Lunar Analytical Theory for Polar Orbits in a 50-Degree Zonal Model Plus Third-Body Effect

Low-altitude orbiters about the Moon require full potential fields for accurate modeling. Therefore, analytical theories are usually discarded in preliminary mission design of close Lunar orbiters for the huge formal expressions that need to be handled. However, specific applications allow for certain reduction. This is the case of polar orbits, where a rearrangement of the perturbing function makes it possible to carry out dramatic simplifications that allow us to cope with fifty zonal harmonics analytically. The theory reflects the real long-term behavior of low-altitude, polar, Lunar orbiters and may be useful in preliminary mission design.