"The Newtonian law is thus stated by Herchel: 'Every particle of matter in the universe attracts every other particles of matter with a force directly proportioned to the mass and inversely to the square of the distance between them. Under the influence of such an attractive force mutually urging two spherical gravitation bodies toward each other, they will each, when moving in each other's neighborhood, be deflected into an orbit concave toward each other, and describe one about the other regarded as fixed, or both around their common center of gravity curves, whose forms are limited to those figures known in geometry by the general name of conic sections. It will depend, in any assigned case, upon the particular circumstances or velocity, distance and direction, which of these curves shall be described, whether an ellipse, a circle, a parabola, or an hyperbola; but one or the other it must be, and any one of any degree of eccentricity it may be; and that in every case, the angular velocity with which the line joining their centers moves, must be inversely proportional to the square of their mutual distance, and that equal areas of the curves described will be swept over by their line of junction in equal times.'
"This statement includes the first and second law of Kepler. His third law is, that "the squares of the periodic times of any two planets are to each other in the same proportion as the cubes of their mean distances from the sun."
For the purposes of this investigation let us take as given:
- 1. A force, simply, by which, if not resisted, a planet would be moved toward the sun, in direction of a right line connecting their centers; and
- 2. A portion of the curve of the planet's orbit in its approach toward the sun.
To find the relative value of the force, and its direction, which, with the force given, will produce that curve.
This force, as to its value and direction, being ascertained, it will be attempted to show that it, cooperative with the force given, will, among other effects, produce those on which the first and second laws of Kepler are founded will not only give to the times and spaces of "falling" bodies agreeably to the Newtonian law, but will exhibit a reason why bodies must be accelerated in their "fall" agreeably to that law, and finally will not conflict with the third law of Kepler.
Incidentally, among other things, it will appear from the condition of conflict of force arising.
- 1. That the path of a circle is impossible in planetary motion.
- 2. That the argument, as to the third law of Kepler, gives rise to the curious result of a permitted libration in the eccentricities of planets, which (the forces in question remaining unchanged in their nature) can only arise from the interference of an extraneous cause.
- 3. That the phenomenon of gravitation, or, of "falling," does not exist, except as the result of a conflict of forces. It can only be considered as an isolated force by way of mental analysis or separation.
And under this seems to reside a very important condition, viz: That under the operation of those natural forces causing planetary motion, bodies and particles of matter are not attracted toward each other in direction of right lines connecting their centers, but are forced toward each other in the curves of spirals closing upon the centers each of the other. Among other things it would seem to result from this, that the tidal wave is not the result of attraction.
- 4. A further result appears that, as one of the effects of the conflict of force, a planet, from its aphelion to its perihelion point, should revolve upon its axis with increased rapidity; uniformity in times of revolution, as, for instance, of the earth, being preserved by increasing and decreasing friction of the moon upon it in its approach to, and its departure from, the sun.
If these are right results, it serves to show that the ascertainment of the nature and value of centrifugal force is of importance, as opening new features as to the effects of natural force. It shows that there is no simple force as of gravitation by which a body must be accelerated, but that acceleration is the result of the antagonism of forces always equal, each perhaps always of a constant value, but exerted within limits constantly narrowing or expanding. In fact, the discussion of this antagonism of force may lead us to new ideas as to the very natural of that of which we speak as productive of planetary motion, even to realizing it as in close and inseparable relationship with the vegetable and animal life around us." Skinner, John Ralston, An Essay Upon Force and its Effect Upon Matter (underlines added)