Stellar Orbits in Spherical Potentials

This lecture covers the analysis of stellar orbits in spherical potentials, including Keplerian orbits, orbits in homogeneous spheres, orbits in axisymmetric potentials, nearly circular orbits, and examples of stellar orbits. The lecture discusses the equations of motion, epicycle frequencies, eccentricity, and the effective potential. It also explores the harmonic oscillations in homogeneous spheres, the Hamiltonian, and the general solutions for the equations of motion. The lecture concludes with a detailed examination of the Miyamoto-Nagai potential, the logarithmic potential, and the radial dependency of typical galaxy velocities.