The Design of Newton’s Proof of Gravity

If any question could be devised for this topic, it would be, why doesn’t the scientific establishment provide this information on a widespread basis? The answer, of course, will be found in the questions it subsequently raises, but when I was in high school, I was exposed to this both in class, and on science television programs.
Newton presented his theory of gravity in a book he titled the Principia. The book was written in Latin to limit the number of critics that had access to the original material (Newton freely admitted this, not wanting the riff-raff to meddle in his thinking process). In addition, the Principia itself was the subject of continuous modification during Newton’s lifetime. It is a mishmash of a supposed compendium of the laws of motion that actually slipped a new one in (one absolutely necessary to Newton’s design scheme) and an exposition of a new form of mathematics, calculus, which was little understood at the time, but didn’t stop universal acclamation that Newton’s Celestial Mechanics revealed the operations of the heavens. (Leibniz subsequently claimed priority in the invention of calculus, and, although he lost the battle to history, won it in notation, how calculus is expressed, with Newton’s notation virtually nonexistent today).
Regardless of Newton’s efforts to hide his theory behind language and mathematics, the outline of what he was attempting is really quite simple. Galileo had measured that gravity diminished inversely with the square of its distance from its source. Newton said its source could be the Earth or it could be the moon. If both had gravity, then the amount of gravity that existed between them could be computed.
How do you compute the amount of gravity in the moon, which is hanging up there in the sky, and for which gravity is merely a supposition? We’ll see how Newton solved this in a minute, but first we have to understand why Newton wanted to compute the force of gravity between the two.
Newton’s starting point was, gravity is a property of matter (not our current mass, but the actual matter that he saw making up the two bodies). If he could prove that the amount of gravity was proportional to the amount of matter, then he would have proven that gravity, being proportional to matter, was indeed a property of the matter.
Newton was operating over 300 years ago, and the concept of an atom, with its protons and neutrons varying in its nucleus to give matter weight, is barely 100 years old, so Newton’s view of how matter was made up was primitive compared to modern views. In fact, Newton’s view of what made up matter was very simple. Matter was uniformly made up of a uniform particle. In short, the same particle made up everything. This meant the Earth and the moon were made up of the same particle and that same particle was identically distributed within both bodies.
Thus, instead of computing the amount of gravity of the Earth and moon, Newton could compute the relative amount of gravity of each (remember, he merely had to prove gravity was proportional to matter) on the basis of their relative size. If he did this, he would have one side of an equation.
I should stop just a second to interject the importance of this equation. Up until Newton’s predominance, people who attempted to explain reality used the Baconian approach. This approach held that there are certain things we can never know, for instance the source of the hidden force that caused objects to move, things to fall, planets to rotate and orbit. The best we could do is create concepts based on the facts at hand, made-up concepts that could be altered as more facts came to light.
Newton’s gravity equation supplanted the mind with an objective truth that the mind had to accept as absolute authority. Once one side of the equation equaled the other side, the proposition the equation stood for became scientific fact, never more to be challenged. Newton, who’d brook no challenge to his conclusions, used equations to cut off dissent, giving empirical science its authoritative tool to stifle all dissent.
Once Newton had one side of his equation, he needed another side to balance it and thus prove that gravity was proportional to and therefore a property of gravity. The other side of the equation involved computing the amount of force it would take to cause the moon to stop traveling in a straight line and force it to move in a circle around the Earth. The computation of this force involved using the moon’s size to determine the amount of matter in it (the same computation he used to determine its gravity) and then to compute its momentum, the amount of force that was causing to travel in a straight line. Once he had computed this force, he knew the amount of force it would take to cause the moon’s straight-line momentum to be bent into the circular orbit we find it in.
If the amount of gravity in the Earth and the amount of gravity in the moon equaled the force it would take to cause the moon to move from its straight-line momentum into a circular orbit, then gravity was proportional to and therefore a property of Earth.
I think it worked out to about 7%, which Newton chalked up to erroneous measurements by Halley (of comet fame) of the moon’s motion,
But the 7% margin of error was nothing compared to the margin of error that occurred when Newton’s mathematical reasoning was applied to the planets later in the century.
And while Newton was celebrated throughout his life as the person who had uncovered the secrets of the universe in his Celestial Mechanics, an astute observer will recognize that Newton’s theory of gravity said nothing about what causes planets to rotate and orbit.
Why?
Newton was a devout Christian who poured over bibles in an attempt to compute the date the world would end. As far as he was concerned, all motion was the result of God’s action in the universe and indeed, when it came down to the actual nature of gravity, Newton believed that gravity was a manifestation of God (in an alchemical sort of way).
It wasn’t until a 100 years after Newton developed his theory that science had to step in and, because its absence in Newton was so evident, take the explanation for motion away from God, creating the ad hoc (and equationless) swirling mass of gas as the cause of motion.
The nature of gravity, being less obvious to the uninitiated, and, if truth be know, the initiated, didn’t have to be addressed. Everybody already knew what gravity was, it was a property of matter, and that was enough to cut off all questions about its nature.