  We hereby study the stability of a massless probe orbiting around an oblate
central body (planet or planetary satellite) perturbed by a third body, assumed
to lie in the equatorial plane (Sun or Jupiter for example) using an
Hamiltonian formalism.
  We are able to determine, in the parameters space, the location of the frozen
orbits, namely orbits whose orbital elements remain constant on average, to
characterize their stability/unstability and to compute the periods of the
equilibria.
  The proposed theory is general enough, to be applied to a wide range of
probes around planet or natural planetary satellites.
  The BepiColombo mission is used to motivate our analysis and to provide
specific numerical data to check our analytical results.
  Finally, we also bring to the light that the coefficient J_2 is able to
protect against the increasing of the eccentricity due to the Kozai-Lidov
effect.
