Giants, Shoulders, Newton


I’ve always wondered how Newton figured that the force acting on the moon is the same as the one that caused, I don’t know, the apple to fall on his head. Remember, back then, the Greek view of the universe prevailed: one set of laws on earth, another set for the heavens. So how did Newton hit upon a common law for entire universe?

Carlo Rovelli answered that question in his page-turning history of physics, Reality is not What it Seems. He talks of Galileo who dropped a lot of objects and realized that their speed increases (during the early part of their fall). But he then noticed that the rate at which the speed of the falling object increases is constant:
“Its value is approximately 9.8 meters per second.”

Decades later, Newton imagined the earth having multiple moons, like Jupiter (something that Galileo had discovered). Newton assumed that one of those extra (and tiny) moons orbiting earth just above the mountain peaks. Newton wonders at what speed it would travel?
-       He used Kepler’s law on the relation between the time to orbit v/s radius of the orbit;
-       Hipparchus had calculated the distance to the moon; its period was known (28 days);
-       Eratosthenes had figured the radius of the earth. Newton added a bit for the height of the mountain peak;
-       Combining all of the above, Newton arrived at the time to orbit for his imaginary moon:
“One hour and a half.”
-       Using this time to orbit and the radius of the orbit, Newton calculates the velocity of his imaginary moon.

Finally, Newton calculated the acceleration of this imaginary moon:
“Newton makes the simple calculation and the result is… 9.8 meters per second per second. The same acceleration as in Galileo’s experiments for falling bodies on Earth.”
Which sets Newton thinking:
“Coincidence? It can’t be, reasons Newton. If the effect is the same -  a downwards acceleration of 9.8 meters per second per second – the cause must be the same.”
Of course, Newton didn’t stop at making a guess. He did the maths (hell, he even invented the maths for it) and produced the theory of gravity.

Are Kepler, Hipparchus, Eratosthenes and Galileo the giants whom Newton was referring to in his famous line about seeing farther by standing on the shoulders of giants?

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