Orbit (anatomy)

“ The cause perpetually operating, the effect is constant—and hence the formation of the terrestrial orbit; and the cause extending to the other bodies in the system, the planetary orbs are deflected from their natural rectilinear paths, and pursue a circuit round the common centre. The force of attraction is, however, proportional to the quantity of matter, and the proximity of the attracting body. Like light, the power of gravitation is weakened by diffusion, and diminishes as the square of the distance increases. ”

“ Now, the length of a planet's orbit is subject only to these very small oscillations, and it may therefore be regarded as fixed or constant. The breadth of the orbit, however, is subject to secular variations, which require ages for their full compensation. The orbit alternately bulges out into a circle, and narrows into an ellipse. The earth is now, and has been for many ages, expanding into a circle, but it will again collapse into an ellipse. ”

“ The orbits of the planets change not only their position, but even their magnitude and their form: the longer axis of each has a slow angular motion; and, though its length remains fixed, the shorter axis increases and diminishes, so that the form of the orbit approaches to that of a circle, and recedes from it by turns. ”

“ Eccentricity of Orbit of Moon.--From astronomical observation we learn, that all the satellites and planets do not possess uniformity of motion, as they are carried round their controlling centres by the circulating aetherial currents, because the respective controlling centres themselves move through space. The result is, that the orbit of any satellite or planet is not always of the same size, but constantly varies, sometimes having a larger circumference than at other times, and sometimes a smaller circumference. ”

“ By this device, the visible movement could be, and was, recorded with great accuracy, but sometimes at the expense of physical truth. Thus the epicyclic arrangement for the moon’s orbit involved, if closely looked into, the consequence that her distance from us at nearest must be half that at the farthest, and her angular diameter double! Kepler, after the work of a lifetime (1571-1630) , discovered the cause of this ‘anomaly’ in the shape of the orbit, which is elliptical, not circular, and substituted ‘eccentricity’ for ‘anomaly’ as the key-word. ”

“ Therefore the orbit by the accession of this new force will become more eccentrical. If now, while the body is returning from the lower to the upper apsis, it should decrease by the same degrees by which it increases before the body would return to its first distance; and therefore if the force decreases in a yet greater ratio, the body, being now less attracted than before, will ascend to a still greater distance, and so the eccentricity of the orbit will be increased still more. ”

“ Then, if the small body had originally a motion across the direction in which the great body attracts it, the result of the combination will be to cause the small body to revolve in an orbit (more or less elliptical according to the direction and velocity of its original motion) about the great body. If the difference of mass is very great, the large body will remain virtually immovable. This is the case with the sun and its planets. ”

“ In the case of a planetary body, there is a real limit to the extent of the transformation of its orbital energy of motion under the influence of the gravitation field. As the orbit of the planet widens, and its mean distance from the primary becomes greater, its velocity in its orbital path must correspondingly decrease. ”

“ Charged only with the small mass of matter which they met on their road, the planet and its moon, on the contrary, remained victorious in the limited districts in which they were rotating. Only the slow orbital movement about the central body was influenced, and that adapted itself to the common direction and the circular orbit. It is not inconceivable that there may be, farther out in space, planets of our solar system, unknown to us, moving in irregular paths like the comets. ”

“ One of these lines or pathways was destined for the orbit of Mercury; another for the orbit of Venus. One was for [pg 168] the pathway of Mars; another for the belt of the asteroids; another for Jupiter; another for Saturn, and still two others, far off on the rim, for Uranus and Neptune. The theory continues that such are the laws of matter that these orbital lines must exist in a disc of fire mist such as that out of which our solar universe has been produced. ”

“ With regard to the variations in the inclination, it is clear, that, when the orbit is symmetrical on each side of the disturbing force, all its variations are compensated after a revolution of the disturbed body, and are merely periodical perturbations in the planet’s latitude; and no secular change is induced in the inclination of the orbit. ”

“ Now let us look at the Earth being circled round the sun by the electro-magnetic Aether currents as it goes on to perform the other half of the orbit. In this case we have the orbital motion of the sun and the centrifugal force working conjointly, with the result that together they overcome the centripetal force, and the Earth is repelled and carried beyond its mean distance. ”

“ For the sun pulls on a planet with a titanic force; it draws it in with the apparent force gravity, and another similar, but opposite force, centrifugal force of its revolution in its orbit, is constantly tending to throw it into the depths of space. These are the two forces that are always balanced. Suppose the planet is drawn nearer the sun; it revolves in a smaller orbit—and it revolves in that smaller orbit with a higher speed—for it has fallen in toward the sun; it has gained speed as any falling body would. ”

“ In order to understand the reason why it does not do thus, we must reflect, that, when a body is revolving in its orbit under the influence of the projectile force and gravity, whatever diminishes the force of gravity, while that of projection remains the same, causes the body to approach nearer to the tangent of her orbit, and of course to recede from the centre; and whatever increases the amount of gravity, carries the body towards the centre. ”

“ To appreciate the significance of the discovery of the elliptical orbit of the planets, it is necessary to understand the complicated confusion that prevailed in the conception of planetary motions. The primal thought was that the motions of the planets were uniform and circular. This intuition of circular orbits was a happy one, and was, perhaps, necessitated by the very structure of the human mind. The sweeping and centrifugal soul, darting manifold rays of equal reach, realizes the conception of the circle, that is, a figure all of whose radii are equidistant from a central point. ”

“ The reason of there being only six seems to be attained. This coincidence assures him he is on the right track, and with great enthusiasm and hope he "represents the earth's orbit by a sphere as the norm and measure of all"; round it he circumscribes a dodecahedron, and puts another sphere round that, which is approximately the orbit of Mars; round that, again, a tetrahedron, the corners of which mark the sphere of the orbit of Jupiter; round that sphere, again, he places a cube, which roughly gives the orbit of Saturn. ”

“ This is very closely related to the fact, mentioned above, that the non-circular orbits will correspond to a firmer binding than the circular orbits having the same value for the principal quantum number, since the electrons will at certain moments penetrate much farther into the interior of the atom. Even though a orbit will not penetrate into the innermost configuration of orbits, it will penetrate to distances from the nucleus which are considerably less than the radii of the circular orbits. ”

“ Let us consider for a moment how little of it gets used in our system. The earth's orbit is a nearly circular figure more than five hundred million miles in circumference, while only eight thousand miles of this path are at any one time occupied by the earth's mass. Through these eight thousand miles the sun's radiated energy is doing work, but through the remainder of the five hundred million it is idle and wasted. But the case is far more striking when we reflect that it is not in the plane of the earth's orbit only that the sun's radiance is being poured out. ”

“ The radius of the orbit in which those bodies travel is sixty-five times the distance of the Earth from the Sun; which means that they travel in an orbit twice the width of that of the planet Neptune. It has been estimated that they complete a revolution in about eight centuries. The united mass of the system is about one-half that of the Sun, and in point of luminosity they are much inferior to that orb. ”

“ But we have just learned that the sun is moving through space, and that it describes an elliptic orbit around some central body in accordance with Kepler's First Law. So that the only philosophical conclusion that we can possibly arrive at in relation to the orbital motion of the sun is, that such motion is caused by similar electro-magnetic Aether currents whose circulating motion is partly caused by the rotation of that central body. ”

“ It is unlikely that any escape that ordeal, and even if they do, their career and orbit are effectually changed. Henceforward they must become attendants on the earth. They may drop on to its surface, or they may duck out of our atmosphere again, and revolve round us unseen in the clear space between earth and moon.
Nevertheless, although the problem of determining the original orbit of any given set of shooting-stars before it struck us would seem nearly insoluble, it has been solved, and solved with some approach to accuracy; being done by the help of observations of certain other bodies. ”

“ Above all these spheres, a primum mobile gave motion to the whole machine, making it turn from east to west, but each planet and each fixed star made an effort against this motion, by means of which each of them accomplished their revolution about the earth in greater or less time, according to its distance, or the magnitude of the orbit it had to accomplish. ”

“ The orbit of the electron may at any moment be considered as an ellipse with the nucleus in the focus, and the length of the major axis will approximately remain constant, but the effect of the field will consist in a gradual variation of the direction of the major axis as well as the excentricity of the orbit. ”

“ If the orbit were a circle it is evident at a glance that the law must be true, because then the sun would be situated in the centre of the circle, the length of the radius vector, no matter where the planet might be in the orbit, would never vary, and the area swept over by it in one day would be equal to the area swept over in any other day, because all these areas would be precisely similar and equal triangles. ”

“ Fourthly, a body in motion will move in a straight line, unless diverted out of that line by some external force; and the body will resume its straight-forward motion, whenever the force that turns it aside is withdrawn. Every body that is revolving in an orbit, like the moon around the earth, or the earth around the sun, tends to move in a straight line which is a tangent [7] to its orbit. Thus, if A B C, Fig. 28, represents the orbit of the moon around the earth, were it not for the [130] constant action of some force that draws her towards the earth, she would move off in a straight line. ”

“ As the adjustment between the energy of the orbit jump and the period of the light carrying away that energy so as to give the constant quantity is perhaps the most striking evidence of the dominance of the quantum, it will be worth while to explain how the energy of an orbit jump in an atom can be measured. ”

“ The proton carries nearly all the mass of the atom and remains rock-like at the centre, whilst the nimble electron moves round in a circular or elliptic orbit under the inverse-square law of attraction between them. The system is thus very like a sun and a planet. But whereas in the solar system the planet’s orbit may be of any size and any eccentricity, the electron’s orbit is restricted to a definite series of sizes and shapes. There is nothing in the classical theory of electromagnetism to impose such a restriction ”

“ It follows that, if we go on computing the elements a, b, c, d from the actual values of x, y, x′ and y′, at each moment when the planet is subject to the attraction of another body, they will no longer be invariable, but will slowly vary from day to day and year to year. These ever varying elements represent an ever varying elliptic orbit,—not an orbit which the planet actually describes through its whole course, but an ideal one in which it is moving at each instant, and which continually adjusts itself to the actual motion of the planet at the instant. ”

“ According to the best tables we now have, the planes of the orbits of Jupiter, the Earth and Mercury are immoveable, though the orbits themselves have a progressive motion in their planes. On the contrary, the poles of the orbits of Saturn, Mars and Venus are supposed to revolve about the poles of the earth’s orbit, with such velocities as at present nearly reconcile calculation to appearances. ”

“ When a hydrogen atom is left to itself, if the electron is in the minimum orbit it will continue to rotate in that orbit so long as nothing from outside disturbs it; but if the electron is in any of the larger possible orbits, it may sooner or later jump suddenly to a smaller orbit, either the minimum or one of the intermediate possible orbits. ”