<div> <div> <div> <p>Resonant orbits in a multi-body environment have been investigated in the past to aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated into the design of trajectories requiring reduced maneuver costs. Poincaré sections are now also extensively utilized in the search for novel, maneuver-free trajectories in various systems. This investigation employs dynamical systems techniques in the computation and characterization of resonant orbits in the higher-fidelity Circular Restricted Three-Body model. Differential corrections and numerical methods are widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost trajectories to support exploration for several planet-moon systems is demonstrated. The efficacy of the resonant orbits is illustrated via transfer trajectory design in the Earth-Moon, Saturn-Titan, and the Mars-Deimos systems. Lastly, Poincaré sections associated with different resonance ratios are incorporated into the search for natural, maneuver-free trajectories in the Saturn-Titan system. To that end, homoclinic and heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques demonstrated in this investigation are useful for the design of trajectories in several different systems within the CR3BP. </p> </div> </div> </div>

<p>Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the Earth-Moon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover period-commensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining period-commensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are  available for in-orbit refueling/maintenance as well as surveillance/communications applications  that depart and return to the same phase in the operating orbit.</p>

<div>There is an increasing interest in future space missions devoted to the exploration of key moons in the Solar system. These many different missions may involve libration point orbits as well as trajectories that satisfy different endgames in the vicinities of the moons. To this end, an efficient design strategy to produce low-energy transfers between the vicinities of adjacent moons of a planetary system is introduced that leverages the dynamics in these multi-body systems. Such a design strategy is denoted as the moon-to-moon analytical transfer (MMAT) method. It consists of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. Subsequently, the strategy builds moon-to-moon transfers based on invariant manifold and transit orbits exploiting some analytical techniques. The strategy is applicable for direct as well as indirect transfers that satisfy the analytical constraints. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons. </div><div> </div><div>The current work includes sample applications of transfers between different orbits and planetary systems. The method is efficient and identifies optimal solutions. However, for certain orbital geometries, the direct transfer cannot be constructed because the invariant manifolds do not intersect (due to their mutual inclination, distance, and/or orbital phase). To overcome this difficulty, specific strategies are proposed that introduce intermediate Keplerian arcs and additional impulsive maneuvers to bridge the gaps between trajectories that connect any two moons. The updated techniques are based on the same analytical methods as the original MMAT concept. Therefore, they preserve the optimality of the previous methodology. The basic strategy and the significant additions are demonstrated through a number of applications for transfer scenarios of different types in the Galilean, Uranian, Saturnian and Martian systems. Results are compared with the traditional Lambert arcs. The propellant and time-performance for the transfers are also illustrated and discussed. As far as the exploration of Phobos and Deimos is concerned, a specific design framework that generates transfer trajectories between the Martian moons while leveraging resonant orbits is also introduced. Mars-Deimos resonant orbits that offer repeated flybys of Deimos and arrive at Mars-Phobos libration point orbits are investigated, and a nominal mission scenario with transfer trajectories connecting the two is presented. The MMAT method is used to select the appropriate resonant orbits, and the associated impulsive transfer costs are analyzed. The trajectory concepts are also validated in a higher-fidelity ephemeris model.</div><div> </div><div>Finally, an efficient and general design strategy for transfers between planetary moons that fulfill specific requirements is also included. In particular, the strategy leverages Finite-Time Lyapunov Exponent (FTLE) maps within the context of the MMAT scheme. Incorporating these two techniques enables direct transfers between moons that offer a wide variety of trajectory patterns and endgames designed in the circular restricted three-body problem, such as temporary captures, transits, takeoffs and landings. The technique is applicable to several mission scenarios. Additionally, an efficient strategy that aids in the design of tour missions that involve impulsive transfers between three moons located in their true orbital planes is also included. The result is a computationally efficient technique that allows three-moon tours designed within the context of the circular restricted three-body problem. The method is demonstrated for a Ganymede->Europa->Io tour.</div>

<p dir="ltr">The recent and upcoming increase in spaceflight missions to the lunar vicinity necessitates methodologies to enable operations beyond the Earth. In particular, there is a pressing need for a Space Domain Awareness (SDA) and Space Situational Awareness (SSA) architecture that encompasses the realm of space beyond the sub-geosynchronous region to sustain humanity's long-term presence in that region. Naturally, the large distances in the cislunar domain restrict access rapid and economical access from the Earth. In addition, due to the long ranges and inconsistent visibility, the volume contained within the orbit of the Moon is inadequately observed from Earth-based instruments. As such, space-based assets to supplement ground-based infrastructure are required. The need for space-based assets to support a sustained presence is further complicated by the challenging dynamics that manifest in cislunar space. Multi-body dynamical models are necessary to sufficiently model and predict the motion of any objects that operate in the space between the Earth and the Moon. The current work seeks to address these challenges in dynamical modeling and cislunar accessibility via the exploration of resonant orbits. These types of orbits, that are commensurate with the lunar sidereal period, are constructed in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) and validated in the Higher-Fidelity Ephemeris Model (HFEM). The expansive geometries and energy options supplied by the orbits are favorable for achieving recurring access between the Earth and the lunar vicinity. Sample orbits in prograde resonance are explored to accommodate circumlunar access from underlying cislunar orbit structures via Poincaré mapping techniques. Orbits in retrograde resonance, due to their operational stability, are employed in the design of space-based observer constellations that naturally maintain their relative configuration over successive revolutions. </p><p dir="ltr"> Sidereal resonant orbits that are additionally commensurate with the lunar synodic period are identified. Such orbits, along with possessing geometries inherent to sidereal resonant behavior, exhibit periodic alignments with respect to the Sun in the Earth-Moon rotating frame. This characteristic renders the orbits suitable for hosting space-based sensors that, in addition to naturally avoiding eclipses, maintain visual custody of targets in the cislunar domain. For orbits that are not eclipse-favorable, a penumbra-avoidance path constraint is implemented to compute baseline trajectories that avoid Earth and Moon eclipse events. Constellations of observers in both sidereal and sidereal-synodic resonant orbits are designed for cislunar SSA applications. Sample trajectories are assessed for the visibility of various targets in the cislunar volume, and connectivity relative to zones of interest in Earth-Moon plane. The sample constellations and observer trajectories demonstrate the utility of resonant orbits for various applications to sustain operations in cislunar space. </p>