Detection limits on 'd' if gravity force was proportional to $1 / (R+d)^2$

Question

Assume the force of gravity is proportional to $1/(R+d)^2$ where $d$ is sufficiently small,

then, how small would $d$ have to be to evade detection by modern experiments?

My thinking is that if $d$ is not zero then it would solve the issue of a singularity when $R$ is 0.

Did you look for papers containing "Non-Newtonian gravity" and "compact extra dimensions"? I think you will find a treasure trove of both experimental and theoretical work. — CuriousOne, Jan 01 '16 at 01:34

score 4 · Answer 1 · edited Apr 13 '17 at 12:39

I answered a related question in this earlier answer where I pointed to a 1988 experiment/paper by Mitrofanov et al, where they determined that any deviation from the inverse square law must happen at length scale < 1 mm.

Note that the assumption of their paper was a different form of the potential function -

$$V(r) = -G_\infty\frac{M}{r}\left(1+\alpha e^{-r/r_0}\right)$$

But the basic length scale will be comparable.

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