Prague Relativistic Astrophysics

Ronaldo S. S. Vieira

In this talk we present a definite vertical stability criterion for equatorial circular orbits in Newtonian razor-thin disks, which takes into account the discontinuity in the gravitational field. This criterion allows us to obtain a simple analytical formula describing an approximate third integral of motion for nearly equatorial orbits in these systems. The formula is extended to 3D disks in order to describe motion of disk-crossing stars in regions where the usual adiabatic approximation gives poor results.