Part III.   Problems with Galileo’s and Newton’s Concepts of Gravity
Q.   Newton’s Missing Propositions for Relative Inertial Resistances and Relative Accelerations of Gravitating Bodies

It is true that Newton, in general terms, correctly described the intensity of the attractive force of gravitating bodies as proportional to the inertial mass of the emitting body, and that reciprocal gravitational forces of attraction are mutually received by each opposing mass in equivalent magnitudes. However, there are two major phenomena totally missing from Newton’s theory of gravitation. Newton completely failed to correctly describe and explain the different relative motions and reciprocal accelerations, actions and reactions between two unequal opposing masses as a result of their equivalent opposing forces received and acting upon their different inertial resistances.

Instead, near the beginning of Proposition 6 of Book 3 of the Principia, Newton stated:

“Others have long since observed that the falling of all heavy bodies toward the earth…takes place in equal times, and it is possible to discern that equality of the times, to a very high degree of accuracy, by using pendulums.”[1]

Newton made these totally incorrect statements, because he had become completely confused by Galileo’s paradoxical Leaning Tower equal results, and by Galileo’s descriptions of the motions of pendulums.

By way of example, Newton then conjectured in Proposition 6 of Book 3 that a hypothetically stationary Moon and a hypothetically stationary apple, if released simultaneously from the same height, would fall to Earth in equal times…despite their vastly unequal masses.[2] Likewise, Newton conjectured that hypothetically stationary Jovian moons, all with different masses, would fall toward Jupiter in equal times from equal heights, to-wit:

“…the satellites of Jupiter…in equal times in falling from equal heights [toward Jupiter]…would describe equal spaces, just as happens with heavy bodies on this earth of ours.”[3]

Why did Newton not describe the motion, action and acceleration of the pulled body (i.e. the apple, the Moon or a planet) as inversely proportional to its own mass? This result should automatically follow from Newton’s three laws of motion. Instead, Newton described the gravitational acceleration of all unequal masses as being equal. What is the answer to this self-contradiction, this paradox?

The obvious answer is that Galileo’s “equal acceleration of unequal falling masses” experiment at the Leaning Tower of Pisa and his experiments with swinging chandeliers had convinced Newton that the very different masses of the Moon, the cannonball and the apple all accelerate toward the Earth at exactly the same rate, diminished by the inverse square of the distance.[4] Newton’s conviction in this regard is specifically evidenced by the above statement in his Proposition 6 of Book 3, that: “others have long since observed that the falling of all heavy bodies toward the earth…takes place in equal times…”

Galileo’s gravitational experiments also convinced Newton that the unequal masses of the planets (Figure 16) must accelerate toward the Sun at exactly the same rate, diminished by the inverse square of the distance;[5] so that “[T]he accelerations of these bodies do not depend upon their masses.”[6] In Newton’s own words, all of the unequal masses of the hypothetically stationary solar planets “let fall from equal distances from the sun, would describe equal spaces in equal times in their descent to the sun.”[7] Thus, according to the conjectures of Galileo, Newton, Einstein, Zeilik, and everyone else, all gravitational accelerations exemplify an absolute concept.[8]