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.
Wow, you have a good point. I always use the concept of surface area (and considering spheres of equal total force) to remember why the r on the bottom is squared. Putting the surface area into the formula is like replacing a factor that raises questions with the answer to those questions.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.