Here we present an exact method for orbit determinations of an astrometric binary for which the primary star can be seen but the companion is unseen like a black hole or an extra-solar planet. Since the laws of the motion of celestial objects were discovered by Kepler in the seventeenth century, many attempts have been made to solve a fundamental problem of how to determine the orbital elements...

Periodic and quasi-periodic orbits are important objects that explain much of the dynamics in several Hamiltonian models in Celestial Mechanics. Adding a friction proportional to the velocity of the particles , an increasingly common asumption in Celestial Mechanics, gives rise to conformally symplectic models. Greene's criterion for twist mappings asserts the existence of a KAM torus by examin...

We construct a normal form suited to fast driven systems. call so systems including actions I, angles ?, and one coordinate y, moving under the action of vector-field N depending only on I y with vanishing I-components. In absence such have been extensively investigated it is known that, after small perturbing term switched on, normalised turn exponentially variations compared size perturbation...

One of main problems in celestial mechanics is the determination of the shape of the equilibrium configuration of celestial bodies. In this paper a model of a fluid mass rotating in space like a rigid body will be developed. To this aim, the equipotential surfaces are developed by using the Neumann series with respect to the Clairaut coordinates, and from these developments, the equilibrium equ...

Using a completely analytic procedure – based on a suitable extension of a classical method – we discuss an approach to the Poincaré-Mel'nikov theory, which can be conveniently applied also to the case of non-hyperbolic critical points, and even if the critical point is located at the infinity. In this paper, we concentrate our attention on the latter case, and precisely on problems described b...