1999/06/04 by Walter Dehnen · 3 citations
Physics and Astronomy · #Astronomy and Astrophysical Research #Astrophysics and Star Formation Studies #Linear approximation #Orbit (dynamics) #Orbital mechanics #Rotational symmetry #Set (abstract data type) #Simple (philosophy) #Stars #Stellar dynamics #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.1086/301009
accepted for publication in AJ; 12 pages LaTeX, 9 figures (coloured only here, not in AJ) uses aas2pp4.sty
arxiv created 1999/06/04 · openalex publication_date 1999/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Orbits that are already slightly eccentric, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here alternative approximations for flat orbits in axisymmetric stellar systems are derived and compared with results from numeric integrations. All of these approximations are more accurate than Lindblad's classical theory. I also present approximate, but canonical, maps from ordinary phase-space coordinates to a set of action-angle variables. Unfortunately, the most accurate orbit approximation leads to nonanalytical R ( t ). However, from this approximation simple and yet very accurate estimates can be derived for the peri- and apocenters, frequencies, and action integrals of galactic orbits, even for high eccentricities. Moreover, further approximating this approximation allows for an analytical R ( t ) and still an accurate approximation to galactic orbits, even with high eccentricities.