Connecting orbits and invariant manifolds in the spatial restricted three-body problem

Abstract

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case. Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L 1 and the other around L 2. Since these connections are asymptotic orbits, no manoeuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.

Optimal Control and Applications to Aerospace: Some Results and Challenges

“…There exist many other families of periodic orbits (called Lissajous orbits) and quasi-periodic orbits around Lagrange points (see [210,211]). The invariant (stable and unstable) manifolds of these periodic orbits, consisting of all trajectories converging to the orbit (as the time tends to ±∞), are four-dimensional tubes, topologically equivalent to S 3 × IR, in the five-dimensional energy manifold (see [212]). Hence they play the role of separatrices.…”

Preliminary Capture Trajectory Design for Europa Tomography Probe

“…As an example, dynamical chains formed by linking heteroclinic connections and homoclinic orbits [9] are proposed for the analysis of fast resonance transitions between exterior and interior resonant orbits (in the Sun-Jupiter system) [10] or "loose" capture trajectories [11]. Similar concepts are exploited for Halo-to-Halo [12] or libration-to-libration [13] transfers between planetary moons in the Jovian system, adopting a "patched" CRTBP model.…”

Libration Transfer Design Using Patched Elliptic Three-Body Models and Graphics Processing Units

“…During preliminary studies, the standard way to deal with this restricted four-body system, where a spacecraft is considered as the forth body with innitesimal mass, is to decouple the system into two overlapping restricted threebody problems, for example the Sun-Earth CRTBP and the Earth-Moon CRTBP. The spacecraft can be shifted from one system to another by implementing maneuvers at the intersection points of two manifolds coming from dierent three-body regimes [9,10]. Usually a renement of the patched transfer in a high-delity ephemeris model is necessary after these preliminary designs.…”