  We study the orbits in the MOND theory within a dwarf galaxy of mass Md at a
distance of ~100kpc from a neighboring galaxy of mass Mg, 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. 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 chang
es in the initial conditions. (The equatorial plane is perpendicular to the
direction of the external gravitational acceleration, which is along the line
joining Md and Mg.) For decreasing values of the conserved component of the
angular momentum, in the direction of the external gravitational acceleration,
equatorial stability is lost.
