There is a much better, more correct and more precise way to compare the accelerations of the Moon and the apple than by Newton’s direct method. It is the indirect empirical method of separately: 1) comparing the observed ratio of the relative motions of the Earth and the Moon, and 2) then comparing the observed ratio of the relative motions of the Earth and the apple. Thereafter these two ratios are also compared.
We observe the ratio of the Moon’s relatively large constant acceleration (orbital velocity) toward the relatively enormous mass of the Earth, and the Earth’s reciprocal and relatively small constant acceleration (orbital velocity) relative to the Moon, to be an acceleration ratio of approximately Moon (82):Earth (1) (Figure 26). We also observe the ratio of the apple’s relatively enormous acceleration (uniformly increasing rate of fall) toward the Earth at 9.8 m/s/s, and the Earth’s infinitesimally and immeasurably tiny reciprocal acceleration toward the apple which is approximately 1 x 10–26 m/s/s, or zero. We have approximated this second acceleration ratio of the apple and the Earth to be about apple (6 x 1026):Earth (1). When we compare these two empirical acceleration ratios (82:1 and 6 x 1026:1), it becomes obvious that the tiny mass of the apple accelerates at a much greater rate relative to the Earth than does the much larger mass of the Moon, starting at the same distance apart (Chart 30, Column D, shaded areas D1 and D6).
If all bodies had absolutely the same rate of gravitational acceleration regardless of their different masses this result would directly and visibly contradict Newton’s second law of motion (Figure 21). Why? Because the relatively large orbital acceleration of the Moon (as compared to the Earth’s tiny orbital acceleration) should be inversely proportional to the relatively small mass of the accelerated Moon. In fact, this prediction and result of Newton’s second law is actually observed. The Moon’s much greater orbital acceleration relative to the Earth is observed each month to be inversely proportional to the Moon’s much smaller mass, whereas the Earth’s relatively tiny orbital motion is difficult to even detect (Figure 26).
An equal gravitational acceleration of unequal masses result (Figure 21) would also directly contradict the prediction of Newton’s third law of motion, vis. that the action of the Sun’s pulling force on the Earth (the great orbital motion of the relatively tiny pulled mass of the Earth) is equivalent to the reaction to that force (the theoretical tiny orbital motion of the enormous pulling mass of the Sun), such mutual actions are directed to contrary parts; and vice-versa with respect to the Earth. But observation belies such a contradiction. The above predictions of Newton’s third law and its equivalent results are actually observed (or detectable) in the great orbital motion of the Earth’s relatively tiny mass as compared to the tiny orbital motion of the Sun’s relatively enormous mass.
It will be further demonstrated and explained in the later sections of this treatise: 1) why Galileo’s first approximation of the equal gravitational acceleration of unequal masses was not valid as a second approximation, and 2) that the real natural law of Relative Gravitational Acceleration is completely consistent with Newton’s three laws of motion, and all current observations. In other words, the different masses of the apple and the cannonball do not free-fall (accelerate) at the same rate near the surface of the Earth; the very different masses of the planets at equal distances would not accelerate equally toward the Sun; the very different masses of Jupiter’s 63 moons and Saturn’s 62 moons at equal distances would not accelerate in equal times toward such planets; and the vastly different masses of the apple, the Moon and the Sun at equal distances would not accelerate equally toward the Earth. Contrary to ubiquitous conventional wisdom, all gravitational accelerations depend upon the relative magnitudes of the opposing masses (and their inertial resistances) involved.