The Multi-Resolution Quadrature (MRQ) Sphere model, is a newly developed multi- resolution gravity model designed to estimate the gravity fields of arbitrary shaped space bodies, such as asteroids. The MRQ Sphere model uses two recently developed mathematical techniques to approximate the standard spherical harmonics. One of these tools approximates the radial decay terms using the sum of Gaussians, while the other is used for estimating the angular functions on the nodes of the quadratures of a sphere. In this work, we apply the MRQ sphere technique to the classic orbit propagation problem and compare the propagated orbit with that generated by the spherical harmonics method. We validate the methods with Earth as the primary body, and propagate the orbit of test cases such as the LAser GEOdynamics Satellite-II (LAGEOS-II) and the GPS BIIA-10 (PRN 32) satellite. We find that the MRQ-Sphere model may be applicable to orbit propagation up to a user dependent approximation. Advisors/Committee Members: Grigoriadis, Karolos M. (advisor), Provence, Robert S. (committee member), Rao, Jagannatha R. (committee member).