The current work will be focused upon the study of the effects of the earth's gravitational field on the motion of an artificial satellite constellation and a computational model for this perturbation on the constellation orbit will be done; the earth's gravitational field up to second zonal harmonics is considered. This perturbation make a drift for the orbital elements of satellite constellation that make continues coverage and lead to a shift of the whole constellation structure. The equations of motion under effects of oblatenees force are solved numerically by using Rung-Kotta method. The results show that this model has efficiency to compute the perturbations for satellite constellation which already congruent with observing data.