In 1685, Newton conducted pendulum experiments of his own to try to replicate and confirm the apparently equal times of Galileo’s Leaning Tower experiments. Newton decided to swing two identical pendulums together, each with a hallow bob that could be filled with different substances. Newton filled one bob with one substance (i.e. gold, silver, lead or sand), and filled the other bob with an equal weight of a different substance (i.e. salt, wood, water or wheat). Each bob was suspended from an 11-foot cord. He then caused the two bobs to swing back and forth together, and Newton stated that they swung in unison “for a very long time.”
Based on these pendulum experiments, Newton concluded that there was the same amount of matter (vis. inertial mass) in each substance, that each equal amount of matter acted with the same “motive force,” and that these facts were the reasons why all heavy bodies fall toward the Earth in equal times. Newton then postulated that “the weight of any body [toward planet Earth] is proportional to the quantity of matter [inertial mass] which the body contains.” Newton’s experiments supposedly determined that the quantity of matter (i.e. inertial mass) contained in different substances of the same weight was equal to within one part in 1,000.
In effect, Newton asserted that the equal mass of each different atomic substance is proportional to its own weight. This is like saying that the mass or weight of a body is equal to itself. It is difficult to comprehend how this meaningless undisputed fact can explain why two cannonballs of unequal mass or weight dropped from the same height should fall to Earth in apparently equal times. On the other hand, it is obvious that if such cannonballs had equal masses or weights, they should fall to Earth in equal times.
Around 1830, German astronomer Friedrick Bessel (1784 – 1846) repeated Newton’s experiments and supposedly improved their accuracy to one part in 100 thousand. Today, Galileo’s and Newton’s law of equal gravitational acceleration of unequal masses is universally accepted by scholars everywhere, in spite of the fact that “this phenomenon…has puzzled physicists ever since” Galileo’s time.
So, is that the end of the story? Hardly! We must take Galileo’s advice: “Never…assume as true that which requires proof.” If Galileo’s and Newton’s gravitational principle of equivalence was correct, then a priori the unequal masses of an apple, a cannonball, a giant asteroid, the Moon, Venus, Jupiter, and the Sun should all free-fall in the gravitational field of the Solar System, at absolutely the same rate toward the Earth. But we now know that this is not true. Therefore, we must re-examine Galileo’s absolute law of equal gravitational acceleration in light of current knowledge and current observations. But, for the moment, let us briefly continue with Galileo’s contributions to the laws of motion.