Planetary orbit

“ 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. ”

“ Stated briefly, the results established by the two astronomers were that the changes in axis, eccentricity, and inclination of any planetary orbit are all permanently restricted within certain definite limits. The perturbations caused by the planets make all these quantities undergo fluctuations of limited extent, some of which, caused by the, periodic disturbing forces, go through their changes in comparatively short periods, while others, due to secular forces, require vast intervals of time for their completion. ”

“ The sun's attraction can have no influence whatever in determining either the direction of a planet's motion, or the eccentricity of its orbit. In other words, this power would sustain a planetary body moving from east to west, as well as from west to east; in an orbit having any possible degree of inclination to the plane of the sun's equator, no less than in one coincident with it ”

“ The scientific verification of this position must of necessity be founded on the terrestrial observation of phenomena. So far as the orbital movements of the planet are concerned these are admittedly orderly; each planetary mass wheels its flight through space with unvarying regularity; the energy processes, also, associated with the variations of planetary orbital path, and which attain limiting conditions at perihelion and aphelion, are readily acknowledged to be reversible and cyclical in nature. ”

“ The sun is the centre of the orbits of the five planets, of which Mercury and Venus move in orbits whose radii are smaller than that of the solar orbit, while the orbits of Mars, Jupiter, and Saturn encircle the earth. This system accounts for the irregularities in the planetary motions which the ancients explained by epicycles and Copernicus by the annual motion of the earth, and it shows why the solar motion is mixed up in all the planetary theories. ”

“ In this limiting condition, also, the energy of position of the planet would be the maximum possible, and its orbital energy zero. The scope of the planetary orbital path is thus rigidly determined by the planetary energy properties. Assuming the reduction of gravity with distance to follow the usual law of inverse squares, the value of the displacement of the planet from the central axis when in this stationary or limiting position may be readily calculated if the various constants are known. ”

“ When, however, we bring thousands of years into consideration, then the displacements of the planetary orbits attain considerable dimensions, and have, in fact, produced a profound effect on the system. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ When it has thus reached a point as M', if we resolve the sun's force into two forces, one perpendicular to the orbit, and one in the direction of the orbit, then that which is perpendicular to the orbit bends it, but that which is in the direction of the orbit retards it; and when it has got to a certain distance, its velocity is small indeed; and though it is so far off that the sun's force is very small, nevertheless, in consequence of the planet's diminished speed, the attractive power of the sun may be able to pull it in and make it describe the same orbit again ”

“ Uranus travels through space in an orbit at an average distance of 1,771,000,000 miles from the sun, encompassing the orbits of Saturn, Jupiter, the Planetoids, Mars, Earth, Venus and Mercury; an orbit so large that it takes the planet 84 years to complete its journey around the sun. ”

“ 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. ”

“ And further, a planet having an axis inclined to the plane of its orbit, must, while its form is very oblate, have its plane of rotation greatly disturbed by the attraction of external bodies; whereas its approach to a spherical form, involving a less extreme precessional motion, implies less marked variations in the direction of its axis. Nor is it only in respect of space-relations that the Solar System in general and in detail has become more precise. ”

“ Light pressure also forces the orbit to go slightly out of round from a perfect circle, and other gradual effects on the satellite’s orbit are caused by the gravitational attraction of the moon and the sun. ”

“ The large arrows show the direction in which the planet travels in its revolution about the sun, and the small curved arrows the direction in which it rotates on its axis. Now, in moving along its orbit from A to B the planet, partly because of its swifter motion when near the sun, and partly because of the elliptical nature of the orbit, traverses a greater angular interval with reference to the sun than the cross, moving with the uniform rotation of the planet on its axis, is able to traverse in the same time. ”

“ Had I used the apergy only to drive me directly outward from the Sun, I should move under the impulse derived from the Earth about 1,600,000 miles a day, or 72 millions of miles in forty-five days, in the direction common to the two planets. The effect of the constantly widening orbit would be much as if the whole motion took place on one midway between those of the Earth and Mars, say 120 millions of miles from the Sun. ”

“ Hence these almost infinitely numerous particles of planet-spray, as we might call it, as well as those formed by the condensation of the metallic vapours accompanying them, would forthwith begin to part company: some going rapidly in advance, and others falling behind; until the stream of them, perpetually elongating, formed an orbit round the Sun, or rather an assemblage of innumerable orbits, separating widely at aphelion and perihelion, but approximating midway, where they might fall within a space of, say, some two millions of miles, as do the orbits of the November meteors. ”

“ 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. ”

“ Thus we see that as long as the planet revolves in its orbit, it will never fall, and to pull it away from the sun is impossible as long as it revolves in its orbit. But if it slows down in its flight about the sun it at once has less centrifugal force. It automatically falls toward the sun until it has gained velocity enough to establish a new orbit of equilibrium. If this energy, too, is withdrawn; if it is made to stand still in its orbit; it will fall straight to the sun. ”

“ 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. ”

“ The sun is twenty-five days in completing its axial rotation; so that in the new planet we have probably another instance in which, as in the case of the inner satellite of Mars, a planetary body performs its orbital revolution in less time than is occupied by the central orb in completing its rotation. Again, as seen from the sun's surface, all the old planets rise in the east and set in the west. ”

“ In virtue of the gravitative attraction or gravitation field between the two, they will mutually attract one another in their motion, and each will, in consequence, be deflected more or less out of that orbital path which it would normally pursue in the absence of the other. This attraction will naturally be greatest when the planets are in the closest proximity; the planet having the widest orbit will then be drawn inwards towards the central axis, the other will be drawn outwards. ”

“ Each ring would break up into masses which would be endued with motions of rotation, and would in consequence assume a spheroidal form. These masses formed the various planets, which, in their turn condensing, cast off in some instances their outlying rings, as the central mass had done, and thus formed the moons or satellites which accompany the planets. As each planet was in turn cast off, the central mass contracted itself within the orbit of that last formed, till, after casting off Mercury, it gathered with immense energy round its own centre and formed the sun. ”