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The objective of the present investigation is to present a framework to produce low-energy trajectories between the vicinities of adjacent moons of a planetary system leveraging libration point orbits in multi-body environments. The current development includes an extension of the Moon-to-Moon Analytical Transfer (MMAT) method previously proposed by the authors, as well as sample applications of transfers between different libration point orbits and planetary systems. The original MMAT technique blends invariant manifold trajectories emanating from libration point orbits in the circular restricted three-body problem to design transfers between distinct moons exploiting some analytical techniques. However, for certain orbital geometries, direct transfers 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 additional impulsive maneuvers to bridge the gaps between trajectories that connect any two moons. Transfers with one or two intermediate arcs between departure and arrival moons are introduced leveraging a change of plane. When this strategy is still not sufficient to guarantee a transfer, an approach that consists of distant two- and three-burn transfers is introduced. These different strategies are demonstrated through a number of applications of different types in the Galilean, Uranian, Saturnian and Martian systems. Results are also compared with traditional Lambert arcs. The propellant and time-performance for the transfers are illustrated and discussed.

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... Following up on the direct transfers developed within the PGT, Fantino and Castelli [18] introduced a patched two-body/three-body (2BP-CR3BP) model to facilitate the design of minimum-cost single-impulse moon-to-moon trajectories in the Jovian system using invariant manifolds of planar Lyapunov orbits in two dimensions (2D). A preliminary extension to trajectories between three-dimensional (3D) halo orbits (Fantino et al. [19]) was completed by Canales et al. through the development of an analytical method, termed the Moon-to-Moon Analytical Transfer (MMAT) technique, to construct impulsive transfers between 2D and 3D LPOs of planet-moon CR3BPs [20][21][22]. ...

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.

... Following up on the direct transfers developed within the PGT, Fantino and Castelli [18] introduced a patched two-body/three-body (2BP-CR3BP) model to facilitate the design of minimum-cost singleimpulse moon-to-moon trajectories in the Jovian system using invariant manifolds of planar Lyapunov orbits in two dimensions. A preliminary extension to trajectories between three-dimensional (3D) halo orbits [19] was completed by Canales et al. through the development of an analytical method, termed the moon-to-moon analytical transfer (MMAT) technique, to construct impulsive transfers between two-dimensional (2D) and 3D LPOs of planet-moon CR3BPs [20][21][22]. Invariant manifold trajectories emanating from a departure and a destination LPO are propagated in the respective CR3BPs to the limit of the sphere of influence for the respective moon, where the states of the spacecraft are expressed in a planetcentered inertial frame and used to produce orbital elements of osculating Keplerian orbits. Thus, the problem of connecting trajectories originating from or leading to distinct moons translates into the analytical computation of the intersection between confocal ellipses, the derivation of the conditions under which such intersections exist, and the evaluation of the transfer performance in terms of cost and time of flight. ...

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 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.

Jupiter exploration is one of the focuses of deep space exploration in the near future. Design and optimization of trajectories in the Jovian system are crucial technologies for Jupiter exploration missions due to the unique and challenging multi-body dynamical environment. Various methodologies have been proposed and developed. However, there is a lack of comprehensive review of these methodologies, which is unfavorable for further developing new design techniques and proposing new mission schemes. This review provides a systematic summarization of the past and state-of-art methodologies for 4 main exploration phases, including Jupiter capture, the tour of the Galilean moons, Jupiter global mapping, and orbiting around and landing on a target moon. For each exploration phase, the related methods are categorized according to the fundamental features. The advantages and capabilities of the methods are described or analyzed, revealing the research progress. Finally, a prospect of future development of the methods is presented, aiming at providing references for further studies on trajectory design and optimization in the Jovian system.

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.
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.
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 threemoon
tours designed within the context of the circular restricted three-body problem. The
method is demonstrated for a Ganymede->Europa->Io tour.

The focus of the present investigation is an efficient and general design strategy for transfers between planetary moons that fulfill specific requirements. The strategy leverages Finite-Time Lyapunov Exponent (FTLE) maps within the context of the Moon-to-Moon Analytical Transfer (MMAT) scheme previously proposed by the authors. Incorporating FTLE maps with the MMAT method allows 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, most notably the design of a moon tour.

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, comprised 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. In particular, connections between the periodic orbits of such two different moons are achieved. The strategy is applicable for any type of direct transfers that satisfy the analytical constraints. Case studies are presented for the Jovian and Uranian systems. 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.

While the interest in future missions devoted to Phobos and Deimos increases, missions that explore both moons are expensive in terms of maneuver capabilities partly due to low-energy transfer options that may not be readily available. The proposed approach in this investigation includes Mars-Deimos resonant orbits that offer repeated Deimos flybys as well as access to libration point orbits in the Phobos vicinity. A strategy to select the candidate orbits is discussed and associated costs are analyzed, both for impulsive and low-thrust propulsion capabilities, within the context of the coupled spatial circular restricted three body problem. The trajectory concepts are then validated in a higher-fidelity ephemeris model.

Given the interest in future space missions devoted to the exploration of key moons in the Solar System and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. A general methodology for transfer design between the moons in any given system is developed 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 determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet.

The major post-Cassini knowledge gap concerning Saturn's icy moon Titan is in the composition of its diverse surface, and in particular how far its rich organics may have ascended up the "ladder of life." The NASA New Frontiers 4 solicitation sought mission concepts addressing Titan's habit-ability and methane cycle. A team led by the Johns Hopkins University Applied Physics Laboratory (APL) proposed a revolutionary lander that uses rotors to land in Titan's thick atmosphere and low gravity and can repeatedly transit to new sites, multiplying the mission's science value from its capable instrument payload.

In this contribution, an efficient technique to design direct (i.e., without intermediate flybys) low-energy trajectories in multi-moon systems is presented. The method relies on analytical two-body approximations of trajectories originating from the stable and unstable invariant manifolds of two coupled circular restricted three-body problems. We provide a means to perform very fast and accurate computations of the minimum-cost trajectories between two moons. Eventually, we validate the methodology by comparison with numerical integrations in the three-body problem. Motivated by the growing interest in the robotic exploration of the Jovian system, which has given rise to numerous studies and mission proposals, we apply the method to the design of minimum-cost low-energy direct trajectories between Galilean moons, and the case study is that of Ganymede and Europa.

The restricted problem of three bodies is of fundamental importance in mechanics, with significant applications to astrodynamics. During the last century, much effort has been focused on the search for periodic solutions since they are a key component in understanding the behavior in the non-integrable three-body problem. Numerous families of PLANAR periodic solutions have been computed and their relationships investigated. With vastly improved computational capabilities, THREE-DIMENSIONAL periodic families have appeared in recent years; halo orbits have, perhaps, been the most visible with their link to spacecraft mission design. Although an infinite number of three-dimensional periodic orbits exist, they are very difficult to locate, as well as compute, and a random numerical search will never be successful. Thus, the study of bifurcations, where several families come together, is critical and used as the basis of the current study. In this effort, the L1 and L2 halo orbits serve as the baseline families; a number of bifurcations and intersections representing the existence of other three-dimensional families are identified. Various orbits are numerically computed as members of these intersecting families. A subset of these additional periodic orbits is examined for potential mission design applications.

In this paper, a technique for the analysis and the design of low-energy interplanetary transfers, exploiting the invariant manifolds of the restricted three-body problem, is presented. This approach decomposes the full four-body problem describing the dynamics of an interplanetary transfer between two planets, in two three-body problems each one having the Sun and one of the planets as primaries; then the transit orbits associated to the invariant manifolds of the Lyapunov orbits are generated for each Sun-planet system and linked by means of a Lambert's arc defined in an intermediate heliocentric two-body system. The search for optimal transit orbits is performed by means of a dynamical Poincaré section of the manifolds. A merit function, defined on the Poincaré section, is used to optimally generate a transfer trajectory given the two sections of the manifolds. Due to the high multimodality of the resulting optimization problem, an evolutionary algorithm is used to find a first guess solution which is then refined, in a further step, using a gradient method. In this way all the parameters influencing the transfer are optimized by blending together dynamical system theory and optimization techniques. The proposed patched conic-manifold method exploits the gravitational attractions of the two planets in order to change the two-body energy level of the spacecraft and to perform a ballistic capture and a ballistic repulsion. The effectiveness of this approach is demonstrated by a set of solutions found for transfers from Earth to Venus and to Mars.

In the circular restricted three-body problem, periodic orbits, stable and unstable manifolds, chaotic regions, and other dynamical features have all proven useful for engineering applications. These phase-space structures can be identified because the system is autonomous in a rotating frame. In more complex multi-body and high-fidelity models, classic invariant sets are not readily identifiable and new approaches are required. The approach here exploits the anisotropy of the growth or decay of perturbations to the trajectories, building on recent ideas from the theory of hyperbolic Lagrangian coherent structures. The present framework yields a mechanism to construct transfers in multi-body systems. In particular, it is applied to a restricted four-body problem and transfers are constructed requiring smaller \(\varDelta v\) values than are necessary to accomplish the corresponding shift in Jacobi constant values for the associated embedded three-body problems.

In order to reduce the knowledge gap associated with long-duration human exploration of Mars, a manned precursor mission destined for one of the Martian moons is currently considered a feasible option for testing and demonstrating critical technologies within the Martian system. The 2013 Caltech Space Challenge, a student mission design competition held at the California Institute of Technology, addressed the interest in human precursor missions. Two teams of 16 students, with varying backgrounds and nationalities, were allocated five days to design a mission to land at least one human on a Martian moon and return them, along with a sample, safely to Earth with a launch date no later than January 1, 2041. This paper provides an overview of Technology Advancing Phobos Exploration and Return (TAPER-1), the manned Phobos sample return mission devised by Team Explorer. As the first manned mission to the Martian system, TAPER-1 is designed as an opposition class mission to Phobos, carrying four astronauts, with a launch date in April 2033, and a nominal time of flight of 456 days. In addition, this paper demonstrates the feasibility and value of exposing students to the process of rapid mission design.

The ice-covered world Europa—one of the four large Galilean satellites of Jupiter—may be the best place in the solar system to look for currently existing life beyond Earth.

An analysis is presented of gravity assisted flybys in the planar, circular, restricted three-body problem (pcr3bp) that is inspired by the Keplerian map and by the Tisserand- Poincaré graph. The new Flyby map is defined and used to give insight on the flyby dynamics and on the accuracy of the linked-conics model. The first main result of this work is using the Flyby map to extend the functionality of the Tisserand graph to low energies beyond the validity of linked conics. Two families of flybys are identified: Type I (direct) flybys and Type II (retrograde) flybys. The second main result of this work shows that Type I flybys exist at all energies and are more efficient than Type II flybys, when both exist. The third main result of this work is the introduction of a new model, called “Conics, When I Can”, which mixes numerical integration and patched conics formulas, and has applications beyond the scope of this work. The last main result is an example trajectory with multiple flybys at Ganymede, all outside the linked-conics domain of applicability. The trajectory is computed with the pcr3bp, and connects an initial orbit around Jupiter intersecting the Callisto orbit, to an approach transfer to Europa. Although the trajectory presented has similar time of flight and radiation dose of other solutions found in literature, the orbit insertion Δv is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.

The design of fuel-efficient trajectories that visit different moons of a planetary system is best handled by breaking the problem up into multiple three-body problems. This approach, called the patched three-body approach, has received considerable attention in recent years and has proved to lead to substantial fuel savings compared with the traditional patched-conic approach. We consider the problem of designing fuel-efficient multimoon orbiter spacecraft trajectories in the Jupiter–Europa–Ganymede spacecraft system with realistic transfer times. First, fuel- optimal (i.e., near-zero-fuel) trajectories without the use of any control are determined, but turn out to be infeasible due to the very long transfer times involved. We then describe a methodology that exploits the underlying structure of the dynamics of the two three-body problems, that is, the Jupiter–Europa spacecraft and Jupiter–Ganymede spacecraft, using the Hamiltonian structure-preserving Keplerian map approximations derived earlier and small control inputs in the form of instantaneous �Delta-V to get trajectories with times of flight on the order of months rather than several years. A typical trajectory constructed using the control algorithm can complete the mission in about 10% of the time of flight of an uncontrolled trajectory.

Satellite-aided capture is a mission design concept used to reduce the delta-v required to capture into a planetary orbit.
The technique employs close flybys of a massive moon to reduce the energy of the planet-centered orbit. A sequence of close
flybys of two or more of the Galilean moons of Jupiter may further decrease the delta-v cost of Jupiter orbit insertion. A
Ganymede-Io sequence can save 207m/s of delta-v over a single Io flyby. A phase angle analysis based on the Laplace resonance
is used to find triple-satellite-aided capture sequences involving Io, Europa, and Ganymede. Additionally, the near-resonance
of Callisto and Ganymede is used to find triple-satellite-aided capture sequences involving Callisto, Ganymede, and another
moon. A combination of these techniques is used to find quadruple-satellite-aided capture sequences that involve gravity-assists
of all four Galilean moons. These sequences can save a significant amount of delta-v and have the potential to benefit both
NASA’s Jupiter Europa orbiter mission and ESA’s Jupiter Ganymede orbiter mission.
KeywordsAstrodynamics–Mission design–Gravity assist–Laplace resonance–Satellite-aided capture–Jupiter system–Jupiter orbit insertion (JOI)

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.

There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by Europa presents formidable challenges to traditional conic analysis since the regimes of motion involved depend heavily on three-body dynamics. New three-body perspectives are required to design successful and efficient missions which take full advantage of the natural dynamics. Not only does a three-body approach provide low-fuel trajectories, but it also increases the flexibility and versatility of missions. We apply this approach to design a new mission concept wherein a spacecraft "leap-frogs" between moons, orbiting each for a desired duration in a temporary capture orbit. We call this concept the "Petit Grand Tour." For this application, we apply dynamical systems techniques developed in a previous paper to design a Europa capture orbit. We show how it is possible, using a gravitational boost from Ganymede, to go from a jovicentric orbit beyond the orbit of Ganymede to a ballistic capture orbit around Europa. The main new technical result is the employment of dynamical channels in the phase space - tubes in the energy surface which naturally link the vicinity of Ganymede to the vicinity of Europa. The transfer Delta-V necessary to jump from one moon to another is less than half that required by a
standard Hohmann transfer.

While the interest in future missions devoted to Phobos and Deimos increases, missions that explore both moons are expensive in terms of maneuver capabilities partly due to the lack of readily available low-energy transfer options. A design framework that generates transfer trajectories between the Martian moons while leveraging resonant orbits to mitigate this challenge is 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 here. The flyby characteristics of the Deimos resonant orbits are quantified to validate their usefulness to perform observations of the moon. A strategy to select the appropriate resonant orbits is discussed, and the associated transfer costs are analyzed, both for impulsive and low-thrust propulsion capabilities, within the context of the coupled spatial circular restricted three body problem. The trajectory concepts are then validated in a higher-fidelity ephemeris model. Finally, to prove the validity and flexibility of the proposed framework, different mission scenarios are also considered and the corresponding costs are provided.

Designing tours that involve two or more moons and potentially libration point orbits is a challenging problem with many factors playing important roles. The focus of the present investigation is an efficient and general strategy that aids in the design of tour missions that involve transfers between two or more moons located in their true orbital planes by means of impulsive transfers. The strategy incorporates Finite-Time Lyapunov Exponent (FTLE) maps within the context of the moon-to-moon analytical transfer (MMAT) scheme previously proposed by the authors. 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.

The endgame scenario that was explored in this analysis consisted of the part of the trajectory starting at the last Ganymede flyby and ending at the final Europa approach. The basic design components included computing the phasing for the final Ganymede encounter, computing the required intermediate Europa flybys, determining the required maneuvers to transition between the intermediate resonances, and interfacing with a computed portal prior to the final approach. The JPL optimization software, COSMIC, was used in the ephemeris model to optimize solutions computed in the circular restricted three-body problem and compute bounds on the attainable set of solutions by sweeping various design parameters.

The discoveries made by Cassini of geyser-like jets of vapour and organic compounds at the southern polar region of Enceladus have given impulse to a detailed study of this moon. As a result, a number of mission plans for the in-situ robotic exploration of Enceladus have been proposed by scientific communities and leading space agencies. The mission objectives of those plans can only be accomplished with orbits that provide extended observations of the southern polar surface of Enceladus. In a previous contribution, heteroclinic connections between halo orbits around the collinear equilibrium points 𝐿1 and 𝐿2 of the unperturbed Saturn-Enceladus circular restricted three-body problem have been proposed for the purpose. Due to the low altitude of these orbits with respect to the surface of Enceladus and the perturbations of the gravity field of Saturn, the effect of the second zonal harmonics of the two bodies on these low-energy solutions need to be assessed. The present contribution refines the previously computed low-energy trajectories in the J2-perturbed circular restricted three-body problem in which the primaries are Saturn and Enceladus. Halo orbits and their stable and unstable hyperbolic invariant manifolds are obtained in this new framework and used to construct heteroclinic connections in the enhanced dynamical model. Maneuver-free trajectories are obtained and compared with their unperturbed counterparts. Eventually, the performance of these solutions as science orbits is assessed by evaluating their speed, lunar surface coverage, time of flight and height above the lunar surface over the transfers. The results show a good agreement with the solutions obtained with the unperturbed model, suggesting that these trajectories can serve the purpose of observing Enceladus and the unperturbed model is a valid tool for a mission preliminary analysis. Furthermore, the second zonal harmonic term of Saturn is found to have a larger effect than the oblateness of Enceladus.

The icy moons are in the focus of the exploration plans of the leading space agencies because of the indications of water-based life and geological activity observed in a number of these objects. In particular, the presence of geyser-like jets of water near Enceladus’ south pole has turned this moon of Saturn into a priority candidate to search for life and habitability features. This investigation proposes a set of trajectories between Halo orbits about Lagrangian points L1 and L2 in the Saturn-Enceladus Circular Restricted Three-Body Problem as science orbits for a future in situ mission at Enceladus. The design methodology is presented, followed by the analysis of the observational performance of the solutions. The conclusion is that the proposed orbits exhibit suitable features for their use in the scientific exploration of Enceladus, i.e., long transfer times, low altitudes, wide surface visibility windows and long times of overflight.

Phobos and Deimos are the only natural satellites of the terrestrial planets, other than our Moon. Despite decades of revolutionary Mars exploration and plans to send humans to the surface of Mars in the 2030's, there are many strategic knowledge gaps regarding the moons of Mars, specifically regarding the origin and evolution of these bodies. Addressing those knowledge gaps is itself important, while it can also be seen that Phobos and Deimos are positioned to support martian surface operations as a staging point for future human exploration. Here, we present a science exploration architecture that seeks to address the role of Phobos and Deimos in the future exploration of Mars. Phobos and Deimos are potentially valuable destinations, providing a wealth of science return, as well as telecommunications capabilities, resource utilization, radiation protection, transportation and operations infrastructure, and may have an influence on the path of the martian exploration program. A human mission to the moons of Mars would maintain programmatic focus and public support, while serving as a catalyst for a successful human mission to the surface of Mars.

Titan, with its organically rich and dynamic atmosphere and geology, and Enceladus, with its active plume, both harbouring global subsurface oceans, are prime environments in which to investigate the habitability of ocean worlds and the conditions for the emergence of life. We present a space mission concept, the Explorer of Enceladus and Titan (E²T), which is dedicated to investigating the evolution and habitability of these Saturnian satellites. E²T is proposed as a medium-class mission led by ESA in collaboration with NASA in response to ESA's M5 Cosmic Vision Call. E²T proposes a focused payload that would provide in-situ composition investigations and high-resolution imaging during multiple flybys of Enceladus and Titan using a solar-electric powered spacecraft in orbit around Saturn. The E²T mission would provide high-resolution mass spectrometry of the plume currently emanating from Enceladus' south polar terrain and of Titan's changing upper atmosphere. In addition, high-resolution infrared (IR) imaging would detail Titan's geomorphology at 50–100 m resolution and the temperature of the fractures on Enceladus' south polar terrain at meter resolution. These combined measurements of both Titan and Enceladus would enable the E²T mission scenario to achieve two major scientific goals: 1) Study the origin and evolution of volatile-rich ocean worlds; and 2) Explore the habitability and potential for life in ocean worlds. E²T's two high-resolution time-of-flight mass spectrometers would enable resolution of the ambiguities in chemical analysis left by the NASA/ESA/ASI Cassini-Huygens mission regarding the identification of low-mass organic species, detect high-mass organic species for the first time, further constrain trace species such as the noble gases, and clarify the evolution of solid and volatile species. The high-resolution IR camera would reveal the geology of Titan's surface and the energy dissipated by Enceladus' fractured south polar terrain and plume in detail unattainable by the Cassini mission.

The “SPICE” system¹ has been widely used since the days of the Magellan mission to Venus as the method for scientists and engineers to access a variety of space mission geometry such as positions, velocities, directions, orientations, sizes and shapes, and field-of-view projections (Acton, 1996). While originally focused on supporting NASA's planetary missions, the use of SPICE has slowly grown to include most worldwide planetary missions, and it has also been finding application in heliophysics and other space science disciplines. This paper peeks under the covers to see what new capabilities are being developed or planned at SPICE headquarters to better support the future of space science.
The SPICE system is implemented and maintained by NASA's Navigation and Ancillary Information Facility (NAIF) located at the Jet Propulsion Laboratory in Pasadena, California (http://naif.jpl.nasa.gov).

The Earth–Moon libration points are of interest for future missions and have been proposed for both storage of propellant and supplies for lunar missions and as locations to establish space-based facilities for human missions. Thus, further development of an available transport network in the vicinity of the Moon is valuable. In this investigation, a methodology to search for transfers between periodic lunar libration point orbits is developed, and a catalog of these transfers is established, assuming the dynamics associated with the Earth–Moon circular restricted three-body problem. Maneuver-free transfers, i.e. heteroclinic and homoclinic connections, are considered, as well as transfers that require relatively small levels of Δv. Considering the evolution of Earth–Moon transfers as the mass parameter is reduced, a relationship emerges between the available transfers in the Earth–Moon system and maneuver-free transfers that exist within the Hill three-body problem. The correlation between transfers in these systems is examined and offers insight into the existence of solutions within the catalog. To demonstrate the persistence of the catalog transfers in a higher-fidelity model, several solutions are transitioned to a Sun–Earth–Moon ephemeris model with the inclusion of solar radiation pressure and lunar gravity harmonics. The defining characteristics are preserved in the high-fidelity model, validating both the techniques employed for this investigation and the solutions computed within the catalog.

This investigation is focused specifically on transfers from Earth-Moon L-1/L-2 libration point orbits to Mars. Initially, the analysis is based on 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-2 orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L-2 libration point orbits to Sun-Earth L-1/L-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.

The paper presents the trajectory designed by the Italian joint team Politecnico di Torino & Sapienza Università di Roma (Team5), winner of the 6th edition of the Global Trajectory Optimization Competition (GTOC6). In the short time available in these competitions, Team5 resorted to basic knowledge, simple tools and a powerful indirect optimization procedure. The mission concerns a 4-year tour of the Jupiter Galilean moons. The paper explains the strategy that was preliminarily devised and eventually implemented by looking for a viable trajectory. The first phase is a capture that moves the spacecraft from the arrival hyperbola to a low-energy orbit around Jupiter. Six series of flybys follow; in each one the spacecraft orbits Jupiter in resonance with a single moon; criteria to construct efficient chains of resonant flybys are presented. Transfer legs move the spacecraft from resonance with a moon to another one; precise phasing of the relevant moons is required; mission opportunities in a 11-year launch window are found by assuming ballistic trajectories and coplanar circular orbits for the Jovian satellites. The actual trajectory is found by using an indirect technique.

The JUpiter ICy Moons Explorer (JUICE) is an ESA mission that will fly by and observe the icy moons Europa, Ganymede, and Callisto, and finally orbit Ganymede.

Phobos occupies a unique position physically, scientifically, and programmatically on the road to exploration of the solar system. It is a low-gravity object moderately inside the gravity well of Mars. Scientifically, it is both an enigma and an opportunity: an enigma because the origins of both it and Deimos are uncertain, and provide insights into formation of the terrestrial planets; and an opportunity because Phobos may be a waypoint or staging point for future human exploration of the Mars system. Phobos is a low albedo, spectrally bland body with a red-sloped continuum. It appears similar to D-type objects more commonly found in the outer asteroid belt and Jovian space (Rivkin et al., 2002), but occurs in an orbit that is difficult to explain by capture (Burns, 1992). It might have a primitive composition like that inferred for outer solar system objects or it could be related to Mars and, for example, be composed of Martian basin ejecta. Regardless, Phobos has acted as a witness plate to Martian debris over the age of the solar system. The moons may possibly be a source of in situ resources that could support future human exploration in circum-Mars space or on the Martian surface. In situ compositional analyses can address many questions relevant to preparation for future human exploration. Sample return resolves those questions while also enabling detailed analyses in terrestrial laboratories to address higher order questions, many of which have not yet been asked.

The Halo orbits originating in the vicinities of both,L
1 andL
2 grow larger, but shorter in period, as they shift towards the Moon. There is in each case a narrow band of stable orbits roughly half-way to the Moon. Nearer to the Moon, the orbits are fairly well-approximated by an almost rectilinear analysis. TheL
2 family shrinks in size as it approaches the Moon, becoming stable again shortly before penetrating the lunar surface. TheL
1-family becomes longer and thinner as it approaches the Moon, with a second narrow band of stable orbits with perilune, however, below the lunar surface.

In response to the scientific interest in Jupiter's Galilean moons, NASA and ESA have plans to send orbiting missions to Europa and Ganymede, respectively. The inter-moon transfers of the Jovian system offer obvious advantages in terms of scientific return, but are also challenging to design and optimize due in part to the large, often chaotic, sensitivities associated with repeated close encounters of the planetary moons. The approach outlined in this paper confronts this shortcoming by exploiting the multi-body dynamics with a patched three-body model to enable multiple “resonant-hopping” gravity assists. Initial conditions of unstable resonant orbits are pre-computed and provide starting points for the elusive initial guess associated with the highly nonlinear optimization problem. The core of the optimization algorithm relies on a fast and robust multiple-shooting technique to provide better controllability and reduce the sensitivities associated with the close approach trajectories. The complexity of the optimization problem is also reduced with the help of the Tisserand–Poincaré (T–P) graph that provides a simple way to target trajectories in the patched three-body problem. Preliminary numerical results of inter-moon transfers in the Jovian system are presented. For example, using only 59 m/s and 158 days, a spacecraft can transfer between a close resonant orbit of Ganymede and a close resonant orbit of Europa.

Classification scheme for symmetric periodic orbits in restricted three body problem with two dimensions and earth-moon mass ratio

JAXA’s martian moons exploration, MMX

- Fujimoto

Efficient two-body approximations of impulsive transfers between halo orbits

- Fantino

- S Plaut
- S Barabash
- L Bruzzone

S. Plaut, S. Barabash, L. Bruzzone, et al., Jupiter Icy Moons Explorer
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(JUICE): Science Objectives, Mission and Instruments, in: Lunar and
Planetary Science Conference, Vol. 45, 2014, p. 2717.

Kuramoto, the MMX Science Board members, JAXA's Martian Moons eXploration, MMX

- M Fujimoto
- H Miyamoto

M. Fujimoto, H. Miyamoto, K. Kuramoto, the MMX Science Board members, JAXA's Martian Moons eXploration, MMX, in: European Planetary
Science Congress, 2017, pp. EPSC2017-136.

Efficient Two-Body Approxi-642 mations of Impulsive Transfers between Halo Orbits, 69th International Astronautical Congress (IAC)

- E Fantino
- R Flores
- A N Al-Khateeb

E. Fantino, R. Flores, A. N. Al-Khateeb, Efficient Two-Body Approxi-642
mations of Impulsive Transfers between Halo Orbits, 69th International
Astronautical Congress (IAC), Bremen, Germany (2018)IAC-2018-C1.1.7.