Almost rectilinear halo orbits
Abstract
Numerical studies over the entire range of mass ratios in the circular restricted threebody problem have revealed the existence of families of threedimensional halo periodic orbits emanating from the general vicinity of any of the three collinear Lagrangian libration points. Following a family towards the nearer primary leads, in two different cases, to thin, almost rectilinear, orbits aligned essentially perpendicular to the plane of motion of the primaries. If the nearer primary is much more massive than the further, these thin L3family halo orbits are analyzed by looking at the inplane components of the small osculating angular momentum relative to the large primary and at the small inplane components of the osculating Laplace eccentricity vector. The analysis is carried either to first or second order in these four small quantities. If the nearer primary is much less massive than the further, the thin L1family and L2family halo orbits are analyzed to first order in these same four small quantities with an independent variable related to the onedimensional approximate motion. The resulting orbits and their stability are compared with those obtained by numerical integration.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1982
 Bibcode:
 1982aiaa.meetQ....H
 Keywords:

 EarthMoon Trajectories;
 Librational Motion;
 Orbital Mechanics;
 Three Body Problem;
 Three Dimensional Motion;
 Angular Momentum;
 Eccentric Orbits;
 Halos;
 Numerical Integration;
 Numerical Stability;
 Astronomy