Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold \tubes" associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold 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. The current work extends the results to the spatial case

Transfers between moons with escape and capture patterns via Lyapunov exponent maps

This contribution focuses on the design of low-energy transfers between planetary moons and presents an efficient technique to compute trajectories characterized by desirable behaviors in the vicinities of the departure and destination bodies. The method utilizes finite-time Lyapunov exponent maps in combination with the Moon-to-Moon Analytical Transfer (MMAT) method previously proposed by the authors. The integration of these two components facilitates the design of direct transfers between moons within the context of the circular restricted three-body problem, and allows the inclusion of a variety of trajectory patterns, such as captures, landings, transits and takeoffs, at the two ends of a transfer. The foundations and properties of the technique are illustrated through an application based on impulsive direct transfers between Ganymede and Europa. However, the methodology can be employed to assist in the design of more complex mission scenarios, such as moon tours

Trajectory design in the spatial circular restricted three-body problem exploiting higher-dimensional Poincare maps

In this investigation, the role of higher-dimensional Poincaré maps in facilitating trajectory design is explored for a variety of applications. To begin, existing strategies to implement Poincaré maps for trajectory design applications in the spatial CR3BP are evaluated. New applications for these strategies are explored, including an analysis of the natural motion of Jupiter-family comets that experience temporary capture about Jupiter, and the search for periodic orbits in the vicinity of the primary bodies in the spatial problem. Because current strategies to represent higher-dimensional maps, generally, lead to a loss of information, new approaches to represent all information contained in higher-dimensional Poincaré maps are sought. ^ The field of data visualization offers many options to visually represent multivariate data sets, including the use of glyphs. A glyph is any graphical object whose physical attributes are determined by the variables of a data set. In this investigation, the role of glyphs in representing higher-dimensional Poincaré maps is explored, and the resulting map representations are demonstrated to search for maneuver-free and low-cost transfers between libration point orbits. A catalog of libration point orbit transfers is developed in the Earth-Moon system, and observations about the catalog solutions yields insight into the existence of these transfers. The application of Poincaré maps to compute transfers between libration point orbits in different three-body systems is additionally considered. Finally, interactive trajectory design environments that incorporate Poincaré maps into the design process are demonstrated. Such design environments offer a unique opportunity to explore the available trajectory options and to gain intuition about the solution space

Access to Mars from Earth-Moon Libration Point Orbits:

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared

Homo- and Heteroclinic Connections in the Planar Solar-Sail Earth-Moon Three-Body Problem

This paper explores the existence of homo- and heteroclinic connections between solar-sail periodic orbits in the planar Earth-Moon circular restricted three-body problem. The existence of such connections has been demonstrated to great extent for the planar and spatial classical (no-solar sail) three-body problem, but remains unexplored for the inclusion of a solar-sail induced acceleration. Similar to the search for homo- and heteroclinic connections in the classical case, this paper uses the tools and techniques of dynamical systems theory, in particular trajectories along the unstable and stable manifolds, to generate these connections. However, due to the time dependency introduced by the solar-sail induced acceleration, common methods and techniques to find homo- and heteroclinic connections (e.g., using the Jacobi constant and applying spatial Poincaré sections) do not necessarily apply. The aim of this paper is therefore to gain an understanding of the extent to which these tools do apply, define new tools (e.g., solar-sail assisted manifolds, temporal Poincaré sections, and a genetic algorithm approach), and ultimately find the sought for homo- and heteroclinic connections. As a starting point of such an investigation, this paper focuses on the planar case, in particular on the search for homo- and heteroclinic connections between three specific solar-sail Lyapunov orbits (two at the L1 point and one at the L2 point) that all exist for the same near-term solar-sail technology. The results of the paper show that, by using a simple solar-sail steering law, where a piece-wise constant sail attitude is applied in the unstable and stable solar-sail manifold trajectories, homo- and heteroclinic connections exist for these three solar-sail Lyapunov orbits. The remaining errors on the position and velocity at linkage of the stable and unstable manifold trajectories are < 10 km and < 1 m/s. Future studies can apply the tools and techniques developed in this paper to extend the search for homo- and heteroclinic connections to other solar-sail Lyapunov orbits in the Earth-Moon system (e.g., for different solar-sail technology), to other planar solar-sail periodic orbits, and ultimately also to the spatial, three-dimensional case

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

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

A study of low-energy transfer orbits to the Moon: towards an operational optimization technique

In the Earth-Moon system, low-energy orbits are transfer trajectories from the earth to a circumlunar orbit that require less propellant consumption when compared to the traditional methods. In this work we use a Monte Carlo approach to study a great number of such transfer orbits over a wide range of initial conditions. We make statistical and operational considerations on the resulting data, leading to the description of a reliable way of finding "optimal" mission orbits with the tools of multi-objective optimization

Low-energy tour of the Galilean moons

This thesis is aimed at studying direct (i.e., without intermediate flybys) trajectories to visit different moons of a planetary system. In particular, the case of study is that of the Galilean moons Europa, Ganymede and Callisto, first observed by Galileo Galilei in 1610, orbiting around Jupiter

Trajectory Design for a Cislunar Cubesat Leveraging Dynamical Systems Techniques: The Lunar Icecube Mission

Lunar IceCube is a 6U CubeSat that is designed to detect and observe lunar volatiles from a highly inclined orbit. This spacecraft, equipped with a low-thrust engine, will be deployed from the upcoming Exploration Mission-1 vehicle in late 2018. However, significant uncertainty in the deployment conditions for secondary payloads impacts both the availability and geometry of transfers that deliver the spacecraft to the lunar vicinity. A framework that leverages dynamical systems techniques is applied to a recently updated set of deployment conditions and spacecraft parameter values for the Lunar IceCube mission, demonstrating the capability for rapid trajectory design

Low Thrust Trajectories in Multi Body Regimes

More and more stringent and unique mission requirements motivate to exploring solutions, already in the preliminary mission analysis phase, going far beyond the classical chemical-Keplerian approach. The present dissertation deals with the analysis and the design of highly non linear orbits arising both from the inclusion of different gravitational sources in the dynamical models, and from the use of electric system for primary propulsion purposes. The equilibrium of different gravitational fields, on one hand, permits unique transfer solutions and operational orbits, on the other hand, the high thrust efficiency, characteristic of an electric device, reduces the propellant mass required to accomplish the transfer. Each of these models, and even better their combination, enables trajectories able to satisfy mission requirements not otherwise met, first of all to reduce the propellant mass fraction of a given mission. The inclusion of trajectory arcs powered by an electric thruster, providing a low thrust for extended duration, makes essential the use of optimal control theory in order to govern the thrust law and thus design the required transfers so as to minimizing/maximizing specific indexes. The goal is, firstly, to review the possible advantages and the main limits of dynamical models and, afterward, to define methodologies to preliminary design non-Keplerian missions both in interplanetary contexts and in the Earth-Moon system. Special emphasis is given to the study of dynamical systems through which the main features of the Circular Restricted Three Body Model (the first one among the non-Keplerian models) can be identified, implemented and used. Purely ballistic solutions enabled by this model are first independently explored and after considered as target orbits for electric thrusting phases. Electric powered arcs are used to link ballistic phases arising from the balancing of different gravitational influences. This concept is applied both for the exploration of planetary regions and for interplanetary transfer purposes. Together with low thrust missions to selenocentric orbits designed taking into account both the Earth and the Moon gravity, also transfer solutions toward periodic orbits moving in the Earth-Moon region are presented. These are designed considering electric thrusting arcs and ballistic segments exploring for free specific space regions. In brief, theoretical models deriving from dynamical system theory and from optimal control theory are employed to design non conventional orbits in non linear astrodynamics models