  Higher order curvature gravity has recently received a lot of attention due
to the fact that it gives rise to cosmological models which seem capable of
solving dark energy and quintessence issues without using "ad hoc" scalar
fields. In this letter, a gravitational potential is obtained which differs
from the Newtonian one because of a repulsive correction increasing with
distance. We evaluate the rotation curve of our Galaxy and compare it with the
observed data in order both to test the viability of these theories and to
estimate the scalelength of the correction. It is remarkable that the Milky Way
rotation curve is well fitted without the need of any dark matter halo and a
similar result tentatively holds also for other galaxies.
