Analytical model for Lunar orbiter revisited

Resumen

Analytical theories based on Lie-Deprit transforms are being used so as to simplify the search for families of periodic orbits around planets, natural satellites or asteroids. Normalized equations of motion allow locating the frozen orbit families depending on values of the inclination, eccentricity and semi-major axis. In order to analyze the qualitative long-term behavior of low-altitude near-circular lunar orbits, we produce, in the present work, a closedform second-order analytical theory, which allows us to completely describe the shape of the frozen orbit surfaces, even for inclinations greater than 69o. From our analytical theory, we have derived a robust and easy-to-use Mathematica package, called Frozenof, for mission planning. We present an effective and low computational-cost method to obtain lunar periodic orbits by combining our analytical package, Frozenof, with a differential corrector procedure, which is accecssible through Astrody ToolsWeb Web Site.