One extra metre of rope
Add a metre to a loop around a sphere. How high can it lift?
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Make a prediction
Does a bigger sphere reduce the uniform gap?
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How it works & assumptions
L=2πR. Adding ΔL to a concentric circular loop increases radius by ΔR=ΔL/(2π), independent of the original radius.
Perfectly circular, concentric loops; a uniform radial gap and no stretch. The diagram is schematic, not to scale; the reported gap follows the model. Earth-sized radius is approximate.
This is an ideal mathematical model, not a measurement or a forecast.