The Earth-Moon CR3BP: A full Atlas of low-energy fast periodic transfer orbits

Abstract

In the framework of the planar CR3BP for mass parameter mu=0.0121505, corresponding to the Earth-Moon system, we identify and describe 80 families of periodic orbits encircling both the Earth and the Moon ("transfer" orbits). All the orbits in these families have very low energies, most of them corresponding to values of the Jacobi constant C for which the Hill surface is closed at the Lagrangian point L2. All of these orbits have also short period T, generally under six months. Most of the families are composed of orbits that are asymmetric with respect to the Earth-Moon axis. The main results presented for each family are: (i) the characteristic curves T(h), y(h), v_y(h), and v_x(h) on the Poincare section Sigma_1={x=0.836915310,y,v_x>0,v_y} normal to the Earth-Moon axis at the Lagrangian point L1, parameterized by their energy h=-C/2 in the synodic coordinate system; (ii) the stability parameter along each family; (iii) the intersections x_i(h) of the orbits with the Earth-Moon axis, on the Poincare section Sigma_2={x,y=0,v_x},v_y>0}; (iv) plots of some selected orbits and details of their circumlunar region; and (v) numerical data for the intersection of an orbit with Sigma_1 at a reference value of h. Some possible extensions and applications of this work are also discussed.