The solution to the problem of a satellite with a small constant thrust and under the influence of a central force field presents difficulties due to equations non-linearity. An investigation was made to determine what range of values of the thrust parameter could be utilized to obtain a valid approximate solution for the case of tangential thrusting. The investigation was accomplished by developing programs for the 1620 High Speed Digital Computer, since the solution to the exact and approximate equations would otherwise be exceedingly laborious. Under the assumption of no atmosphere, and neglecting the earth's oblateness, the study showed that the validity of the Kryloff and Bogoliuboff method was dependent on both the specific thrust aud the vehicle speed. For a Speed corresponding to an orbit of smaller eccentricity it was determined that the method of Kryloff and Bogoliuboff remained valid for larger values of W than when V was a velocity corresponding to an orbit with a greater eccentricity. The method of Kryloff and Bogoliuboff represents a practical approach to the solution of satellite motion both from the aspect of ease of application and reasonable calculation times. / Master of Science