How exacly did **Sir Isaac Newton** went from now knowing any formula describing gravity to the conclusion that: F = G (m1 * m2)/r^2
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Let me approach this from the side. Instead of grinding through the stories of the apple and the moon (well covered elsewhere), let me talk about the maths behind it.
Once you get to a certain point in Mathematics / Algebra / Calculus, you start seeing patterns. For example, n^2 always gives you a parabola of some kind. When you start seeing measurements giving you 2, 4, 8, 16, 25 …, then there’s a parabola pattern and n^2 is there somewhere.
Or, consider V=I/R, a ratio. If V goes up, then either I goes up too, or R goes down. If I and R both go up, then V goes up. Georg Ohm figured this out in the 1800s about Voltage, Resistance, and Current (I), and it’s now called Ohm’s Law.
In the early 1900s, Henrietta Leavitt was an Astronomy student given the grunt work of measuring the brightness of hundreds and hundreds of stars on photographic plates. In the process of detailing these thousands of observations, she noticed various stars that changed brightness — variable stars. But — she noticed certain of those stars varied consistently despite their brightness, which was against theory at that time. Much more grunt work later, she saw the pattern in the brightness and brightness cycles was extremely regular. This led to those stars, called Cephid Variables, becoming used as a measuring stick to determine distance according to brightness and cycle time. She was able to see this because she had the maths understanding to build equations to suit the data, and test it.
So back to Sir Newton — he not just saw a relationship, but had the ability to put that relationship into a mathematical structure that fit the data, and tested predictions.
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