Precise Lunar Gravity Assist Transfers to Geostationary Orbits

Abstract

Introduction T HE transfer to geostationary orbit (GSO) is usually achieved by placing the spacecraft initially in a geostationary transfer orbit (GTO) with perigee altitude around 200 km and apogee around 36,000 km. The GTO orbital planes are inclined to the Earth equator because of launch station locations. A large amount of propellant is required to effect the plane change to achieve zero inclination as well as to raise the perigee altitude to 36,000 km. These maneuvers make the mission expensive, especially when the initial GTO inclinations are high. Alternate approaches1−3 that advocate the use of lunar gravity assist are discussed in the literature to reduce the fuel budget. When a geocentric trajectory goes through the lunar gravity field, it undergoes a plane change and gains or loses energy relative to the Earth. This phenomenon can be judiciously used to raise the perigee of the return trajectory, rotate the apsidal line, and change the orbital inclination by choosing appropriate initial transfer orbit characteristics relative to the Earth. Thus, the transfer of a spacecraft to GSO from GTO involves identification of appropriate initial transfer trajectory characteristics that result in a low inclination and GSO altitude as its perigee altitude after encounter with the moon. In this Note, a numerical search technique that uses genetic algorithms (GA) is formulated. Because of the extreme sensitivity of the outgoing trajectory to the initial conditions, the performance of the regular GA4 is found to be inadequate. A modified version of GA, GA with adaptive bounds (GAAB),5 has successfully been employed to overcome the problem of high sensitivity. In this approach, the parameter bounds of GA are modified during the search process. The adaptation process helps generate precise lunar gravity assist trajectory design. Furthermore, the influence of different propagation force models on the initial conditions and on the achieved target parameters is assessed. The significance of Earth’s second zonal harmonic is established.