Part V.   Center of Mass and Relative Gravitational Acceleration
EE.   The Relativity of Gravity

The above conclusions are more clearly exemplified as follows: by theoretically substituting much larger masses for the apple and the cannonball.

First, let us hypothetically substitute the Earth’s stationary Moon for the apple or the cannonball near the surface of the stationary Earth (Chart 30, line 6). The Moon obviously has much more mass than the apple or the cannonball, but still the Earth has about 82 times more mass than the Moon (Figure 16). Empirically, the Moon in its relatively huge lunar orbit is actually observed to move and accelerate toward the Earth about 82 times faster and farther in t time than the Earth in its relatively tiny orbit moves and accelerates toward the Moon (Figures 27 and 31C). The inverse correlation between the masses (forces applied and inertial resistances) and the motions (accelerations, actions and reactions) of the Earth and the Moon are shown and described in detail on Chart 30, Line 6. Does any reader believe that the stationary Moon would fall toward the Earth at the same rate as the apple (9.8 m/s/s), while the stationary Earth would not noticeably accelerate toward the Moon?

Second, let us next consider a mass almost the size of the Earth, such as the planet Venus, which has about 82% of the mass of the Earth (Figure 16 and Chart 30, Line 7). If the stationary planet Venus was hypothetically substituted for the stationary Moon near the surface of the stationary Earth, a priori each similar planetary mass would accelerate toward the other at an approximately equal observable rate (albeit Venus being slightly smaller would accelerate slightly faster toward the Earth). Does any reader believe that the stationary planet Venus would fall (accelerate) toward the Earth at the same rate as the apple (9.8m/s/s), while the stationary Earth would not noticeably accelerate toward Venus? A similar result would occur a priori if a twin of the Earth was hypothetically substituted for the stationary planet Venus (Figure 31B).

Third, let us next consider a mass the size of the planet Jupiter, which is about 318 times the mass of the Earth (Figure 16 and Chart 30, Line 9). If the stationary planet Jupiter were hypothetically substituted for the stationary planet Venus near the surface of the stationary Earth, then a priori the Earth (having a relatively 318 times smaller mass) would accelerate toward Jupiter about 318 times as fast and as far during t time as Jupiter would accelerate toward the Earth (Newton’s three laws of motion). Is there any reader who would be willing to assert that the stationary planet Jupiter near the surface of the stationary Earth would accelerate toward the Earth at the same rate as an apple (9.8 m/s/s), while the Earth would not noticeably accelerate toward Jupiter?

Finally, let us consider the ultimate analogy. If a stationary mass the size of the Sun, which has 330,000 times as much mass as the Earth (Figure 16), was hypothetically substituted for the stationary planet Jupiter near the surface of the stationary Earth, then a priori the vastly smaller Earth would accelerate toward the Sun about 330,000 times as fast and as far during t time as the Sun would accelerate towards Earth (Chart 30, line 10, and Figure 31A). This enormous relative gravitational acceleration ratio is actually observed between the Earth and the Sun, and it is similar to the enormous gravitational acceleration ratio between the apple and the relatively much larger Earth (Chart 30, line 1, and Figure 31D).

In both cases, the relative acceleration of the much larger opposing mass remains largely unperceived and undetectable. Is there any reckless reader who would be willing to claim that the stationary Sun would accelerate toward the nearby stationary Earth at the same terrestrial rate as the apple or the cannonball (9.8 m/s/s), while the Earth remains empirically relatively at rest (or stationary)?

Based on the foregoing examples, it should become patently obvious to even the most ardent skeptic, that the smaller the opposing mass of an object relative to the larger mass of the Earth (vis. the greater the unique mass-ratio) the faster will be its relative gravitational acceleration relative to the Earth. Likewise, the larger the opposing mass of an object relative to the mass of the Earth, the slower will be its relative gravitational acceleration relative to the Earth.

The fact that the minuscule difference in accelerations between the apple and the cannonball relative to the enormous mass of the Earth cannot be perceived or measured, or the fact that the different, subtle, and minuscule accelerations of the Earth relative to the two tiny slightly unequal masses also cannot be perceived or measured, does not affect the reality of the above examples.

Based upon all of the above examples, we must now postulate a much more general law of nature: All gravitational interactions of any masses in the universe are completely relative. We shall call this law of nature: “the Relativity of Gravity.”