Orbits in a Neighboring Dwarf Galaxy According to MOND

We study the orbits in the MOND theory within a dwarf galaxy of mass Md ∼ 108M⊙ at a distance of ∼ 100kpc from a neighboring galaxy of mass Mg = 5 × 1011M⊙, such as ours. It is assumed that a second mass m << Md is gravitationally bound to Md by a previously calculated potential for the MOND theory. This potential is obtained for a free falling mass Md in a constant external gravitational acceleration field ∇φg. The numerical technique of surfaces of section is used to study the stability of the phase-space orbits in the dwarf galaxy. Equatorial orbits with sufficiently small eccentricities e < 0.65 are found to be stable with respect to small changes in the initial conditions. (The equatorial plane is perpendicular to the direction of ∇φg, which is along the line joining Md and Mg.) For decreasing values of the conserved component of the angular momentum, in the direction of ∇φg, equatorial stability is lost. Subject headings: cosmology — gravitation — galaxies: dwarf.