5 - Quasi-Circular Orbits

Summary

This chapter presents the basic properties of quasi-circular orbits in axisymmetric stellar systems. In fact, axisymmetric models are often sufficiently realistic descriptions – beyond the zeroth-order spherical case – of elliptical and disk galaxies. The associated potentials (with a reflection plane, the equatorial plane) admit circular orbits, and in this chapter we focus on the properties of orbits slightly departing from perfect circularity, describing in some detail the second-order epicyclic approximation. We also derive, in a geometrically rigorous way, the expression of the Oort constants, important kinematical quantities related to the rotation curve of disk galaxies, and in particular to the orbit of the Sun around the center of the Milky Way.