newton, he was able to satisfactorily account for and explain on a mathematical basis, the reason why the earth and all the other planets move round the sun in elliptic orbits, according to Kepler's First Law.
In the development of the physical cause of gravitation, therefore, the same physical medium, which accounts for that law, must also give a satisfactory explanation of the first of Kepler's Laws.
Art. 27. Kepler's Second Law.--This law states that the Radius Vector describes equal areas in equal times. The Radius Vector is the imaginary straight line joining the centres of the sun and the earth or planet. While the First Law shows us the kind of path which a planet takes in revolving round the sun, the Second Law describes how the velocity of the planet varies in different parts of its orbit.
If the earth's orbit were a circle, it can be readily seen that equal areas would be traversed in equal times, as the distance from the sun would always be the same, so that the Radius Vector being of uniform length, the rate of motion would be uniform, and consequently equal areas would be traversed in equal times. Take as an illustration the earth, which describes its revolution round the sun in 365–¼ days. Now if the orbit of the earth were circular, then equal parts of the earth's orbit would be traversed by the Radius Vector in equal times. So that with a perfectly circular orbit, one half of the orbit would be traversed by the Radius Vector in half a year, one quarter in one quarter of a year, one-eighth in one-eighth of a year, and so on; the area covered by the Radius Vector being always exactly proportionate to the time.
From Kepler's First Law, however, we know that the planet's distance does vary from the sun, and therefore the Radius Vector is sometimes longer and sometimes shorter than when the earth is at its mean distance; the Radius Vector being shortest at the perihelion of the orbit, and longest at the aphelion. We learn from Kepler's Second Law that when the Radius Vector is shortest, that is, when the planet is nearest the sun, it acquires its greatest orbital velocity; and when the Radius Vector is longest, that is, when the planet is farthest from the sun, the orbital velocity of a planet is the slowest.
Let A, B, D, C represent the elliptic orbit of a planet, with S sun at one of the Foci, and let the triangles A, S, B and D, S, C be triangles of equal area. Then, according to Kepler's Second Law, the time taken for the Radius Vector to traverse the area A, S, B is equal to the time that the Radius Vector takes to traverse the area D, S, C. So that the planet would take an equal time in going from A to B of its orbit, as it would take in going from D to C. Thus the nearer the planet is to the sun, the greater is its orbital velocity, and the farther it is away from the sun the slower is its velocity, the velocity being regulated by the distance. The manner in which the difference of velocity is accounted for by the Law of Gravitation has already been explained in the preceding article. Thus Newton proved that Kepler's Second Law was capable of being mathematically explained, and accounted for, by the universal Law of Gravitation.
If, therefore, a physical cause can be given for Newton's Law of Gravitation, then such physical cause must also be able to account for, and that on a strictly philosophical basis, the second of Kepler's Laws as well as the first.
Art. 28. Kepler's Third Law.--The Third Law of Kepler gives the relation between the periodic time of a planet, and its distance from the sun. The periodic time of any planet is the time which it takes to go once round the sun. Thus the periodic time of the earth is 365–¼ days. The periodic time of Venus is 224.7 days, while that of Mars is 686.9 days.
Kepler had found out that different planets had different periodic times; he also found out that the greater the mean distance of the planet, the greater was the time which the planet took to perform its journey round the sun, and so he set to work to find out the relationship of the periodic time to the planet's mean distance.
After many trials and many failures he arrived at the right conclusion, and at last discovered the true law which is known as Kepler's Third Law, which states that for each and every planet, the squares of their periodic times are proportional to the cubes of their mean distances.
For purposes of illustration let us take the earth and the planet Venus and compare these two. The periodic time of the earth is 365 days, omitting the quarter day. The periodic time of Venus is 224 days approximately. Now, according to Kepler's Third Law, the square of 365 is to the square of 224, as the cube of the earth's mean distance is to the cube of Venus's mean distance, which are 92.7 millions of miles and 67 millions of miles respectively. The problem may be thus stated--
As 3652: 2242:: 92.73: 673:
This worked out gives--
133,225: 50,176: 796,597.982: cube of Venus's mean distance.
So that by Kepler's Third Law, if we have the periodic time of any two planets, and the mean distance of either, we can find out the mean distance of the other by simple proportion.
In making astronomical calculations, the distances of the planets are generally obtained by means of Kepler's Third Law, as the periodic time of the planet is a calculation that may be made by astronomers with great certainty, and when once the periodic times are found, and the mean distance of a planet, as our earth for example, is known, the mean distances of all the other planets in the solar system may soon be obtained.
In like manner this Third Law of Kepler's is equally applicable to the satellites of any planet. For example, when the periodic time of both of Mars' satellites, Phobos and Deimos, are known, being about 8 hours and 30 hours respectively, and the distance of either is known, as Phobos with a mean distance of 5800 miles, then the mean distance of Deimos can easily be calculated by this law, and is found to be 14,500 miles.
As discovered by Kepler, the Third Law was simply the result of observation. He was unable to give any mathematical basis for its existence. The Laws as they were given to the world by Kepler were simply three great truths which had been discovered by observation. It rested with Newton to show how these laws could be accounted for on a mathematical basis, and to show how they all sprang from one and the same source, namely the universal Law of Gravitation. In his Principia, he proved that all Kepler's Laws were fully expounded and explained by his great discovery of Universal Gravitation.
Now what Newton has done for Kepler's Laws from the mathematical standpoint, we propose to do from the physical standpoint. In the development of the physical agency or cause of Gravitation, therefore, among the phenomena and laws, which have to be satisfactorily accounted for on a physical basis, are these three Laws of Kepler's just referred to.
So that in addition to the satisfactory explanation of a physical cause for the Laws of Motion, and the Centripetal and Centrifugal Forces, the hypothesis of a physical cause of Gravitation must fully and satisfactorily account for the Laws of Kepler, whose mathematical explanation was given by Newton.
Further, and what is as equally important, the explanation so given must be strictly in harmony with the Rules of Philosophy as laid down in Art. 3. That is, the explanation must be simple in character, must not be contrary to experience or observation, and must satisfactorily account for the laws which the hypothesis of the physical cause of Gravitation seeks to explain. This I premise we will do as we pass from stage to stage in the development of the theory.
I can safely premise that it will be simple in character and conception, that it will be entirely in harmony with all experience and observation, and that the physical cause so advanced will give as physical a basis to Kepler's Laws as Newton's mathematical calculations gave them a mathematical basis.
In summing up, I need hardly point out, that if all that I have premised in this and the preceding chapter is accomplished in the after chapters of this book, then for the first time since the discovery of Universal Gravitation by Sir Isaac Newton, his great discovery will have received the long-expected and long-desired physical explanation, that explanation and cause being founded on his own Rules of Philosophy given in his immortal Principia, and for the first time our Philosophy will be brought strictly into harmony with our universal experience.
