On the dynamics of weak stability boundary lunar transfers

Recent studies demonstrate that lunar and solar gravitational assists can offer a good reduction of total variation of velocity V needed in lunar transfer trajectories. In particular the spacecraft, crossing regions of unstable equilibrium in the Earth-Moon-Sun system, can be guided by the Sun towards the lunar orbit with the energy needed to be captured ballistically by the Moon. The dynamics of these transfers, called weak stability boundary (WSB) transfers, will be studied here in some detail. The crucial Earth-Moon-Sun configurations allowing such transfers will be defined. The Sun's gravitational effect and lunar gravitational capture will be analyzed in terms of variations of the Jacobi 'constants' in the Earth-Sun and Earth-Moon systems. Many examples will be presented, supporting the understanding of the dynamical mechanism of WSB transfers and analytical formulas will be obtained in the case of 'quasi ballistic captures'.