The question of orbit stability for the Dawn spacecraft while in a low altitude orbit around the asteroid Vesta is addressed. To ensure safety, it is necessary to know that if the spacecraft's main engines enter safe mode or lose thrust during the period of orbit transfer from a high altitude mapping orbit to a low altitude mapping orbit, will the resulting coast orbit be stable? If it is unstable, is there danger of the spacecraft colliding with Vesta, escaping from orbit, or entering into eclipse. To answer these questions, a Monte-Carlo simulation, developed in FORTRAN 90, has been conducted to propagate a sufficiently large set of coast orbits under the influence of a high fidelity (20×20) model of Vesta's gravity field. The gravity field has been derived using values for the non-spherical harmonics terms provided by the Jet Propulsion Laboratory (JPL). The perturbations arising from the non-spherical harmonics were derived using Hotine's partially non-singular geopotential formulation. The propagation of the coast orbit equations of motion with gravitational perturbations, in a Vesta-centered body-fixed reference frame, will provide clearer insight into the stability of the coast orbits. The simulation examines the effects of Vesta's gravity field on osculating orbital radius and right ascension of the ascending node. The analysis of these two osculating values will provide a time history of minimum orbital radius 'and regression of the node which when compiled will provide a better picture of the danger of spacecraft crash and eclipse. This will provide the mission designers with a better understanding of the orbit stability characteristics around Vesta, thus helping to ensure a higher level of operational safety. This simulation tool can also be applied to the second phase of the Dawn mission (an orbit around the asteroid Ceres) and other similar missions.