Changes

:You raise some interesting points. To your question "Do you think that is impossible that the correct behavior of gravity is that of Newtonian gravity, but with the gravitational force proportional to 1/r^2.00000001, rather than 1/r²?", I might still answer no, on the grounds that if there is divergence in the gravitational field, then I wouldn't consider the force to be Newtonian gravity: you need dark energy, or an object creating a force from outside itself (possibly I'm wrong about this -- would you agree with this statement at least?)

:I agree that a theory must fit observation, and some question along these lines would be fine -- it strikes me as odd to ask things about gravity being an inverse square law, since (at least as I understand physics), outside of the Newtonian context we don't really want think about gravity as a force with such and such strength at such and such distance anyway. And if we're talking about gravity not being an inverse-square law, then to me, we're no longer talking about Newtonian physics anyway. Some of your other suggested formulae I don't know the derivations of -- I bet there's another one that I'd prefer to use for this question.