Mass distribution of highly flattened galaxies and modified Newtonian dynamics

Abstract

Dynamics of spiral galaxies derived from a given surface mass density has been derived earlier in a classic paper. We try to transform the singular elliptic function in the integral into a compact integral with regular elliptic function. Solvable models are also considered as expansion basis for RC data. The result makes corresponding numerical evaluations easier and analytic analysis possible. It is applied to the study of the dynamics of Newtonian system and MOND as well. Careful treatment is shown to be important in dealing with the cut-off of the input data.