Derivation of formula using dimensions

johncena
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Can we derive the equation ,

F = (Gm1m2) / r2

using dimensional analysis?
 
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Hi johncena! :smile:

Assume that force does not get "lost" …

ie, the force flowing through a sphere of radius r is the same for all values of r. :wink:
 
comparing a flat solar panel of area 2π r² and a hemisphere of the same area, the hemispherical solar panel would only occupy the area π r² of while the flat panel would occupy an entire 2π r² of land. wouldn't the hemispherical version have the same area of panel exposed to the sun, occupy less land space and can therefore increase the number of panels one land can have fitted? this would increase the power output proportionally as well. when I searched it up I wasn't satisfied with...

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