DYNAMICS OF TWO PLANETS IN THE 2/1 MEAN-MOTION RESONANCE N. CALLEGARI JR., T. A. MICHTCHENKO and S. FERRAZ-MELLO Instituto de Astronomia, Geofı´sica e Cie ˆncias Atmosfe´ricas, Universidade de Sa ˜o Paulo, Rua do Mata ˜o 1226, Sa ˜o Paulo, SP, Brazil (Received: 28 July 2003; revised: 14 February 2004; accepted: 26 February 2004) Abstract. The dynamics of two planets near a first-order mean-motion resonance is modeled in the domain of the general three-body planar problem. The system studied is the pair Uranus–Neptune (2/1 resonance). The phase space of the resonance and near-resonance re- gions is studied by means of surfaces of section and spectral analysis techniques. After a thorough investigation of the topology of the phase space, we find that several regimes of motion are possible for the Uranus–Neptune system, and the regions of transition between the regimes of motion are the seats of chaotic motion. Key words: chaos, neptune, periodic orbits, planetary systems, resonant dynamics, secular dynamics, uranus 1. Introduction Until recently, researches considering the long-term stability of planetary systems were based on the studies of the dynamics of the nine planets of our Solar System and the orbital evolution of the massive satellites of the giant planets. These studies were performed in different ways through the solutions of averaged models (Sessin and Ferraz-Mello, 1984; Hadjidemetriou, 1985; Laskar, 1989; Gladman, 1993; Michtchenko and Ferraz-Mello, 2001a, hereafter MF2001a), or long numerical integrations of the equations of motion of these systems (Sussman and Wisdom, 1988; Nobili et al., 1989; Lecar et al., 2001; Michtchenko and Ferraz-Mello, 2001b, hereafter MF2001b). In present day, however, the discovery of a great number of extra-solar planets has increased the domain of these investigations. One of the main reasons for this new interest is that some systems including more than one planet are actually in resonant orbital configura- tions. In this situation, the mean motion of two planets are commensurable. In the Solar planetary system, three near mean-motion resonances occur: the 5/2 near-resonance in Jupiter–Saturn system, the 3/1 near-resonance in Sat- urn–Uranus system, and the 2/1 near-resonance in the Uranus–Neptune. Among the known extra-solar planets, we can cite several examples of sys- tems in near resonant configuration. In the case of planetary systems in near Celestial Mechanics and Dynamical Astronomy 89: 201–234, 2004. Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands.