Dynamics of extrasolar systems at the 5/2 resonance: application to 47 UMa

A complete study is made of the 5/2 resonant motion of two planets revolving around a star, in the model of the general planar three body problem. Families of 5/2 resonant symmetric periodic orbits are computed numerically, for the masses of the extrasolar system 47 UMa. The phase of the two planets (alignment or antialignment of perihelia and position of each planet at perihelion or aphelion) plays an important role, and the change of the phase, other things being the same, may destabilize the system. Stable motion exists even in the case where the two planetary orbits intersect. A small value of the eccentricities, for the same phase, stabilizes the system. The above results are applied to the study of 47 UMa, which according to some observations is close to the 5/2 resonance.