"There are two great forces in this universe. Your grandfathers called them Centripetal and Centrifugal forces; your fathers called them Gravity and Apergy, names which still cling to them; and you call them Attraction and Repulsion.
"It was Kepler, not Newton, who discovered that Attraction or
Gravity was in inverse proportion to the square of the distance.
"You know the meaning of this mystic phrase, 'as the squares of the distance.' You understand that it means the attraction at two feet is only one-fourth the attraction at one foot; at four feet only one-sixteenth; at eight feet, only one sixty-fourth.
"But who knows or cares for Kepler's great law of Repulsion, or Apergy? That was that the 'square of the times are as the cubes of the distance.' It has lain fallow for centuries. No one of your western physicists has ever studied it, or tried to explain it. It remains just where Kepler left it, as the mere law of orbital revolution of the planets only.
"It is the key to the proper understanding of the universe.
"'The squares of the times are as the cubes of the distance' means that all motion is the result of two forces acting upon prakriti, and that where the two forces are balanced, or equal, the result in motion is a circle or ellipse, the square of the Repulsion being equal to the cube of the Attraction to make them equal and produce a circle. In other cases they produce hyperbola and parabola.
"This is a little dry—nearly all fundamental knowledge is—but the reward of patience is great.
"The orbital speed of the earth is about 60,000 miles per hour. The attraction of the sun exactly equals the repulsion created by the motion; more accurately, the speed created by the repulsion. The result of the two forces working together at exact balance is a circle. An ellipse is a circle bent a little, and the ellipse in which the earth actually moves comes from varying attraction and repulsion. Kepler's second law covers that.
"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.
"Suppose a planet were to be placed so that it would have a time of two years. Its distance from the sun would be 1.6 that of the earth. Why? Because to get the time doubled we would have to take the square root of 4; and to get the distance the cube root of the same number, 4. If you wish to be very exact the cube root is 1.5889, but 1.6 is near enough for all ordinary work.