Aether and Gravitation Part 5

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...o...b..t 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.

[Ill.u.s.tration: Fig: 1.]

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 s.p.a.ce 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 s.p.a.ce, 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...o...b..t, 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 s.p.a.ce of about 4-1/2 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 s.p.a.ce owing to its Centrifugal Force, but it is held in check by the Centripetal Force, so that instead of it flying off into s.p.a.ce, 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 s.p.a.ce 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...o...b..tal velocity is the least.

By the time the planet has arrived at point _C_, its motion through s.p.a.ce has gradually decreased, and the Centripetal Force begins to re-a.s.sert 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 diminis.h.i.+ng 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...o...b..t.

If the earth's...o...b..t 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 ill.u.s.tration the earth, which describes its revolution round the sun in 365-1/4 days. Now if the orbit of the earth were circular, then equal parts of the earth's...o...b..t 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...o...b..t, as it would take in going from _D_ to _C_.

Thus the nearer the planet is to the sun, the greater is its...o...b..tal 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.

[Ill.u.s.tration: Fig: 2.]

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 365-1/4 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 relations.h.i.+p 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 ill.u.s.tration 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 365^2: 224^2:: 92.7^3: 67^3:

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 pa.s.s 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.

CHAPTER III

MATTER

ART. 29. _What is Matter?_--The law of Universal Attraction states that "Every particle of matter attracts every other particle," etc., and the question at once arises as to what is meant by the term Matter, what are its properties and its const.i.tution? Tait, in his _Natural Philosophy_, gives the following as the definition: "Matter is that which can be perceived by the senses, or is that which can be acted upon by, or can exert force."

It has already been pointed out in Art. 13 that force is due to motion, and that wherever we get motion of any kind or sort, there we get energy, or what used to be termed force. The consideration of this phase of the question will be more fully dealt with in the chapter on Energy and Motion. Suffice to say, that all experience teaches us that force is the outcome of motion.

Accepting this definition therefore of force, Tait's definition of matter will read thus, if brought up to date: "Matter is that which can be perceived by the senses, or is that which can be acted upon by motion, or which can exert motion."