Orbital period

“ 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. ”

“ 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. ”

“ 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 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ The central problem was that of the secular alterations in the elements of a planet's orbit regarded as a varying ellipse. Three of these elements, the axis of the ellipse, its eccentricity, and the inclination of its plane to a fixed plane (usually the ecliptic) , are of much greater importance than the other three. The first two are the elements on which the size and shape of the orbit depend, and the first also determines (by Kepler's Third Law) the period of revolution and average rate of motion of the planet ”

“ 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. ”

“ 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. ”

“ Mercury, for instance, travels at a rate of 35 miles a second while Neptune, seventy-five times as far off, has an orbital velocity of only 3.4 miles a second. The following table shows the distances of each planet from the sun and the time it takes it to complete its journey around its orbit, beginning with Mercury, the nearest planet to the sun, and continuing outward. ”

“ 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. ”

“ Since the spectroscope can give us no information as to the inclination under which we see the orbit, it follows that the actual orbital velocities of the spectroscopic binaries must remain unknown. We can only say that they cannot be less, but may be greater to any extent than that shown by our measures. ”

“ The fluid mass thus formed will, by this prodigious heat, be exploded outwards in vapour or gas all round. Its boundary will reach to a distance considerably less than one hundred times the radius of the earth’s orbit on first flying out to its extreme limit. A diminishing series of out-and-in oscillations will follow, and the incandescent globe, thus contracting and expanding alternately, in the course, it may be, of 300 or 400 years, will settle to a radius of forty times the radius of the earth’s orbit. ”

“ 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. ”

“ Put the semi-axis of the earth's orbit 100000, and the semi-axes of the orbits of Saturn, Jupiter, Mars, Venus, and Mercury, from their periodic times, will come out 953806, 520116, 152399, 72333, 38710 respectively. But from the sun's motion every semi-axis is increased (by Prop. LX) by about one third of the distance of the sun's centre from the common centre of gravity of the sun and planet (p. 405, 406.) And from the actions of the exterior planets on the interior, the periodic times of the interior are something protracted, though scarcely by any sensible quantity ”

“ 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. ”

“ In like manner, if the periodic time is 33·25 years, only a small portion of the orbit near the perihelion fulfills it. On the other hand, if the annual motion is 1 ± 1/33·25 revolutions, the required condition is answered through a large part of the orbit. Inasmuch as no reason appears why the earth should meet a group near its apsides rather than elsewhere, we must regard it as more probable that the group makes in one year either 1 + 1/33·25, or 1 - 1/33·25 revolutions. ”

“ 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. ”

“ 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 ”

“ A comet, for example, having an orbit extending to the path of the planet Neptune, approaching so near the sun as to almost graze his surface in passing, would have a velocity within 86 miles of what we have assumed. Twice this assumed velocity would give 200,000,000 years’ heat; four times the velocity would give 800,000,000 years’ heat; and so on.
We are at perfect liberty to begin by assuming the existence of stellar masses in motion; for we are not called upon to explain how the masses obtained their motion, any more than we have to explain how they came to have their existence. ”

“ 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. ”

“ When electrons pass from higher to lower energy levels of orbital revolution, quanta are always given off. Orbital shifting of electrons results in the ejection or the absorption of very definite and uniform measurable particles of light-energy, while the individual electron always gives up a particle of light-energy when subjected to collision. ”

“ There is a period during which the atom is patiently waiting for a light-wave to run into it and throw up the electron. There is another period during which the electron revolves steadily in the higher orbit before deciding to come down again. Professor Milne has shown how to calculate from observations of the chromosphere the durations of both these periods. The first period of waiting depends on the strength of the sun’s radiation. ”

“ That part of the force which is in the direction NM, perpendicular to the orbit, produces an effect similar to that which gravity produces in the motion of a cannon ball : it makes the orbit curved. But that part which acts in the direction of OM, parallel to the orbit, produces a different effect; it accelerates the planet's motion in its orbit. Thus, in going from l towards L, the planet is made to go quicker and quicker. ”

“ So far as the general conception of orbits which behave in the main, especially in the simpler atoms, in accordance with the Bohr assumptions, is concerned, if the test of truth in a physical theory is large success both in the prediction of new relationships and in correctly and exactly accounting for old ones, the theory of non-radiating orbits is one of the well-established truths of modern physics. ”

“ The components are five seconds apart, and of the fourth and sixth magnitudes. Their light period is stated to be twenty years, and the combined mass of the system is nearly three times that of the Sun. The pair travel in an orbit from fourteen to forty-two times the radius of the Earth’s orbit; so that when at apastron they are three times as distant from each other as when at periastron. They complete a revolution in eighty-eight years. ”

“ It is evident, in the first place, that for the correction of our fundamental equation we need not trouble ourselves with the position of the orbit in the solar system. The intervals of time, which determine this correction, depend only on the three heliocentric distances and the two heliocentric angles, which will be represented by and if we write for the true anomalies. ”