AN ANALYTICAL STUDY THROUGH THE JACOBI INTEGRAL TO OBTAIN MULTIPLE REVOLUTION TRAJECTORIES TO THE MOON
Luiz Arthur Gagg Filho1; Sandro da Silva Fernandes1
1 Instituto Tecnológico de Aeronáutica
doi:10.20906/CPS/COB-2015-0397
Resumo
A study about Kepler's energy of the space vehicle on the arrival trajectory at the insertion point in a low Moon orbit for Earth-Moon bi-impulsive internal trajectories is performed in this paper. The classic planar circular restricted three-body problem (PCR3BP) is utilized as the dynamical model to describe the motion of the space vehicle. In order to determine the internal trajectories, a new two-point boundary value problem (TPBVP) is proposed in such way that the Jacobi Integral is prescribed. In this new problem, analytical expressions for the velocities increments are derived from the Jacobi Integral expression and a relation between the Jacobi Integral and the arrival Kepler's energy is obtained. In this way, a critical value for the Jacobi Integral is obtained in which the Kepler's energy becomes negative and a ballistic capture by the Moon can be accomplished by the space vehicle. The results also prove that an increasingly value of the time of flight is not followed by the increase of the Jacobi Integral value, which means that the determination of new trajectories becomes more difficult with large Jacobi Integral values.
Palavras-chave: Jacobi Integral; three-body problem; ballistic capture; Earth-Moon trajectories; large times of flight