  The space missions designed to visit small bodies of the Solar System boosted
the study of the dynamics around non-spherical bodies. In this vein, we study
the dynamics around a class of objects classified by us as Non-Spherical
Symmetric Bodies, including contact binaries, triaxial ellipsoids, spherical
bodies with a mass anomaly, among others. In the current work, we address the
results for a body with a mass anomaly. We apply the pendulum model to obtain
the width of the spin-orbit resonances raised by non-asymmetric gravitational
terms of the central object. The Poincare surface of section technique is
adopted to confront our analytical results and to study the system's dynamics
by varying the parameters of the central object. We verify the existence of two
distinct regions around an object with a mass anomaly: a chaotic inner region
that extends beyond the corotation radius and a stable outer region. In the
latter, we identify structures remarkably similar to those of the classical
restrict and planar 3-body problem in the Poincare surface of sections,
including asymmetric periodic orbits associated with 1:1+p resonances. We apply
our results to a Chariklo with a mass anomaly, obtaining that Chariklo rings
are probably related to first kind periodic orbits and not with 1:3 spin-orbit
resonance, as proposed in the literature. We believe that our work presents the
first tools for studying mass anomaly systems.
