Planetary motion

“ 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. ”

“ So far has this view been strained, that the temperature of the planets has been referred to their motions, and speculation has aided the mathematician in determining the cessation of planetary motion, by the conversion of it into heat. It is true that other theorists have supposed points in space upon which this heat might be concentrated and reflected back again to produce motion. ”

“ If it teaches us anything at all, it teaches us that every satellite and planet moves with varying velocity in a varying orbit around some central body. So far as our observation goes, then, in relation to planetary motion, or the motion of satellites, we learn that every body which moves in space fulfils Kepler's First Law, and describes an orbit round a central body, that body occupying one of the foci. ”

“ The atmosphere of the planet forms an integral portion of its material, partakes of its rotatory motion, and is bound to the solid core by the mutual gravitative forces. Any mass, then, on the solid surface of a planet is, in reality, in the planetary interior, and the rising of such a mass from that surface does not imply any actual separative process, but simply the radial movement, or displacement of a portion of the planetary material from the central axis. ”

“ 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. ”

“ Is not the earth rotating on its axis, so that in the course of a few hours the observatory on the equator is carried bodily round for thousands of miles? As the morning approaches the observations are to be repeated. The planet is found to have changed its place very considerably with regard to the stars. This is partly due to its own motion, but it is also largely due to the parallactic displacement arising from the rotation of the earth, which may amount to so much as twenty seconds. ”

“ 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. ”

“ Thus, when a planet is in its aphelion or at the point where the orbit is farthest from the sun, his action overcomes its velocity, and brings it towards him with such an accelerated motion, that it at last overcomes the sun's attraction, and shoots past him; then, gradually decreasing in velocity, it arrives at the aphelion where the sun's attraction again prevails. In this motion the radii vectores, or imaginary lines joining the centres of the sun and planets, pass over equal areas in equal times. ”

“ We shall account for these motions by supposing, that which can hardly be denied, that the planets have a certain natural appetite for uniting themselves with the globe round which they revolve, and that they really tend, with all their efforts, to approach to such globe; the planets, for instance, to the sun, the Medicean Stars to Jupiter. It is certain, also, that circular motion gives a body a tendency to recede from the centre of such revolution, as we find in a wheel, or a stone whirled in a sling. Let us suppose, then, the planet to endeavor to approach the sun ”

“ Augment the velocities of the planets, and their orbits will enlarge—the Solar System will occupy a wider space. Diminish their velocities, and their orbits will lessen—the Solar System will contract, or become more integrated. And in like manner we see that sensible motions given to bodies on the Earth’s surface involve partial disintegrations of the bodies from the Earth; while the loss of their motions are accompanied by their re-integration with the Earth. In all changes we have either an integration of matter and concomitant dissipation of motion ”

“ So that by the time the earth has made its annual revolution round the sun, the whole system has been carried 157,680,000 miles through space, and therefore the earth does not complete a perfect ellipse, but its orbital motion round the sun will be represented by a similar kind of diagram to the one which represents the orbital motions of the moon, or any other satellite round its central body. ”

“ With such a regular decrease of kinetic energy, there must necessarily be imparted to the planets, as their mean distance is increased, a decreased velocity of motion, with the natural result, that the further a planet is from the sun, the less will be its orbital velocity, and that in a regular and uniform proportion as the distance is increased. ”

“ Again, the motion of a planet is a progressive effect, produced by causes at once permanent and progressive. The orbit of a planet is determined (omitting perturbations) by two causes: first, the action of the central body, a permanent cause, which alternately increases and diminishes as the planet draws nearer to or goes farther from its perihelion, and which acts at every point in a different direction; and, secondly, the tendency of the planet to continue moving in the direction and with the velocity which it has already acquired. ”

“ From this consideration, in combination with the considerations which I stated, relative to the dependence of curvature of path upon velocity and deflecting force, I shall endeavour to give you a little idea of the motion of a planet in its orbit. The thing that I wish specially to explain to you is, how it happens that when a planet has once begun to approach to the sun, it does not go quite to the sun, but after a time recedes again from it. ”

“ But if the sun can be assumed to possess at some point in its history no orbital motion, or rotatory motion on its axis, then the physical interpretation of the first law of motion can be physically conceived, and a planet at rest will remain at rest relatively to its central body, the sun, for ever. ”

“ The effects of deviations from spherical form could then be treated separately289 when required, as in the cases of precession and of other motions of a planet or satellite about its centre, and of the corresponding action of a non-spherical planet on its satellites; to this group of problems belongs also that of the tides and other cases of the motion of parts of a body of any form relative to the rest.
Again, the solar system happens to be so constituted that each body’s motion can be treated as determined primarily by one other body only. ”

“ 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. ”

“ The attractive power of the Earth therefore extends to the Moon; and, in combination with her projectile force, causes her to move round the Earth in the same manner as the circulating body above supposed.
The Sun and Planets attract each other. 103. The Moons of Jupiter and Saturn are observed to move round their primary Planets: therefore there is such a power as gravity in these Planets. All the Planets move round the Sun, and respect it for their centre of motion: therefore the Sun must be endowed with attracting force, as well as the Earth and Planets. ”

“ The earth turns on its axis at the rate of more than 1,000 miles an hour, and passes around the sun with the speed of upwards of 68,000 miles in the same time. [8] The earth and the other planets of our system move in ellipses around a common centre: therefore their motion cannot have been originally communicated merely by the impressed force of projection. Two forces, at least, must have operated, one making the planets tend directly to the centre, and the other impelling them to fly off at a tangent to the curve described. ”

“ Every physical impulse, it is said, which is initiated anywhere on the earth, is felt to the extremities of our solar system—every motion of the smallest particle of matter communicating its effect, however inappreciable, to the [Pg 27] most distant planet, and as far beyond as the power of gravitation may extend. ”

“ 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. ”

“ 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. ”

“ That the motions of the planets in the heavens may subsist an exceedingly long time.
In the Scholium of Prop. XL, Book II, I have shewed that a globe of water frozen into ice, and moving freely in our air, in the time that it would describe the length of its semi-diameter, would lose by the resistance of the air 1⁄4586 part of its motion; and the same proportion holds nearly in all globes, how great soever, and moved with whatever velocity. But that our globe of earth is of greater density than it would be if the whole consisted of water only, I thus make out. ”

“ Since the positions of planets in their orbits change rapidly, the former part of the disturbing force changes rapidly, and produces in general, at short intervals of time, effects in opposite directions, first, for example, accelerating and then retarding the motion of311 the disturbed planet; and the corresponding inequalities of motion are the periodic inequalities, which for the most part go through a complete cycle of changes in the course of a few revolutions of the planets, or even more rapidly. ”

“ These manifestations of energy, in fact, constitute planetary phenomena. Since the action or movement of the rotating material of the planet through the incepting fields of the primary is most pronounced in the equatorial or regions of highest linear velocity, and least in the regions of low velocity adjoining the poles of rotation, the transforming effect may naturally be expected to decrease in intensity from equator to poles. Planetary energy phenomena will thus vary according to the location of the acting material. ”

“ These rings gradually approach the planets, till finally they fall upon their surfaces, and become part of them; while the planets themselves are approaching their primaries to succumb to a like fate.
Having absorbed their planetary attendants, and having cooled off so as to become cold, dark bodies, like the earth, they enter the sphere of each other's sensible attraction, and begin to approach with continually increasing velocity, till finally they meet, each arriving at the point of contact with a velocity of from 400 to 500 miles a second, depending on their mass and density. ”

“ Each power or force may be modified under certain conditions, as shown in the two preceding articles; but, whether the planet be repelled further away, or attracted nearer to the sun, through the onward motion of the sun, the two forces ever seek to maintain their equilibrium, and to place the planet at its mean position assigned to it in the solar system. ”

“ The outer planets would cool off first, become inhabitable, and, as the sun contracted and they radiated their own heat, become refrigerated and left behind by the retreating sun. Of course the outer planets would move slowly; but as that portion of the sun which gave them their motion drew in toward the centre, keeping its absolute speed, and revolving in the lessening circles of a contracting body, it would give the faster motion necessary to be imparted to Earth, Mercury, and Vulcan. ”

“ Thus, as stated, the orbital motion of the sun and the centrifugal forces are now working conjointly together, with the result that the Earth is repelled gradually further and further from its central body, until it reaches its maximum distance of 94,500,000 miles. ”

“ In leafage they mark the forces of its growth and expansion, but some among the most beautiful of them are described by bodies variously in motion, or subjected to force; as by projectiles in the air, by the particles of water in a gentle current, by planets in motion in an orbit, by their satellites, if the actual path of the satellite in space be considered instead of its relation to the planet ”

“ 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. ”