  In this work we show that corrections to the Newton's second law appears if
we assume that the phase space has a symplectic structure consistent with the
rules of commutation of noncommutative quantum mechanis. In the central field
case we find that the correction term breaks the rotational symmetry. In
particular, for the Kepler problem, this term takes the form of a Coriolis
force produced by the weak gravitational field far from a rotating massive
object.
