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Here's a cool link I just found going over this exact scenario: https://www.mathpages.com/home/kmath530/kmath530.htm

Interesting to note, the napkin creates a uniform gravitational field above and below it. Meaning that the force applied to an object is the same regardless of how far away it is from the napkin! That force is 2pi * G * m * rho where rho is the mass density of the napkin.



How is that possible since the force on a test particle on the surface of the napkin is 0?


It is the same result as infinite planar light sources or infinite planar electrostatic charges. Move the test particle a small delta above or below the napkin, and the result will become apparent.




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