Part V.   Center of Mass and Relative Gravitational Acceleration
AA.   The Center of Mass of the Earth-Moon and Sun-Earth Gravitational Systems

Another obvious example of this center of mass concept is observed in the Earth-Moon gravitational system. The Earth-Moon system is also comprised of two bodies with quite different masses. The Earth’s mass is about 82 times greater than the mass of the Moon (Figure 16 and Figure 17.1). Like the unequal binary star system, the center of mass between the Earth and the Moon is located about 82 times closer to the larger Earth’s physical center than it is to the physical center of the smaller Moon. Like the Sun-Earth system, the Earth-Moon center of mass is located at a point within the sphere of the larger mass (the Earth), and about 4,683 km from the Earth’s physical center (Figure 27).

As with the Sun-Earth system, the Earth and the Moon orbit around their common center of mass. The orbit of the Earth’s greater mass is relatively so small that it cannot normally be detected by the observer on Earth. On the other hand, the Moon’s physical center orbits this common center of mass from a radial distance of approximately 384,000 km. Each month we humans on Earth actually observe the Moon’s orbit around the Earth as it proceeds through its four lunar phases.

The radius of the Moon’s orbit around the Earth is about 82 times greater than the radius of the Earth’s tiny orbit. Thus, each second the Moon accelerates (falls) relative to the Earth about 82 times faster (1.043 km/s) and farther (0.14 cm/s) than the Earth accelerates (falls) relative to the Moon (about 0.0127 km/s and about 0.0017 cm/s respectively) (Figure 20 and Figure 27). Once more, this scenario is another perfect example of Newton’s law of gravitational attraction at work, in combination with his three laws of motion.

If Galileo’s equal acceleration of unequal masses experiment was really correct, then the very unequal masses of the Moon and the Earth should somehow fall (accelerate) equally relative to each other (Figure 21B), and they should somehow equally orbit around each other (Figure 26B). But, again, this obviously and empirically does not happen. Every second, each very different opposing mass accelerates or falls relative to the other, a certain distance and with a certain motion which is inversely proportional to its mass; again just as predicted by Newton’s second and third laws, and as stated by Feynman.

With centers of mass and opposing masses in space, there are so many reciprocal forces (intensities and quantities received), accelerations, motions, inertial resistances, actions, reactions, directions, and magnitudes, not to mention masses again, that it can become very difficult to keep them all straight in one’s mind. Nevertheless, both Newton and Einstein were very aware of this center of mass concept (or “center of gravity,” as Newton called it).

Newton correctly postulated in the Principia: “[T]he causes assigned to natural effects of the same kind must be…the same.” In accord with this postulate, it becomes quite obvious from the above empirical examples that the reciprocal gravitational accelerations between any two opposing bodies in any two-body gravitational system must have the same cause as their reciprocal intensities of gravitational attraction and their reciprocal inertial resistances: the masses of the bodies involved are this common cause. All of these reciprocal natural effects (gravitational attractions, inertial resistances of masses, and gravitational accelerations) empirically and logically depend upon the unique mass-ratio of the two opposing masses involved.

This time, Gamow agreed:

“According to one of the basic laws of mechanics formulated by Newton, a given force acting on a certain material body communicates to this body an acceleration which is proportional to the force and inversely proportional to the mass of the body.”

Again, Feynman also agreed:

“[A] body reacts to a force by accelerating, or by changing its velocity each second to an extent inversely to its mass…”

Strangely enough, even Einstein ultimately came to a similar logical conclusion in 1927: “[T]he only causes of the acceleration of masses of a system are these masses themselves.”