Orbital inclination

“ As the two bodies approach conjunction, the small one will be drawn inward to meet the larger one, and this contraction of its orbit so increases its orbital velocity that, at the time of meeting, this velocity is greater than that of the controlling mass, and on striking it will give the latter an impulse to rotate in the direction of its orbital motion ”

“ Anomalous spectral effects, probably due to the very considerable eccentricity of the orbit, long impeded its satisfactory determination. The mean distance apart of the component stars, as now ascertained, is just twenty-two million miles, and their joint mass quadruples that of the sun. But these are minimum estimates. For if the orbital plane be inclined, much or little, to the line of sight, the dimensions and mass of the system should be proportionately increased.
An analogous discovery was made by Miss Maury in 1889. ”

“ That the intermolecular forces are not altered by factors many times less than those obtained by Rayleigh, is found to be the case in the media used.
Experiments with Water.
Two arrangements suggest themselves: the one, a system rotating about a vertical axis, the other a similar system rotating about a horizontal axis so as to shift the plane of polarization from a position at 45° to the earth's orbital motion through an angle of 90°. In the matter of simplicity, sensibility, and stability the latter method would be preferable. ”

“ 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. ”

“ After that the eccentricity of the earth's orbit will begin to increase, and will continue to increase for about 40,000 years, according to some scientists, which implies that the sun will then have started from its aphelion point, so to speak, and will begin its return journey towards its central body, gradually getting nearer and nearer. As it gets nearer its orbital velocity will be proportionately increased, with the result that the eccentricity of the earth's orbit will increase also. ”

“ This decreased distance means an increased aetherial density and an increased velocity of the aetherial currents, with the result, that as the distance is decreased, the orbital velocity of the Earth is gradually increased, so that by the time the Earth gets to F, at its perihelion, it has now acquired its greatest orbital velocity, and is carried round the sun by the electro-magnetic Aether currents at its maximum velocity. ”

“ But, because of it's great mass, our orbital velocity is something terrific!
"We're going around that thing better than three hundred times every second; our 'year' is three milliseconds long! Our orbital velocity is seven hundred thousand kilometers per second!
"We're moving along at about a fifth of the speed of light!"
"Are we safe in this orbit?" Fuller asked.
"Safe enough," said Arcot bitterly. "So damned safe that I don't see how we'll ever break free. We can't pull away with all the power on this ship. We're trapped!
"Well, I'm worn out from working under all that gravity ”

“ 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. ”

“ It is probable that there are more systems with variations of speed under six kilometers than there are with larger ones; and all such are awaiting discovery. The velocity of our sun through space varies slightly, because it is attended by companions—very minute ones compared with the invisible bodies discovered in spectroscopic binaries. It is revolving around the center of mass of itself and its planets and their moons. Its orbit around this center is small, and the orbital speed very slight. The total range of speed is but three one hundredths of a kilometer per second. ”

“ 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. ”

“ 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. ”

“ Herschel first attacked the question as to whether the sun, like all the other stars, was in motion, and if in motion, what was the shape of its orbit, and the laws which governed its orbital velocity.
We know that the sun is the centre of the solar system, and the question to be considered is, whether that system is circled round a controlling centre while the sun is at rest in space, simply possessing its one axial rotation, or whether, like every planet and satellite, it is subject to two motions, an axial rotation and an orbital velocity through space. ”

“ All of the solar system material derived from the sun was originally endowed with a homogeneous direction of orbital swing, and had it not been for the intrusion of these three foreign space bodies, all solar system material would still maintain the same direction of orbital movement. ”

“ In the system () derived from () by a Lorentz-transformation with the axis () and the modulus , the Sun and the planet have a common velocity in the direction () , and the relative orbit is no longer circular, but is defined by (43) . Let, again, the orbital plane be chosen as plane of () in the first system of reference, and let the axis of be perpendicular to the axis of the transformation. The observer belonging to the system has no means of ascertaining the position of the plane of () , he can only observe the plane of the orbit, i.e. the plane of . ”

“ If the orbital speed of the earth were a mile less per hour, or even a foot less, then the earth would wind up around the sun as a dog gets wound up with his chain around a tree. If this speed were a mile more per hour, then the earth would wind out, each year getting farther and farther away, until finally it would be lost. When the speed is exactly proportional to the pull—that is, when it is as 1.6 is to 2,—the result is a circular orbit, the eccentricity of which is caused by certain fluctuations in the attraction and repulsion. ”

“ 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. ”

“ So far too as the evidence carries us, we can perceive some quantitative relation between the motions produced, and the gravitative forces expended in producing them. The planets formed from that matter which has travelled the shortest distance towards the common centre of gravity, have the smallest velocities: the uniform law being that in advancing from the outermost to the innermost planets, the rate of orbital motion progressively increases. It may indeed be remarked that this is explicable on the teleological hypothesis; since it is a condition to equilibrium. ”

“ It may also seem incredible that any orbital movements could be permanent enough to sustain oscillatory vibrations of such inconceivable frequency as those which luminous rays are known to execute; but I have computed, from the probable dimensions of the hydrogen molecule as assigned by the molecular physicists, and an orbital velocity due to an ethereal origin for the components, that many hundreds of revolutions must occur for each transverse oscillation or elliptical deformation. ”

“ A match could be immediately obtained by rotating the compensator 10. By noting the position of the pointer for a match and then shifting the same until such a change could just be detected, a measure of the sensibility of the system could be obtained. This angle was found to be 0°.2 under favourable conditions. At each observation the sensibility was determined. A match was obtained with, say, the trough in the meridian at noon, this was then turned through 90° into the direction of the earth's orbital motion. ”

“ It is noteworthy that almost all the observations which have been made with negative results as to the effect of the Earth's orbital motion on the ether are equally consistent with complete connexion and complete independence between ether and matter. If there is complete connexion, the ether near the earth is relatively stagnant, and negative terrestrial results are natural. If there is complete independence, the ether is either absolutely stationary or has a velocity-potential, and the negative results are, as has been shown, thereby explained. ”

“ In two hours he detected its motion, and in a month he sent his observations to Gauss, who returned as answer the calculated orbit. It was distant 2·67, like Ceres, and was a little smaller, but it had a very excentric orbit: its plane being tilted 341⁄2°, an extraordinary inclination. ”

“ 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. ”

“ He thought it more likely that the earth rotated than that the stars moved with great speed in their large orbits. He proposed that the earth spins on its own axis about once every twenty-four hours, with a spin axis at about a 23 1/2 degree tilt from the orbital axis, thus explaining a slow change in the overall appearances of the fixed stars which had been observed since the time of Ptolemy. ”

“ When the breadth is very much greater than the height, the orbit is very eccentric. Bohr holds that in each ring the more eccentric orbits are filled first, and the less eccentric later; he bases this view on considerations of stability, because we always have to account for the fact that the system of electrons does not break down more often than it does. ”

“ 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. ”

“ 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. ”

“ Therefore, in order to ascertain what is the curvature of an orbit, we must consider not only the amount of the sun's attraction at any part of it, but also what is the amount of velocity with which the planet is moving at that point. If, then, it can be shown that when the planet is nearest to the sun it moves with a greater velocity, it will follow that, though the attractive force is greater than when farthest from the sun, its orbit may not be more curved than when it is farthest from the sun. ”

“ 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 other words, the stability of the orbit is so slight, even if the variation in the mass is taken into account, that small external forces are in a position to change the eccentricity in the course of time to a finite extent. ”

“ 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. ”

“ 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. ”