A better epicyclic approximation for plane galactic orbits

Details A better epicyclic approximation for plane galactic orbits A better epicyclic approximation for plane galactic orbits

Nov 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979aj.....84.1697k&link_type=abstract

Astronomical Journal, vol. 84, Nov. 1979, p. 1697-1700.

Astronomy and Astrophysics

Astronomy

6

Circular Orbits, Orbit Perturbation, Orbital Mechanics, Position Errors, Root-Mean-Square Errors, Spiral Galaxies, Approximation, Convergence, Eccentricity, Epicycloids

Scientific paper

Epicyclic orbits are perturbed circular orbits. In the traditional approach the radius of the orbit is perturbed, and the ensuing linearized orbits are good approximations as long as the amplitude of the radial oscillation is small compared with the mean radius. A better approach is to perturb the square of the radius. Such an approximation converges faster, and more importantly, gives a good description of finite-eccentricity orbits in the central region of a galaxy where the rotation curve rises linearly with the radius. It also simplifies axisymmetric mode calculations of disk galaxies.

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