Earth-Moon Transfer Research Articles

A Method for Constructing Low-Energy Trajectories for Earth–Moon Transfers

A Method for Constructing Low-Energy Trajectories for Earth–Moon Transfers

Low-energy Earth–Moon transfer autonomous guidance considering high-fidelity orbital dynamics

Low-energy Earth–Moon transfer autonomous guidance considering high-fidelity orbital dynamics

On optimal three-impulse Earth–Moon transfers in a four-body model

Within the emerging age of lunar exploration, optimizing transfer trajectories is a fundamental measure toward achieving more economical and efficient lunar missions. This study addresses the possibility of reducing the fuel cost of two-impulse Earth–Moon transfers in a four-body model with the Earth, the Moon, and the Sun as primaries. Lawden’s primer vector theory is applied within this framework to derive a set of necessary conditions for a fuel-optimal trajectory. These conditions are used to identify which trajectories from an existing database could benefit from the insertion of an additional intermediate impulse. More than 10,000 three-impulse transfers are computed with a direct numerical optimization method. These solutions contribute to enriching the database of impulsive trajectories, useful to perform trade-off analyses. While the majority of trajectories exhibit only marginal improvements, a significant breakthrough emerges for transfers featuring an initial gravity assist at the Moon. Implementing a corrective maneuver after the lunar encounter yields substantial reductions in fuel costs.

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.

Preliminary design of lunar high-resolution remote sensing micro-nano satellite

The development and utilization of lunar resources and the construction of lunar scientific research stations are important parts of China’s future lunar exploration plan. Aiming at the problems of China’s micro-nano satellites with low radiation resistance, lack of autonomous Earth-Moon transfer capability, and limited optical system volume and quality, a preliminary design scheme of a lunar remote sensing micro-nano satellite with autonomous Earth-Moon transfer capability is proposed. Using the analytical orbit average technology and transcription and collocation method to calculate the satellite’s Earth-Moon transfer orbit, the satellite can use the Hall thruster with large specific impulse and low thrust to realize the autonomous Earth-Moon transfer. The passive + active method is used to optimize the radiation resistance of the system, and the total radiation dose of some single machines can reach more than 25krad. A compact high-resolution multispectral camera is designed, and imaging simulation and verification are carried out. In the end, the satellite can achieve high-resolution imaging of the moon with a resolution of 0.2 m at an orbital height of 100 km to achieve the purpose of fine exploration of information such as lunar surface topography and geological structure.

Five-impulse low-energy earth-moon transfer using manifolds

The libration points in the Earth-Moon and Sun-Earth systems are widely regarded as cost-effective gateways into interstellar space. The associated manifold tubes have been utilized by numerous researchers in the development of transfers between distinct systems. In this paper, a five-impulse transfer method, based on the manifold, has been proposed for designing the low-energy transfer trajectory for the Earth-Moon system. The Sun-Earth-Moon-Spacecraft four-body problem is decomposed into two circular restricted three-body problems: Sun-Earth-Spacecraft and Earth-Moon-Spacecraft. Moreover, a time parameter is employed to describe the positional relationship between the Sun-Earth and Earth-Moon systems, thereby facilitating their conversion. A phase angle is utilized to characterize the position of the Poincare section, and multiple orbital elements, such as orbital altitude and inclination, are considered in the constraints. To solve the design of multi-constrained transfer trajectories, sequential differential correction algorithms are proposed. The results demonstrate that this method can be used to create compliant low-energy transfer trajectories for various combinations of time parameters and phase angles. Additionally, excellent velocity increments and time-of-flight metrics can be found within a single Sun-Earth-Moon conjunction cycle. In parallel, the method is validated by reconstructing transfer trajectories in a bicircular restricted four-body problem model (BCR4BP) of the Sun-Earth/Moon system.

Energy analysis of the single impulsive Earth–Moon transfer with the temporary lunar capture

The single impulsive planar Earth–Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun–Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth–Moon transfers.

A Sun–Earth Stable Manifold-Based Method for Planar Two-Impulse Earth–Moon Transfer Design

A Sun–Earth Stable Manifold-Based Method for Planar Two-Impulse Earth–Moon Transfer Design

Debris Collision Risk Analysis Following Simulated Cislunar Spacecraft Explosions

This research simulates spacecraft explosions in cislunar space and analyzes the resulting risk to other notional spacecraft. Three case studies are considered, which include simulations of spacecraft explosions during Earth–moon Hohmann transfers, along the manifold of the Earth–moon Lagrange point, and at the stable and Earth–moon Lagrange points. Debris from the explosions is propagated using a four-body dynamical model that incorporates the gravitational forces of the Earth, moon, and sun. Finally, the risk to nearby cislunar spacecraft is quantified using two different models for the vulnerability of spacecraft to debris, which include a logistic vulnerability model that incorporates only debris particle mass and a ballistic limit vulnerability model that incorporates both particle mass and velocity. The results from each model are compared to evaluate their application to cislunar debris scenarios. The results of this study showed potential debris hazards to spacecraft near Earth from a mishap during an Earth–moon transfer and hazard probabilities to nearby cislunar spacecraft on the order of from Lagrange point mishaps. Overall, research into cislunar debris propagation enhances operational planning outside the traditional near-Earth paradigm of spacecraft mission operations and increases understanding of the debris-related consequences of mishaps within this orbital regime.

Overview of Earth-Moon Transfer Trajectory Modeling and Design

The Moon is the only celestial body that human beings have visited. The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions. In the 21st century, new lunar missions including the construction of the lunar space station, the permanent lunar base, and the Earth-Moon transportation network have been proposed, requiring low-cost, expansive launch windows and a fixed arrival epoch for any launch date within the launch window. The low-energy and low-thrust transfers are promising strategies to satisfy the demands. This review provides a detailed landscape of Earth-Moon transfer trajectory design processes, from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods. Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp the basic overview of the current Earth-Moon transfer orbit design methods and a deep academic background is unnecessary for the context understanding.

Phasing with near rectilinear Halo orbits: Design and comparison

In the next future, space agencies are planning to return to the Moon. The objective is to assemble an orbiting space station, called Gateway, on a Near Rectilinear Halo Orbit around the Moon as a base for future Moon and deep space missions. Within this framework, multiple side missions will be planned to sustain the Gateway (Artemis mission). The proposed work is thought in framework of the preliminary design of future cargo missions, in particular on the design of an efficient phasing trajectory, under the Circular Restricted Three body problem hypotheses, to bring a cargo vehicle from the end of the Earth-Moon transfer to the beginning of the proximity operations such as rendezvous and docking with the space station. The work aims covering the lack of literature in phasing trajectories with the NRHO by proposing three different strategies to connect the Earth-Moon transfer trajectory with the proximity operations. The three strategies are classified based on the choice of the parking orbits or the choice of the manifolds. Two strategies use butterfly and Halo orbits to park the vehicle before transferring to the target orbit. The third strategy, instead, uses manifolds to allow a direct phasing. In the paper, the three innovative strategies are designed and compare in a specific scenario.

Bayesian Optimization of crewed lunar free return abort trajectory

Maneuvering to a free return trajectory is a vital abort means for crewed lunar missions. A novel method of solving the fuel optimization of free return abort trajectory for Earth-Moon transfer by two-stage transformation on optimization model and Bayesian optimization is documented. Two new design variables—perilune altitude and transfer time from earth to perilune, instead of the original injection velocity vector, are introduced to transform the general model into a two-dimensional model. Each feasible abort trajectory is determined by a numerical method including initial estimate and exact solution. Then the characteristics of the relationship between the new variables and the fuel objective of impulse maneuver are applied to further transform the model into a one-dimensional model. Based on the Bayesian optimization method, fuel optimization is successfully and efficiently implemented for the free return abort trajectory at multiple abort moments during the Earth-Moon transfer. Furthermore, the influence of the initial Earth-Moon phase on the result of fuel optimization is presented. Numerical simulations are conducted to demonstrate the efficacy of the proposed method.

Energy analysis and optimizations of two-impulse Earth-Moon transfers in the Sun-Earth-Moon system

This paper investigates the energy change of the two-impulse Earth-Moon trajectory in the Sun-Earth-Moon bicircular model analytically. An analytic expression is first derived to describe the change of the Jacobi value of the two-impulse Earth-Moon trajectory in the Sun-Earth-Moon system. Then the analytical results of the total cost of the Earth-Moon transfer can be obtained by solving the equations related to the change in the Jacobi value of the transfer trajectory. Numerical results show that the analytic expressions can provide good descriptions of the energy changes of the two-impulse Earth-Moon transfer. Moreover, it indicates that the total cost mainly depends on a critical angle, termed the perilune angle. Accordingly, we explore the correlation of the total cost and the perilune angle. Finally, optimizations of two-impulse Earth-Moon transfers are further carried out.

Global Sensitivity Analysis of Earth-Moon Transfer Orbit Parameters Based on Sobol Method

In the process of Earth-Moon transfer orbit, many parameters are involved and the degree of influence varies among the parameters. How to accurately distinguish the influence relationship between different parameters is of great significance to engineering missions. Based on Sobol sequence sampling method and Sobol global sensitivity analysis method, a calculation process of global sensitivity analysis is proposed in this paper for high-fidelity Earth-Moon transfer orbit. A numerical simulation method is used to verify that the Sobol sequence sampling method has better convergence and higher precision than other sampling methods and has better adaptability in global sensitivity analysis. The effects of different state parameters and the combination of different parameters on the perilune parameters of Earth-Moon transfer orbit are given by simulation examples, which verifies the effectiveness and feasibility of the calculation process proposed in this paper. Simulation results show that the radial position and tangential velocity at the trans-lunar injection point are the main sensitivity parameters, and the other parameters have little effect on the results. The sensitivity of the orbital elements at the trans-lunar injection point to the perilune parameters is different and needs to be determined according to the specific parameters. The results of this study can provide important reference for future Earth-Moon transfer orbit design and related engineering missions.

Design and Analysis of Direct Abort Orbits in the Earth-Moon Transfer Phase of Crewed Lunar Exploration Missions

A direct abort orbit design method is presented for direct abort missions in the Earth-Moon transfer phase of crewed lunar exploration missions. First, according to the demand of an emergency rescue in the Earth-Moon transfer phase, two direct abort orbit schemes are introduced. Then, a serial orbit design method is proposed for a high-fidelity direct abort orbit. An analytical model is established for the calculation of initial values, and the optimization design is performed in the high-fidelity orbit model to determine a single-impulse abort orbit. A hybrid optimization design process is proposed to generate a two-impulse abort orbit. The results of simulation examples verify the validity and feasibility of the proposed direct abort orbit design method. Finally, extensive simulations are carried out to analyze the characteristics of abort impulse and abort return time and reveal the general rules of direct abort orbits. The research conclusions can provide a reference for the design of emergency rescue schemes in future crewed lunar exploration missions.

A Study of the Orbit Determination Ability and Time-Sharing Acquisition Mode for China’s Deep Space Network VLBI Data

According to the interferometric observation data of Jiamusi deep space station and Kashi deep space station of China deep space network during the mission of Chang'E-4 prober, the orbit determination accuracy of real-time data and post-correction data respectively combined with the USB data is analyzed. The difference between the Earth Moon transfer section and the precise orbit is 100 meters, and the difference between the ring moon section and the precise ephemeris is 10 meters. At the same time, the influences of VLBI data weight setting on the orbit accuracy is analyzed. In view of theChina deep space network in subsequent deep space missions such as Chang’E 5, a time-sharing acquisition mode is proposed to reduce the amount of VLBI data. The influence of this mode on orbit accuracy is analyzed by using the measured VLBI data of Chang’E 4 prober. The results show that the real-time data accuracy of China’s deep space network VLBI data has reached the accuracy of post-correction data, which can support the follow-up deep space exploration tasks in China. At the same time, for 2 to 3 hours per day of common viewing time of two stations, in the time-sharing acquisition mode, the total 20 minutes per day data and 1 minute acquisition step can ensure that the orbit accuracy does not decrease.

Orbit determination, positioning strategy design, and accuracy evaluation of Chang’e-5

The Chang’e-5 spacecraft has some new characteristics, such as direct entry into the Earth-Moon transfer orbit, lunar surface sampling, rendezvous and docking, high-speed re-entry and return, and after completing the main mission, the orbiter being able to fly to the first Lagrangian libration point of the Sun-Earth orbit. This paper evaluates the orbit determination and prediction accuracy and lunar surface-positioning accuracy of the mission key nodes. Results showed that the position error of the orbit determination prediction 6 h before midway correction and 6 h before lunar capture is 100 m. During rendezvous and docking, the position error is ~700 m from the forecast to the handover point after the fourth remote guidance and control. This is caused by the accumulation of the ascent’s orbit and control error. Using 12-h data can effectively meet the task requirements. Besides, for the Chang’e-5 expansion mission, the overlapping arc analysis method is used, and the position error is ~500 m.

Optimization of bi-impulsive Earth-Moon transfers using periodic orbits

Low-energy bi-impulsive Earth-Moon transfers are investigated by using periodic orbits. Two Earth-Moon transfer design strategies in the CR3BP are proposed, termed direct and indirect design strategy. In the direct design strategy, periodic orbits which approach both vicinities of the Earth and Moon are selected as candidate periodic orbits, which can provide an initial guess of bi-impulsive Earth-Moon transfers. In the indirect design strategy, new bi-impulsive Earth-Moon transfers can be designed by patching together a bi-impulsive Earth-Moon transfer and a candidate periodic orbit which can approach the vicinity of the Moon. Optimizations in the CR3BP are undertaken based on the Gradient Descent method. Finally, bi-impulsive Earth-Moon transfer design and optimizations in the Sun-Earth-Moon bi-circular model (BCM) are carried out, using bi-impulsive Earth-Moon transfers in the CR3BP as initial guesses. Results show that the bi-impulsive Earth-Moon transfer in the CR3BP can serve as a good approximation for the BCM. Moreover, numerical results indicate that the optimal transfers in the BCM have the potential to be of lower cost in terms of velocity impulse than optimal transfers in the CR3BP.

A Sun-Earth Stable Manifold-Based Method for Two-Impulse Earth-Moon Transfer Design

A Sun-Earth Stable Manifold-Based Method for Two-Impulse Earth-Moon Transfer Design

Optimal Earth-Moon Transfer Trajectory Design via Differential Dynamic Programming with Input Saturation Constraints

Optimal Earth-Moon Transfer Trajectory Design via Differential Dynamic Programming with Input Saturation Constraints