Philosophy 167: Class 12 - Part 10 - The Moon Test: Concluding that the Moon Isn't Influenced by Terrestrial Gravity.
Smith, George E. (George Edwin), 1938-
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Now Newton does something rather striking with it. The term has come to be known, and you'll hear it all the rest of this course and next semester, the Moon Test. So, let's assume that the radius of the earth is 3,500 Italian miles. That's a value from Galileo's dialog, it is a wrong value.
Okay, 3,500 Italian miles, 5,000 feet per mile, that's English feet per mile. Then the Kanefusa centro at the equator of the earth amounts to a distance of receding from the surface of 0.4625 feet in the first second, compared with the distance of 16 feet of fall in the first second from gravity.
How did he know that result? Huygens' result is public. In English feet, keeps giving it a 16 feet per second. So he doesn't know Huygens' original result because it's not given in English feet, but that's our 32 feet per second per second. That is, gravity is 346 times stronger, and the conatus a centro of objects at the equator of the rotating Earth.
What's he solving the problem of? The argument, why don't we fly off the Earth if the Earth is rotating? And the answer is because the force of gravity is 346 times stronger than the tendency to fall off the Earth. The number is wrong, the correct value, I say here, is 288.
It's 288 in a fraction. You will see, you've already seen it from me with Huygens, but the official number becomes one over 289 once you round the fraction and take into account the earth not being perfectly spherical. I almost changed this slide, then decided I couldn't figure out why I said one over 288 so I left it there, but that's the number now.
All right, that's a perfectly sensible thing to ask in the context of Capernicumism, right, and he's been very clever to get it. Now, assuming that the moon is 60 Earth radii from the center of the Earth, that's a number that different people had proposed, but 60 is as good as any of the proposals.
And the period of the moon is 27.3216 days, 60 if you had figures, we did know it that well. Then the conatus a centro at the equator of the Earth, is about 12 and a half times the conatus a centro of the moon to recede from the Earth.
In other words, the tendency for us to spin off in the Earth, is about 12 and a half times the tendency of the moon to recede from the Earth. Therefore, the force of gravity at the surface of the Earth is 4,000 and more times greater than the endeavor of the moon to receive from the center of the Earth.
It's interesting he chose 4,000, because in fact if you do the numbers it's 4,375. Now going back to the manuscript, you'll notice something funny here. The 350 number he's overwritten with a different pen, but he did not overwrite. I'm looking for it, it's in here, I don't even see it at the moment.
The 4,000 number is scattered either in there or the top of the next page. Yeah, there it is. The 4,000 number is not overwritten. So he's computed the number separately. It's larger than 4,000, but he instead concludes it's 4000 and more times greater.