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