For all of the foregoing reasons, we must conclude that all opposing unequal masses gravitationally accelerate unequally. These conclusions are obviously demonstrated by binary star systems involving differently gravitating opposing masses; the Sun-Earth system involving extremely different opposing masses; and the Earth-Moon system involving very different opposing masses. As we see in Figure 29, the relatively smaller an opposing mass is, the proportionally closer the common center of mass comes to the physical center of the larger mass.
When the opposing masses become the tiny apple or cannonball relative to the enormous mass of the Earth, for all practical purposes, the center of mass of this two body system and the physical center of the Earth become unity (Figure 29E). This enormous mass-ratio with respect to such center of mass produces a huge relative acceleration ratio of the apple/cannonball (approximately 6 x 1025) as compared to the Earth (1). Galileo unknowingly witnessed this huge relative acceleration ratio at the Leaning Tower of Pisa, but he was totally distracted and blinded by the illusion of apparently equal accelerations of two relatively tiny falling cannonballs of different yet similar mass relative to the apparently stationary Earth.
We must now postulate that the Relative Gravitational Acceleration of any two opposing masses depends upon the mass-ratio involved, be it an apple, a cannonball, an astronaut, the Moon, Mars, the Earth, Jupiter, the Sun, or two binary stars.
There can be no controversy that the above observations and conclusions represent a universal law of nature. Assuming the validity of this natural law, vis. the Law of Relative Gravitational Acceleration, then to quote and paraphrase Feynman on a similar subject: “Everything…[concerning the Relativity of Gravity and Relative Gravitational Acceleration] is a mathematical consequence of those [natural laws].” Feynman, 1965, p. 5. As even Einstein concluded in 1927: “The only causes of the acceleration of masses of a system are these masses themselves.”
If the above postulate of causation holds true for all of the above described unequal opposing masses, it must also hold true for all of the unequal opposing masses of the planets relative to the Sun and relative to each other, and for all of the other unequal opposing masses in the universe no matter how large or how small their respective masses or motions may be. This includes the very unequal opposing masses (and mass-ratios) of the apple, the cannonball, the Moon, and the Sun, relative to the Earth and relative to each other (Chart 30). Remember Newton’s postulate: “[T]he causes assigned to natural effects of the same kind must be…the same.”
Confronted with the above demonstrations and empirical observations involving a wide range of mass-ratios, how can we suddenly change philosophies and the laws of nature in midstream and conclude that opposing unequal masses must fall (accelerate) equally? Can we justify changing these laws of nature just because the opposing mass-ratios involve the very tiny masses of apples and cannonballs as compared to the relatively enormous masses of the Moon, the Earth, and the Sun, or because the subtle differences between the accelerations of similar free-falling masses are not obvious to the observer? Of course not!