If two equal opposing masses are attracting each other in space, be they binary stars or any other bodies then a priori the inertial resistance of each equal opposing mass will also be equal, as will the quantity of attracting force received by and acting upon each opposing mass (Newton’s laws). Does this mean that the equal attraction force and the equal inertial resistance of each opposing body’s mass will cancel each other out, as claimed by Hawking and others? Does this mean that the two equal masses will not move or will not accelerate relatively toward each other?
Of course not. It only means that each equal opposing mass will accelerate equal distances in equal times relative to one another, and (if orbiting each other) will circumnavigate each other in equal orbits during equal periods (Figure 26). Thus, this equality of mass, force and inertial resistance means that the reciprocal motions, accelerations, actions, and reactions of the two equal opposing masses will also be equal. We know this empirically from observing the mutual motions, accelerations, orbits, orbital distances and orbital periods of binary stars with substantially equal or substantially similar masses. In fact, the only way that two nearby gravitating bodies could theoretically have relative equal accelerations would be if they have equal masses and are gravitationally opposing and attracting one another as described above; or if they have equal masses and are being attracted and accelerated by a third mass from equal distances.
On the other hand, if the two opposing masses are not equal, then the reciprocal motions, accelerations, actions, and reactions of the two opposing masses will also be unequal. We know this empirically from observing the reciprocal unequal motions, accelerations, orbits, orbital distances, and orbital periods of the opposing unequal masses of the Moon and the Earth, and of the Earth and the Sun.
Specifically, why does an unequal mass-ratio result in unequal reciprocal gravitational accelerations? The answer is: because the greater the force-resistance ratio between two opposing gravitating masses…the proportionally greater is the same force acting upon the lesser inertial resistance of the smaller mass. For example, the equivalent relative force received by and acting upon both the Earth and the Moon is 1 (Figure 21). This equivalent force of 1 acting on the inertial resistance of the Earth (82) results in a force-resistance ratio of 1:82. But such equivalent force of 1 when acting on the inertial resistance of the Moon (1) results in a force-resistance ratio of 1:1. Thus, the Moon’s mass (lesser resistance) will accelerate 82 times faster and farther in t time than the mass (greater resistance) of the Earth.
Restated in a somewhat different way, the equivalent force of attraction received by each body causes the relatively smaller inertial resistance of the smaller mass (the Moon) to accelerate proportionally faster and farther during the same time interval than the relatively larger inertial resistance of the larger mass (the Earth).
All of these above concepts must hold true regardless of whether the two unequal opposing masses are galaxies, binary stars, planets, moons, asteroids, cannonballs, or apples.
Thus, a priori, Galileo’s two unequal cannonballs could not have accelerated equally relative to the much greater third mass of the Earth. It only appeared that they were accelerating equally because two similar and relatively tiny unequal masses were gravitating together and being attracted relative to the enormous mass (inertial resistance) of the Earth. In this particular case, the force-resistance ratio between the two unequal cannonballs was substantially the same, vis. approximately 1:6×1025 as compared to 1:6×1024. But between each relatively tiny unequal cannonball on the one hand (Chart 30, B1 and B2), and the relatively enormous Earth, the force-resistance ratio was also enormous: 6×1025: 1 or 6×1024:1. (Chart 30, D1 and D2). The minute difference in acceleration of these two very similar tiny masses relative to the enormous and relatively stationary mass of the Earth (vis. 1:6×1025 as compared to 1:6×1024) could not be observed nor detected (Chart 30, D1 and D2). The observed illusion was an equal rate of acceleration.
These are essentially the reasons why Galileo, Newton, Bessel, Eötvös, Einstein, De Sitter, Born, Gamow, Feynman, Dicke, Schwinger, Hawking, and everyone else has been fooled and convinced into believing that unequal masses accelerate (fall) equally relative to the Earth. They were all comparing the mass-ratio and the resulting forces, inertial resistances, motions, and accelerations of the smaller cannonball relative to the larger cannonball, which motions and accelerations appear to be very similar because their relatively tiny masses are really quite similar when compared to the enormous mass of the Earth. The minute difference in the large accelerations of the two unequal cannonballs relative to the reciprocal but infinitesimal acceleration of the Earth was not perceivable, detectible, or measurable; nor was it even considered. Thus, both tiny objects are empirically perceived to accelerate toward the Earth at the same rate. But this is only a paradoxical illusion.