This paper intends to highlight the effect of the third-body in an inclined orbit on a spacecraft orbiting the primary mass. To achieve this goal, a new origin of coordinate is introduced in the primary and the X-axis toward the node of the spacecraft. The disturbing function is expanded up to the second order using Legendre polynomials. A double-averaged analytical model is exploited to produce the evolutions of mean orbital elements as smooth curves.

1. INTRODUCTION
 2. ELLIPTICAL AND INCLINED DISTURBING POTENTIAL
 3. LAGRANGE’S PERTURBATION EQUATIONS
 4. NUMERICAL SIMULATIONS
 5. DISCUSSION AND CONCLUSION
 ACKNOWLEDGEMENTS
 REFERENCES

• W. A. Rahoma(Department of Astronomy, Faculty of Science, Cairo University) Corresponding Author