Geometry of Weak Stability Boundaries

The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has been investigated in a number of studies, where partial results have been obtained. We propose a generalization of the weak stability boundary. We prove analytically that, in the context of the planar circular restricted three-body problem, under certain conditions on the mass ratio of the primaries and on the energy, the weak stability boundary about the heavier primary coincides with a branch of the global stable manifold of the Lyapunov orbit about one of the Lagrange points

Qualitative study of ballistic capture at Mars via Lagrangian descriptors

Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work investigates to what extent Lagrangian descriptors provide information about non-Keplerian motion in Mars proximity, which is modeled under the planar elliptic restricted three-body problem. We propose a novel technique to reveal ballistic capture orbits extracting separatrices of the phase space highlighted by Lagrangian descriptor scalar fields. The Roberts' operator to approximate the gradient is used to detect the edges in the fields. Results demonstrate the chaos indicator ability to distinguish sets of initial conditions exhibiting different dynamics, including ballistic capture ones. Separatrices are validated against reference weak stability boundary derived on similar integration intervals. Compared to other techniques, Lagrangian descriptors provide dynamics insight bypassing the propagation of the variational equations.Comment: Post-print submitted to "Communications in Nonlinear Science and Numerical Simulation". EXTREMA - Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy, European Research Council (ERC), European Union (EU), Horizon 2020. The content of this document reflects only the author's view. ERC is not responsible for any use that may be made of the information it contain

Contingency Trajectory Design for a Lunar Orbit Insertion Maneuver Failure by the LADEE Spacecraft

A contingency trajectory analysis was performed for NASA Ames Research Centers (ARCs) Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft in case of a missed lunar orbit insertion (LOI) maneuver. Recovery trajectory options are shown to exist for all LADEE launch opportunities throughout a one year period. Recovery V costs primarily depended on the spacecrafts apogee location on or near the Sun-Earth weak stability boundary (WSB) and the time needed by the spacecraft to recover (e.g. to wake up from safe mode) to perform an escape prevention maneuver after the missed LOI

Transfer and rendez-vous strategies for the deployment and the servicing of an inhabited space station at Earth-Moon L2

The next step for human exploration in the solar system could be the deployment of an inhabited station at Earth-Moon Libration points (EML), as a gateway for further destinations such as the Moon (lunar surface settlement), Mars or asteroids, according to International Space Exploration Coordination Group (ISECG) roadmap [1] and several recent publications [5]. In this context, this paper examines how to design a low cost mission, using the natural dynamics for Station integration, crew rotations, cargo delivery and disposal. Preliminary studies lead us to select a Halo orbit around EML2 to locate the space station. Then, the entire trajectory, from the selection of the departure Low Earth Obit to the rendez-vous strategy in EML2, was analyzed with several possible transfer types (direct, indirect, lunar flyby or weak stability boundary). Actually, optimization criteria strongly depend on the mission phase. For instance, when crew transit is considered, mission duration has to be minimized, while in the case of cargo transportation, we rather seek to optimize the global delta-v. This paper presents the results (in term of duration and cost) obtained for the two strategies we selected: lunar flybys for the crew and weak stability boundaries trajectories for cargo. We carefully considered the constraints for rendez-vous in EML2 and evaluated their impact on the performances. Moreover, we assessed the impacts of the model selection (ephemeris, four bodies versus restricted circular three bodies problem...). The main contribution of this project lies in the global optimization of the entire mission from LEO to EML2 and return with regards to two criteria (mission duration and delta-v), with a focus on the rendez-vous feasibility in EML2

Earth--Mars Transfers with Ballistic Capture

We construct a new type of transfer from the Earth to Mars, which ends in ballistic capture. This results in a substantial savings in capture $\Delta v$ from that of a classical Hohmann transfer under certain conditions. This is accomplished by first becoming captured at Mars, very distant from the planet, and then from there, following a ballistic capture transfer to a desired altitude within a ballistic capture set. This is achieved by manipulating the stable sets, or sets of initial conditions whose orbits satisfy a simple definition of stability. This transfer type may be of interest for Mars missions because of lower capture $\Delta v$, moderate flight time, and flexibility of launch period from the Earth

Low-energy Earth–Moon transfers via Theory of Functional Connections and homotopy

Numerous missions leverage the weak stability boundary in the Earth–Moon–Sun system to achieve a safe and cost-effective access to the lunar environment. These transfers are envisaged to play a significant role in upcoming missions. This paper proposes a novel method to design low-energy transfers by combining the recent Theory of Functional Connections with a homotopic continuation approach. Planar patched transfer legs within the Earth–Moon and Sun–Earth systems are continued into higher-fidelity models. Eventually, the full Earth–Moon transfer is adjusted to conform to the dynamics of the planar Earth–Moon Sun-perturbed, bi-circular restricted four-body problem. The novelty lies in the avoidance of any propagation during the continuation process and final convergence. This formulation is beneficial when an extensive grid search is performed, automatically generating over 2000 low-energy transfers. Subsequently, these are optimized through a standard direct transcription and multiple shooting algorithm. This work illustrates that two-impulse low-energy transfers modeled in chaotic dynamic environments can be effectively formulated in Theory of Functional Connections, hence simplifying their overall design process. Moreover, its synergy with a homotopic continuation approach is demonstrated

Strategies to engineer the capture of a member of a binary asteroid pair using the planar parabolic restricted three-body problem

This paper investigates two strategies to engineer the capture of one member of a binary asteroid pair by a planetary body after close encounter with that planetary body. It is assumed that the binary pair consists of a smaller minor asteroid in orbit about a larger main asteroid, which encounters a planetary body. In order to develop an engineering model of the problem, first we neglect the mass of the smaller minor asteroid in the binary pair and approximate the model as planar parabolic restricted three-body problem (PPRTBP). Second, the related regularised dynamical equations for the problem are developed. An approximate analytical solution to the problem is then obtained for motion in the vicinity of the main asteroid using the regularised coordinates through a linearized model. This provides insight into the motion of the minor asteroid about the main asteroid, allowing strategies to engineer the capture process to be developed. Based on the topology of the zero velocity curves (ZVCs) for the PPRTBP, we determine the capture region for the problem by developing initial condition maps (ICMs) and investigate the details of the dynamical process for capture. Two capture strategies are then proposed to engineer and extend the possibility for capture of the minor asteroid in binary pair. One is a re-phasing manoeuvre before encounter, which guarantees that the particle is within the capture region of the ICMs. The other is an optimal, single-impulse transfer during encounter to ensure transfer through the ZVC bottleneck and capture of the minor asteroid by the planetary body. The purpose of the paper is to explore such engineering strategies, rather than to provide new insights into natural capture dynamics

Hayabusa2's Superior Solar Conjunction Phase Trajectory Design, Guidance and Navigation

Hayabusa2 is the ongoing JAXA’s sample and return mission to the asteroid Ryugu. In late 2018, Ryugu was in superior solar conjunction with the Earth. It is the first time that a spacecraft experiences the blackouts in the communication link with the Earth while hovering around a small celestial body. In this article, the design of the nominal conjunction trajectory flown by the Hayabusa2’s spacecraft is presented. The requirements for the conjunction trajectory were (1) to guarantee a low fuel consumption, (2) to ensure the visibility of the asteroid by the spacecraft’s wide angle camera (60∘ FoV), and (3) to increase the spacecraft altitude to a safety location (∼109 km) from the nominal BOX-A operation of 20 km (Home Position - HP). Finally, (4) to return at BOX-A after the conjunction phase. Given the mission constraints, the designed conjunction trajectory appears to have a fish-shape in the Hill coordinates therefore we renamed it as “ayu” (sweetfish in Japanese) trajectory. The optNEAR tool was developed for the guidance (ΔVs planning) and navigation design of the Hayabusa2’s conjunction mission phase. A preliminary sensitivity analysis in the Hill reference frame proved that the ayu trajectory is a good candidate for the conjunction operation of hovering satellite. The solution in the Hill coordinates is refined in the full-body planetary dynamics (optNEAR Tool) before flight. The ayu conjunction trajectory requires (a) two deterministic ΔVs at the Conjunction Orbit Insertion (COI) point and at the Home-position Recovery Maneuver (HRM) point respectively. (b) Two stochastic ΔVs, known as Trajectory Correction Manoeuvres (TCMs), before and after the deep conjunction phase are also required. The constraint linear covariance analysis in the full-body dynamics is here derived and used for the preliminary guidance and navigation planning. The results of the covariance analysis were validated in a nonlinear sense with a Monte Carlo approach which proved the validity of the semi-analytic method for the stochastic ΔVs planning derived in this paper

Energy-saving capture at Mars via backward stable orbits

The orbit capture, which transfers the spacecraft from the interplanetary trajectory to the target orbit about a celestial body, is a key event in an exploration mission. A low-energy capture strategy, termed ballistic capture, has been developed and applied to lunar transfer, such as Hiten [1] and GRAIL [2]. Such capture exploits the gravitational force of the multi-body system to change the orbit energy of the spacecraft with respect to the target planet from positive to negative