Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder

Andrew D Cox, Purdue University


Any possible LISA Pathfinder extended mission will immediately follow the primary mission after completion of scientific observations and technical demonstrations in a Sun-Earth L1 libration point orbit. One extended mission concept with scientific appeal is a spacecraft path that includes multiple encounters with a gravitational equilibrium point. This point, also termed a saddle point, exists where the total gravitational acceleration sums to zero and is distinct from the five Lagrange points in the three-body problem. This investigation seeks a strategy to design such a path subject to a variety of constraints. Periodic, quasi-periodic, and manifold structures are explored to supply useful transit behavior as well as arcs that repeatedly encounter the saddle point. A selection of these structures from the Earth-Moon and Sun-Earth circular restricted three-body problems are linked together via Poincaré mapping techniques and corrected in a higher-fidelity Sun-Earth-Moon bicircular restricted four-body problem (BC4BP) and in an ephemeris environment. Additionally, natural motion in the BC4BP is leveraged to achieve the required encounters, and is similarly corrected to meet mission constraints. Results from both methods are detailed and compared to the mission requirements.




Howell, Purdue University.

Subject Area

Aerospace engineering

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