Stability of retrograde orbits of moons in the non-spherical planet's gravitational field

The gravitational field of a planet in the first approximation by the gravitational field of the sphere. When considering the retrograde satellites that are circulating in elongated orbits at great angles to the plane of Laplace, must take into account the fact that each planet has a compression due to the rotation and its gravitational potential is much better described by an ellipsoid of revolution. All retrograde satellites of giant planets known to date, meet the criteria for persistence of Lagrange, demonstrating the stability of their orbits, in spite of the significant osculation of their orbits by the gravitational field of the Sun.