Galileo’s 1590 A.D. Leaning Tower of Pisa experiment appeared to demonstrate that unequal cannonballs gravitationally fall equally in tandem toward the Earth in equal times. Newton then incorporated this paradoxical absolute result into his 1687 theory of the force of gravity.
However, Galileo evidently forgot that there was a third much larger ball in his Leaning Tower experiment. That is, the relatively gigantic mass of the Earth which did not noticeably move or gravitate toward either cannonball.
When we now compare Galileo’s Leaning Tower result to other unequally gravitating bodies in the Solar System on a much larger scale (by analogy and extrapolation), we must realize that Galileo’s Leaning Tower result was merely an illusion. It occurred because the two relatively tiny cannonballs (which fell toward the enormous Earth) were so nearly alike, as compared to the huge mass of the Earth.
Let us now adapt and apply Galileo’s Leaning Tower experiment to a much larger scale. For example, it is obvious that the much larger unequal bodies of the two-body Earth-Moon gravitational system do not fall equally towards each other. In fact, the relatively small Moon is observed to fall around the much larger Earth over an orbital distance of about 2.5 million kilometers during each calendar month, whereas the much larger Earth hardly even moves or gravitates toward the Moon.
Likewise, it is also obvious that the unequal bodies of the two-body Sun-Earth gravitational system do not fall equally towards each other. The relatively small Earth is observed to fall around the enormous mass of the Sun over an orbital distance of about 470 million kilometers once each calendar year, while the enormous mass of the Sun hardly even moves or gravitates toward the Earth.
Because of these obvious gravitational examples, we must conclude (by extrapolation) that all smaller bodies must gravitationally fall faster and farther toward or around all larger bodies. The extremely unequal gravitational motions of these much larger unequally gravitating bodies can easily be detected or observed because of their much larger scale.
Therefore, these much larger unequally falling bodies empirically demonstrate (also by analogy and extrapolation) that the smaller cannonball in Galileo’s Leaning Tower experiment must have fallen slightly faster and farther toward the enormous mass of the Earth than did the slightly bigger mass of the larger cannonball. But because the scale of such Leaning Tower experiment was so small, such minute difference in time and distance could not be observed or detected by Galileo, Newton or anyone else. In other words, everyone was fooled by an illusion of scale.
Based on the above, and numerous other convincing empirical demonstrations, we must now conclude that all unequal bodies in the universe gravitationally accelerate (or fall) toward each other unequally. More generally, we must also conclude that the gravitational interactions of all bodies in the universe are completely relative (and not absolutely the same). We will call these concepts, and these laws of nature: the “Relativity of Gravity.”
So is this the end of our story about gravity? Hardly! In 1915, Albert Einstein based and premised his entire General Theory of Relativity (i.e., his theory of gravity not based on force) upon the empirical validity and absolute equality of Galileo’s Leaning Tower experiment. But if we now must realize that Galileo’s paradoxical Leaning Tower of Pisa result was neither valid nor equal, then we must ask the question: where does this leave Einstein’s General Theory of Relativity? The answer is obvious: nowhere!