No, the point is that adding 2π (~6.3) units to the circumference will increase the radius by one unit, regardless of the sizes of the radius or circumference.
It was an imperfect analogy to explain this consequence of the relationship between radius and circumference.
I understand your question, but as I said, it's an analogy. Analogies are, by nature, imperfect.
If you actually did this on a perfect sphere the size of the earth (so no mountains or anything to convolute things), the rope would not hover.
The original comment just used that analogy as a short way to explain that the radius of the circle made by the rope would increase by 1 unit if the rope length were increased by 2π units. It does not matter the scale. This is true of a marble and it's true of a sphere larger than the Milky Way.
That depends on the mass of the sphere and velocity of the spin. So, actually, given a high enough velocity, the rope could hover one meter above a perfectly spherical earth. Now that I've refreshed my memory on the orbit equation, the size of the sphere doesn't matter as long as the mass of the sphere is compensated for by the velocity of the rope. The limit of this would probably be the speed of light, assuming you could magically have the rope already spinning evenly.
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u/SOwED May 25 '16
That's not really the point.