Orbits in a neighboring dwarf galaxy according to modified nonrelativisticdynamics

We study the orbits in the modified nonrelativistic dynamics (MOND) theory within a dwarf galaxy of mass M-d similar to 10(8) M. at a distance of simi lar to 100 kpc from a neighboring galaxy of mass M-g = 5 x 10(11) M., such as ours. It is assumed that a second mass m much less than M-d is gravitati onally bound to M-d by a previously calculated potential for the MOND theor y. This potential is obtained for a free-falling mass M-d in a constant ext ernal gravitational acceleration held del phi(g). The numerical technique o f surfaces of section is used to study the stability of the phase-space orb its in the dwarf galaxy. Equatorial orbits with sufficiently small eccentri cities e < 0.65 are found to be stable with respect to small changes in the initial conditions. (The equatorial plane is perpendicular to the directio n of del phi(g), which is along the line joining M-d and M-g.) For decreasi ng values of the conserved component of the angular momentum, in the direct ion of del phi(g), equatorial stability is lost.