Every grammar school student knows that Galileo simultaneously dropped two unequally sized cannonballs from the top of the Leaning Tower of Pisa, and that they appeared to free-fall to the Earth at the same time.[1] Similar experiments have been performed many times, all with similar absolute results. It is thus common knowledge that gravity causes all bodies to free-fall (accelerate) equally, regardless of their mass.[2]

This simple, visibly convincing and seemingly innocuous empirical law convinced Isaac Newton to include it in his law of universal Gravitational Attraction. Based on Galileo’s law of equal gravitational acceleration, Newton concluded that all of the planets fall equally toward the Sun, regardless of their very different masses.[3] Newton even attempted to explain Galileo’s paradoxical law with his own pendulum experiments,[4] with his proposition that “the weight of any body is proportional to its own mass,”[5] and with the concept that gravitational mass is equal to inertial mass. But, as we shall later demonstrate in other sections of this treatise, he failed. Many other scientists have also asserted various different explanations for Galileo’s mysterious law, but likewise to no avail.[6]

In the early part of the 20th century, Albert Einstein attempted to explain and completely redefine the phenomena of gravity in a treatise which he called the General Theory of Relativity. Einstein premised his entire theory of gravity upon the validity of Galileo’s simple absolute law: all unequal bodies (masses) gravitationally fall equally. Based on Galileo’s and Newton’s gravitational acceleration experiments and conclusions, Einstein also postulated that “[T]he gravitational mass [weight or heaviness] of a body is equal to its inertial mass.”[7]

In due course, most of the scientific community accepted Einstein’s General Theory of Gravity as valid. Thereafter, Einstein and his followers attempted to apply his General Theory of Relativity in order to explain many other mysterious phenomena of nature, and especially the creation, structure, age, operation, and expansion of the universe in which we live.

But, what would happen if it now turned out that Galileo’s simple law of the equal gravitational fall of all unequal masses…was not valid? What if the apparent equal fall of two unequally sized cannonballs toward the Earth was just a very close approximation: in effect, an illusion? What if it could be demonstrated that the smaller cannonball actually fell faster than the larger cannonball? What if, on a much larger scale, the very different gravitational accelerations of various sized opposing masses can actually be observed? In other words, what if Galileo’s simple “law” of equal gravitational acceleration of all unequal masses was just an explainable paradox? Might the entire theoretical house of cards, which is built upon Galileo’s “simple law” of equal gravitational acceleration of all unequal bodies, also fall (Figure 1)?

It shall be a major purpose of this treatise to demonstrate that Galileo’s and Newton’s simple absolute law of gravitational acceleration was not correct, and thus the foundations and fundamental premises upon which Einstein built his bizarre and elaborate General Theory of Relativity, were also not correct. In the process, we shall discuss why Galileo’s and Newton’s empirical law of equal gravitational fall (acceleration) of unequal masses was just an illusion—an explainable paradox. We will then explain the reasons for this paradox and discuss the correct phenomena of nature, which we shall call: “Relative Gravitational Acceleration.”

Rarely in the history of science has a major physical genre of nature produced such lasting confusion with such widespread impact, as the phenomenon of gravity. Galileo and Newton were two of our greatest scientists, and it is completely understandable why they and the many other great physicists and mathematicians who followed them were fooled by such paradoxical observations and illusions of nature. Nevertheless, this simple empirical paradox, the equal gravitational acceleration of all unequal masses, has caused enough mischief in physics during the past four centuries.

It is now time to expose this absolute paradoxical law and its theoretical progeny, to reality. Galileo would understand this necessity, for it was he who authored the phrase: “Never…assume as true that which requires proof.”[8]

In this age of rocketry, artificial satellites, and interplanetary voyages, correct concepts of mass, force, resistance, motion, and gravitational acceleration are vital to protect the lives of space travelers, and to enhance the success of costly space explorations. In a very real sense, we are all space travelers, and we all need to know and understand the realities of the universe (past, present, and future) in which we live.