Material capture by double lunar gravity assist

Abstract

The equations yielding the performance of a single lunar flyby in removing incoming hyperbolic excess velocity to capture payloads on interplanetary trajectories are briefly derived. The impossibility of using a single lunar flyby to capture a body entering the earth-moon system with a hyperbolic velocity in excess of about 1.9 km/s is discussed, and a method of using a double flyby of the moon to significantly improve this performance is developed. The equations for achieving a double lunar flyby are derived by solving the orbital equations and Lambert's problem both for the incoming trajectory in the plane of the moon's orbit and for arbitrary declination. For the in-plane case it is shown that the maximum removable hyperbolic excess velocity is 2.2687 km/s. For the inclined case, it is shown that the use of a double lunar flyby allows capture for declinations in excess of 54 degrees, and that for declinations less than 38 degrees the double lunar flyby offers better performance than the single lunar flyby.