Frozen orbit is an attractive option for orbital design owing to its characteristics (its argument of pericenter and eccentricity are kept constant on an average). Solar sails are attractive solutions for massive and expensive missions. However, the solar radiation pressure effect represents an additional force on the solar sail that may greatly affect its orbital behavior in the long run. Thus, this force must be included as a perturbation force in the dynamical model for more accuracy. This study shows the calculations of initial conditions for a lunar solar sail frozen orbit. The disturbing function of the problem was developed to include the lunar gravitational field that is characterized by uneven mass distribution, third body perturbation, and the effect of solar radiation. An averaging technique was used to reduce the dynamical problem to a long period system. Lagrange planetary equations were utilized to formulate the rate of change of the argument of pericenter and eccentricity. Using the reduced system, frozen orbits for the Moon sail orbiter were constructed. The resulting frozen orbits are shown by two 3Dsurface (semimajor, eccentricity, inclination) figures. To simplify the analysis, we showed inclination–eccentricity contours for different values of semi-major axis, argument of pericenter, and values of sail lightness number.

1. INTRODUCTION
2. DYNAMICAL MODEL
    2.1 Lunar Gravity Potential
    2.2 Third-Body Attraction
    2.3 Effect of the Solar Radiation Pressure
    2.4 Solar Sail Lightness Number
3. REDUCED SYSTEM
4. COMPUTATION OF FROZEN ORBITS
5. RESULTS AND ANALYSIS
6. CONCLUSIONS
REFERENCES

• Elamira Hend Khattab(Department of Astronomy and Space Science, Faculty of Science, Cairo University)
• Mohamed Radwan(Department of Astronomy and Space Science, Faculty of Science, Cairo University)
• Walid Ali Rahoma(Department of Astronomy and Space Science, Faculty of Science, Cairo University) Corresponding Author