Trajectory Design for Space Missions to Libration Point L2
Abstract: This work is focused on the detection and computation of free transfer trajectories from parking orbits around the Earth to quasiperiodic orbits around the collinear libration point L2, in the Sun-Earth system; no correction or insertion maneuvers into the final orbits have been considered. The circular restricted three-body problem is the mathematical model used to describe the motion of a spacecraft, in the gravitational field of the two primaries, computed by integrating the nonlinearized equations of motion. A shooting method has been designed and developed to determine the increment of velocity required for the perigee maneuver, which injects a spacecraft into its transfer trajectory: first the velocity boundary for the Earth escape/capture condition is detected and then an iterative bisection method is applied until the burnout velocity, tangential to the parking orbit, leads the spacecraft to its final Lissajous orbit. For a launch from Kourou at local noon, Ariane5 GTO and Soyuz GTO equivalent have been studied and compared, considering fuel minimization for the transfer maneuver and general mission constraints, as maximum excursion of the final Lissajous orbit from the ecliptic plane and eclipses avoidance during the mission. This analysis highlights advantages and drawbacks of various parking orbits. Mission goals are the key factor for the tradeoff among orbit selection, launch options, and the other constraints, fixed by mission requirements.
trajectory design libration points lissajous orbits