A Radial Axial-symmetric Intermediary Model for the Roto-orbital Motion

We study the roto-orbital dynamics of a uniform sphere and a body with axial symmetry by means of a radial intermediary, which defines an integrable system. Numerical comparisons of the MacCullagh’s truncation of the gravity gradient potential and intermediary models are performed, concluding that the intermediary provides a valuable approximation with small differences when compared with the MacCullagh’s one. Our analysis includes the analytical integration and a study of the special solutions and relative equilibria.