The Ferraz Mello's problem appears in the study of the stability of extrasolar planetary systems. It is the study of the evolution in the plane, three-body, secular, planetary problem. That problem is integrable (in principle) but nevertheless very complex. Most systems have only small perturbations and remain stable but their exist catastrophic evolutions with either the fall of the inner planet into the central star or very close approaches of the two planets with major fast perturbations and even, sometimes, the escape of one of the two planets (generally the lightest one).

The usual resonances are larger when the planets rotate in the same direction (inclination = 0°) than when they rotate in the opposite direction (inclination = 180°) and a similar effect appears for the secular problem : retrograde orbits are more stable than direct ones.