A completely successful mathematical theory of stellar dynamics has never been developed. This failure can be ascribed to a paucity of knowledge concerning the basic dynamical properties of stellar systems. This paper presents a numerical approach to stellar dynamics that affords a comprehensive description of the mechanical development of a spherical galaxy. It is to b e hoped that the results of the numerical calculations will aid in the development of a successful analytical theory by providing basic information which is, at present, not accessible to observation.
Reference to some theory of the galactic formation process is necessary in order to justify certain assumptions which must be made in order to carry out the dynamical calculations. Consequently, several semi-quantitative considerations of the properties of the turbulent pre-stellar state are included as an integral part of the study.
The numerical calculations indicate that spherical galaxies have reached a state of dynamical equilibrium in which no measure of equipartition of energy is achieved between stars of different mass. The distribution of luminosity is, therefore, a direct measure of the distribution of mass in such a system.
It was found that the initial conditions at the time of galactic formation were characterized by a general isothermal condition. Observational evidence is presented to support this conclusion. The steady-state frequency function for a spherical galaxy was calculated numerically and found to be in general agreement with what little is known from the general theory.
Campbell, Phil Montgomery, "The stellar dynamics of spherical galaxies" (1963). University Libraries Digitized Theses 189x-20xx. 193.