Numerical Determination of Natural Spacecraft Formations Near the Collinear Libration Points

Abstract

The work this paper describes identifies continuous natural relative trajectories near the collinear libration points numerically from the nonlinear CR3BP differential equations by utilizing a shooting method with a two-level differential corrector. The focus is on determining natural formations in the vicinity of the Earth-Moon $\mathrm{L}_{2}$ point when using the nonlinear equations of motion of the CR3BP. Upon identifying these relative trajectories analysis is conducted to determine drift rates of the uncontrolled trajectories compared to linearized formations near the collinear libration points. In addition, stationkeeping techniques are applied to determine the required maneuvers and frequencies and to assess $\triangle \mathcal{V}$ maintenance of the nominal trajectories.