The uneven mass distribution of the Moon highly perturbs the lunar spacecrafts. This uneven mass distribution leads to peculiar dynamical features of the lunar orbiters. The critical inclination is the value of inclination which keeps the deviation of the argument of pericentre from the initial values to be zero. Considerable investigations have been performed for critical inclination when the gravity field is assumed to be symmetric around the equator, namely for oblate gravity field to which Earth’s satellites are most likely to be subjected. But in the case of a lunar orbiter, the gravity field of mass distribution is rather asymmetric, that is, sectorial, and tesseral, harmonic coefficients are big enough so they can’t be neglected. In the present work, the effects of the first sectorial and tesseral harmonic coefficients in addition to the first zonal harmonic coefficients on the critical inclination of a lunar artificial satellite are investigated. The study is carried out using the Hamiltonian framework. The Hamiltonian of the problem is cconstructed and the short periodic terms are eliminated using Delaunay canonical variables. Considering the above perturbations, numerical simulations for a hypothetical lunar orbiter are presented. Finally, this study reveals that the critical inclination is quite different from the critical inclination of traditional sense and/or even has multiple solutions. Consequently, different families of critical inclination are obtained and analyzed.

1. INTRODUCTION
 2. HAMILTONIAN FORMULATION
 3. SHORT PERIODIC TERMS ELIMINATION
 4. SOLUTION OF THE CUBIC EQUATION (7)
 5. MODEL SIMULATION
 6. SIMULATION RESULTS
 7. CONCLUSION
 REFERENCES

• Walid A. Rahoma(Department of Astronomy and Space Science, Faculty of Science, Cairo University) Corresponding Author
• Fawzy A. Abd El-Salam(Department of Astronomy and Space Science, Faculty of Science, Cairo University, Department of Mathematics, Faculty of Science, Taibah University)