The current definition of the gravitational constant maximizes the simplicity of Newton's law F = Gmm'/r^2. Adding a 4π to its definition would maximize the simplicity of the Poisson equation that Metus wrote. Adding instead 8π, on the other hand, would maximize the simplicity of Einstein's field equations. No matter what you do, some equation will look a bit more complicated.
The current definition of the gravitational constant maximizes the simplicity of Newton's law F = Gmm'/r^2.
Absolutely, and Planck's constant maximizes the simplicity of finding the energy of a photon from its wavelength, and π maximally simplifies finding the circumference of of a circle from its diameter. But in all those cases, it feels to me like we're simplifying the wrong equation.
ETA: To be explicit, it feels like there should be a 4π in Newton's law. The formula is calculating the gravitational flux on the surface of a 3-dimensional sphere, and 3-dimensional spheres have a surface area 4π times their radii.
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