Let us now examine the Newtonian universal constant value of “G,” which is generally described in Newton’s postulate that the “centripetal or gravitational force of a body is proportional to its mass.” In order to determine the value of G, “[W]e have to measure the gravitational force between two bodies…” A priori the constant value of G should be able to be determined: 1) indirectly by comparing the forces received and applied by and between two opposing celestial bodies m1 & m2 in space, by empirically measuring and comparing their different reciprocal accelerations, a1 & a2; or similarly, 2) by measuring the miniscule forces between two tiny masses in the laboratory, and their resulting accelerations.
By the first method, if the magnitude of continuous attractive relative force (1) received and applied by and between the Earth and the Moon is equivalent (Figure 17.1), then a priori the Earth’s much larger relative inertial resistance (82) should move (accelerate) only slightly relative to the Moon, whereas the Moon’s much smaller relative inertial resistance (1) should move (accelerate) a much greater distance relative to the Earth (Figure 9). This result should follow automatically from Newton’s three laws of motion.
We observe the empirical confirmation of these laws in the comparative masses and motions (accelerations and orbits) of the Earth/Moon system (Figure 26). But Newton, Galileo, Einstein, Feynman, Zeilik, Cohen, Young, and everyone else appears to deny that such observed reciprocal accelerations have anything to do with the magnitude of the masses involved. Why? Because Galileo’s Leaning Tower of Pisa experiment (and other terrestrial experiments) appeared to demonstrate that all masses fall in equal times.
So perhaps at this point in our discussion we should resort to the second method. A magnitude of G was empirically determined by British scientist Henry Cavendish (1731 – 1810). In 1798, Cavendish attempted to directly measure the gravitational force (in Newton’s and kilograms) between two small opposing masses (m1 and m2) in a laboratory torsion balance experiment (Figure 22A). The larger masses (m1) were fixed and stationary while the smaller opposing masses (m2) were allowed to freely gravitate toward the larger mass. The motions or twisting force of the smaller masses theoretically indicated the total force between the masses. This torque or twisting force was measured and based on it the value for G was calculated to be: G = 6.67 x 10-11 N.m2/kg2.
In effect, Cavendish’s experiment to determine the magnitude of G constituted a miniscule gravitational system. What Cavendish was really measuring was that portion of the intensity of the attractive force of the larger masses in all directions which was received by and acting upon the smaller masses, and the resulting action of their smaller inertial resistance with respect to the relatively stationary larger masses.
If instead, Cavendish had allowed both sets of opposing masses to move freely, a priori he could have indirectly measured the gravitational force of the larger masses received by and acting upon the smaller masses, by comparing and measuring their relative gravitational accelerations. This would have empirically established that the inertial resistances of the smaller masses accelerate proportionally faster and farther toward the larger masses, rather than equally. The larger masses, because of its relatively larger inertial resistances, would have been observed to hardly move at all (Figure 22B). A priori this hypothetical experiment would also have empirically disproved Galileo’s Leaning Tower of Pisa experiment, by demonstrating that smaller gravitating masses accelerate proportionally faster and farther in a two-body gravitational field than larger gravitating masses accelerate.