In the process of writing part of an upcoming and super-secret story, I was forced to think deeply about Sir Isaac Newton’s theory of universal gravitation & I stumbled upon a fascinating example of this wily alchemist’s elegant yet unconventional thought-processes: the gedankenexperiment that led to some of his profoundest realizations. “Gedankenexperiment” is German, by the way, for “thought experiment,” and many great scientists have often made use of them to intuitively flesh out theories before setting themselves to all of the mathematical work involved in proving them. What follows is one of Newton’s…

Sir Isaac Newton: Imagine, if you will, that you are now on top of a tall mountain by the ocean; it is a beautiful day and you have an unobstructed view of the glittering blue sea. You also happen to have a cannon with you, as well as unlimited ammo. Next, you shatter the silence by firing a cannon ball out over the ocean (don’t worry, there are no ships nearby). What happens is that the cannon ball starts out by traveling in what is basically a straight line – but this straight line will gradually fall lower in height until it splashes into the sea because gravity is pulling it down, resulting in a long, straight-ish line that curves gently downwards until it reaches the sea. Not too remarkable, you say? Okay, let’s increase the power of our cannon by using our cannon-power-increasing machine (which we’ve luckily brought along with us). Now, just as one would expect, as we are firing the increasingly powerful cannon, the gradually down-curving line is growing longer & longer & longer – but wait! Something interesting is beginning to happen now… As the cannon becomes more powerful, the line that’s carved by the cannon ball gets long enough that we notice that the curvature of the earth (which is round) is beginning to move away from the cannon ball, which allows it to go even further before gravity pulls it down! You didn’t notice this earlier because the earth’s curvature is barely, if at all, noticeable over the distance that human beings can usually see. But now that the cannon is able to shoot the cannon ball over these extraordinary distances, the earth is curving away from it! So, now there are three things happening: the force of the cannon propels the ball forward, gravity pulls the ball downward, and now, the earth’s surface is curving away from the cannon ball. But if we increase our cannon’s power just a little bit more… Good God, man! Get down!

[the cannon ball rushes over both of your heads, but coming from behind you]

Sir Isaac Newton: Whew! That was close! – My apologies, I forgot to tell you that the cannon ball had now achieved what I call “orbit.” That is, because the ball is moving fast enough, the earth is now curving away from the cannon ball before gravity has a chance to pull it down. Once the curvature of the earth is moving away from an object at the same rate that gravity is pulling it down, orbit occurs – and unless something else stops it, it will now keep going around the earth indefinitely*. Basically, something is in orbit because gravity has bent its relative motion into a circle!

If Newton was able to discover the mechanism behind orbits and understand gravitation using this and other gedankenexperiments, what other things might we be able to discover using thought alone? Why don’t you give it a spin by creating some of your own gedankenexperiments?

*Well, not quite, and in this situation there is wind resistance and such – but you get the idea…

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