Transfers Between the Earth-Moon and Sun-Earth Systems Using Manifolds and Transit Orbits
- Paper number
IAC-05-C1.6.01
- Author
Prof. Kathleen Howell, Purdue University, United States
- Coauthor
Mr. Masaki Kakoi, Purdue University, United States
- Year
2005
- Abstract
The L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. The Lunar libration points, in conjunction with the collinear libration points in the Sun-Earth system, may also become primary hubs for future human activities in the Earth’s neighborhood. The Sun-Earth L2 point is expected to become the location of a number of large astronomical observatories. These L2 telescopes may require human servicing and repair as the missions become more ambitious and, thus, more complex. Closer to Earth, the Earth-Moon L1 libration point is suggested as a staging node for the missions to the Sun-Earth L2 point as well as the Moon, Mars, and the rest of the solar system. Thus, the Earth-Moon L1 point has been suggested as a “portal” to move beyond the Earth’s neighborhood. The manifold tubes have been introduced by a number of researchers as the basis for a design strategy to produce the trajectories to move between these systems. It has also been examined in the Jovian system. In any case, intersections may ultimately be sought between many tubes from many different libration point orbits in each system; the complexity forces a new look at the computations. Thus, individual solutions to the transfer problem between three-body systems have been the focus of some recent investigations. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied in this work. This paper presents an approach to solve the general problem for transfers between the Earth-Moon system (lunar orbits and/or lunar libration point orbits) and Sun-Earth/Moon L2 libration point orbits. It is based on the families of periodic orbits and the invariant manifolds within each system. Beginning with the circular restricted problem, the solution is generated by overlapping the two different three-body systems. Earth-to-halo transfers, as well as halo-to-Earth arcs, have been computed by exploiting the invariant manifolds associated with a particular periodic halo orbit (or quasi-periodic Lissajous trajectory). Developing transfers between Earth and a halo orbit or between different three-body systems involves the numerical integration of different sets of initial conditions near a desired halo orbit manifold until a trajectory is identified that is most suitable for the application of interest. Of course, the stable/unstable invariant manifolds that correspond to a single periodic halo orbit reside on the surface of a single tube. In the analysis of trajectories to/from a halo orbit, for example, the size of the most useful periodic orbit may be unknown and its amplitude may serve as a design parameter. The design space then includes not just a tube corresponding to the invariant manifolds of one halo orbit; rather, it becomes a volume consisting of many tubes. For the related problem of system-to-system transfers, the first goal is the intersection of two manifold tubes – one from each system. A maneuver at an intersection point will shift the vehicle from one tube to the other. In the circular restricted three-body problem, the flow in this region of space can also be visualized by noting that the tube is a separatrix, i.e., it bounds different regions of the flow. Thus, transit trajectories might also be sought that pass inside the tubes and shift from one tube to the next. In this case, the spatial intersection of the tubes is still the key information to complete the computations. If multiple tubes are involved, intersections of the volumes may ultimately be most useful. Computing these intersections is facilitated by efficient but accurate approximations of the tubes. Determination of the most useful intersections is accomplished by evaluation of Poincaré sections corresponding to the tubes. The problem is formulated in three-dimensional configuration space so that the Poincaré sections are projected into different subspaces. This analysis yields transfers to/from lunar orbit or libration point orbits in the Earth-Moon system to the Sun-Earth/Moon L2 libration point orbits. These solutions are then transitioned to the full ephemeris models with additional gravitational perturbations (and other perturbations as appropriate). The transfers can be determined for various lunar phases. The solution process will also determine the particular Lissajous trajectory in each system to accomplish the transfer at lowest cost. Some results will be presented for various types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.
- Abstract document
- Manuscript document
IAC-05-C1.6.01.pdf (🔒 authorized access only).
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