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Using our mathematical framework developed in \cite{cresson-pierret_scale}called \emph{scale dynamics}, we propose in this paper a new way ofinterpreting the problem of adding or modifying potentials in mechanics andspecifically in galactic dynamics. An application is done for the two-bodyproblem with a Keplerian potential showing that the velocity of the orbitingbody is constant. This would explain the observed phenomenon in the flatrotation curves of galaxies without adding \emph{dark matter} or modifyingNewton's law of dynamics.

Scale dynamical origin of modification or addition of potential in mechanics. A possible framework for the MOND theory and the dark matter