Bicircular Four-body Problem Research Articles

Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem

As evidenced by the Global Exploration Roadmap, international interest exists in a new era of human exploration of the solar system. Such an effort is commencing with the examination of options for maintaining a facility—at times crewed—in an orbit nearby the Moon. Thus, the key objectives in advancing colonization of interplanetary space include positioning and maintaining an inhabited facility in a long-term and relatively stable orbit in the lunar vicinity. At this time, one orbit of interest for a habitat spacecraft is a Near Rectilinear Halo Orbit (NRHO). Near rectilinear halo orbits near the Moon are members of the L1 or L2 halo orbit families and are characterized by favorable stability properties. As such, they are strong candidates for a future habitat facility in cislunar space. This type of trajectory is identified in cislunar space in terms of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP). However, for arrival to and departure from the Earth-Moon region, the impact of the solar gravity generally cannot be ignored. Thus, the orbital characteristics and stability properties are examined within the context of the bicircular restricted four-body problem.

Numerical investigation of transport mechanism in four-body problem using Lagrangian coherent structure

Transport mechanism is critical for understanding natural phenomena in the solar system and is beneficial to space mission design. In this study, transport mechanism in the bicircular four-body problem is numerically explored by using Lagrangian coherent structure (LCS), a tool widely used for identifying transport barriers in fluid flow. First, equations of motion of the bicircular problem are derived and five topology configurations of forbidden region are presented. Then, definition and computational method of LCS are introduced. Finally, properties of LCS which are useful for revealing transport mechanism in the four-body problem are numerically investigated.

Low-energy lunar transfers using spatial transit orbits

This paper is concerned with natural and artificial low-energy lunar transfers in three-dimensional space. The main contribution of this paper is that the limitations of the planar manifold assumption, which is adopted in previous low-energy orbit design methods, are avoided by describing the transfer orbits with more realistic spatial transit and non-transit orbits. To start, the limitations of the previous design methods for the low-energy trajectories are highlighted, and the boundaries of the spatial transit orbits, which can enter into or escape from the potential well near the Moon through the L1 or L2 bottleneck regions of the zero velocity surface, are defined on a Poincaré section by using the necessary and sufficient condition of transition. Next, by considering the dominant gravity bodies in different orbit segments the motion near the Moon is analyzed in the Earth–Moon circular restricted three-body problem (CR3BP). For natural celestial bodies, the statistical characteristics of the lunar collision trajectories are studied. For the artificial celestial bodies, the investigation is focused on the achievable range of inclination and height of the low lunar orbit (LLO). Then, the motion between the Earth and the Moon is studied in the Earth–Moon based Sun-perturbed bicircular four-body problem (B4BP). For natural and artificial celestial bodies, the Earth-origin trajectories and the trajectories from the low Earth orbits are analyzed. Compared to the current planar manifold based design methods, the technique introduced in this paper can evaluate the lunar transfer orbits more accurately. Also, some lunar transfer trajectories which do not exist in the manifold based models can be found, and the heights and inclinations of the parking orbits around the Earth and the Moon can also be analyzed.

Libration point orbits for lunar global positioning systems

With the development of lunar exploration, a lunar global positioning system (LGPS) is demanded for both on-ground and in-flight lunar exploration missions. The traditional configuration of constellation requires at least eighteen satellites to cover the whole lunar surface continuously. In this paper, the configurations of the libration point orbits (LPOs) constellations are investigated. By using the constellations on the Earth–Moon L1 and L2 LPOs, the basic functions of the LGPS can be realized by using eight to fourteen satellites. First, the LPO and the combinations of LPOs, which can be used in the constellations of the LGPS, are investigated. The criteria and procedures of the configuration design are introduced. Second, the configurations of LPOs constellations are investigated in the Earth–Moon circular-restricted three-body problem (CR3BP). The size of the LPOs and the distribution of the satellites on these LPOs are determined by using an exhaustive algorithm and a global optimization method, respectively. The key performance parameters of these constellations are computed. Third, the constellations with good performance in the CR3BP are redesigned in the more accurate Earth–Moon based Sun-perturbed bicircular four-body problem (B4BP). Moreover, in order to avoid the ground coverage problem caused by the perturbation of the Sun, some modifications are implemented, and the configuration of the no blind area LGPS in the B4BP is obtained.

Real-time control of optimal low-thrust transfer to the Sun–Earth L1 halo orbit in the bicircular four-body problem

In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun–Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L 1 is the destination of the mission which is one of the equilibrium points in the Sun–Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.

Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario

This work deals with the design of transfers connecting LEOs with halo orbits around libration points of the Earth–Moon CRTBP using impulsive maneuvers. Exploiting the coupled circular restricted three-body problem approximation, suitable first guess trajectories are derived detecting intersections between stable manifolds related to halo orbits of EM spatial CRTBP and Earth-escaping trajectories integrated in planar Sun–Earth CRTBP. The accuracy of the intersections in configuration space and the discontinuities in terms of Δ v are controlled through the box covering structure implemented in the software GAIO. Finally first guess solutions are optimized in the bicircular four-body problem and single-impulse and two-impulse transfers are presented.

Numerical study of the time required for the gravitational capture in the bi-circular four-body problem

A gravitational capture occurs when a spacecraft (or any particle with negligible mass) changes from a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third and the fourth bodies involved in the dynamics. In this way, those forces are used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon to minimize fuel consumption. The concept of gravitational capture is used, together with the basic ideas of the gravity-assisted maneuver and the bi-elliptic transfer orbit, to generate a trajectory that requires fuel consumption smaller than the one required by the Hohmann transfer. The objective of the present paper is to study the time required for the ballistic gravitational capture in a dynamical model that has the presence of four bodies. In particular, the Earth–Moon–Sun–Spacecraft system is considered.