Non-relativistic Extended Gravity and its applications across different astrophysical scales

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.