Near Rectilinear Halo Orbit Research Articles

A note on the computation of multi-revolution NRHO under the ephemeris model

Near Rectilinear Halo Orbits (NRHOs) are vital to manned lunar and deep space exploration, which nowadays are of great interest for different space agencies and in particular with regard to the future space station. However, the required computation of multi-revolution NRHO under the ephemeris model is difficult, especially for the NRHOs with low periapsis relative to the secondary body. This paper explores this issue from the perspective of multiple shooting, first analyzing the influence of the state transition matrices by means of their condition number and then, focusing on a good selection of trajectory segments with suitable patch points. The methodology considerably improves the convergence and the computation under the ephemeris model. Numerical simulations show that at least 30 revolutions can be achieved for NRHOs with perilune radius of less than 12,000 km around L1 or period less than 8.8 days around L2; meanwhile, the number of segments used can be as low as 2 for each single revolution. As for the position of patch points, the first and last points of each revolution should be apart from the Moon, and the distance can be reduced only when the number of segments increases. The proposed method requires no dedicated optimization algorithm or commercial software to produce the multi-revolution NRHOs.

Autonomous Lunar rendezvous trajectory planning and control using nonlinear MPC and Pontryagin’s principle

This paper explores the application of Nonlinear Model Predictive Control (NMPC) techniques, based on the Pontryagin Minimum Principle, for a minimum-propellant autonomous rendezvous maneuver in non-Keplerian Lunar orbits. The relative motion between the chaser and the target is described by the nonlinear dynamics of the circular restricted three body-problem, posing unique challenges due to the complex and unstable dynamics of near-rectilinear halo orbits. Key aspects of the proposed NMPC include trajectory optimization, maneuver planning, and real-time control, leveraging on its ability to satisfy complex mission requirements while ensuring safe and efficient spacecraft operations and in the presence of input and nonlinear/non-convex state constraints. The proposed formulation allows the design of a minimum-propellant controller, whose optimal control signal results to be bang–bang in time. A case study based on the Artemis III mission – where the docking of the Orion spacecraft to the Gateway station is planned – is illustrated in order to demonstrate the efficiency of the proposed approach, showcasing its potential for enhancing target tracking accuracy, while reducing propellant consumption.

Extended perilune rendezvous method for low Delta-V transition to NRHO for cargo transportation mission to gateway

The construction of Gateway in lunar orbit is planned as a post-ISS mission by NASA, and JAXA is considering a cargo supply mission to provide service. The Near-Rectilinear Halo Orbit (NRHO) is a candidate for a Gateway orbit, and several methods for the transfer trajectory are being researched. The In-Direct Transfer (IDT) has a short transition period of seven days, but the ΔV application is inefficient. The Weak Stability Boundary (WSB) transfer maintains a small ΔV, but the transition takes over 100 days. However, a trajectory intermediate between IDT and WSB has not yet been actively studied. This paper proposes the Extended Perilune Rendezvous Method (EPRM) of intermediate transfer to NRHO. This method reduces ΔV by orbiting in an elliptical lunar orbit for over two weeks. EPRM has several transition methods corresponding to ΔV and transition periods. This paper systematically reveals the transition mechanisms. Moreover, an effective TCM, considering several error types, is presented for an actual mission. Finally, the rendezvous accuracy with Gateway is discussed.

Cislunar [formula omitted] and [formula omitted] axial orbits and their applications

Cislunar L4 or L5 axial orbit families are continuous asymmetrical periodic orbits from the figure-8 orbit around L4 or L5 Lagrange point of the Earth–Moon system to the halo-family around the Moon. They provide special locations of lunar relay satellites for the lunar south pole due to their offset locations. In this paper, we investigate the orbital characters and applications of cislunar L4 and L5 axial orbits. A construction method of cislunar L4 and L5 axial orbit families is proposed according to their topological feature in the torus space. Then, lunar relay performances, including coverage and eclipse, are analyzed for different cislunar L4 and L5 axial orbits. Numerical computation indicates that 3:1 resonant L4 and L5 axial orbits are the optimal options in terms of the stability, coverage and eclipse avoidance. Lunar relay performances of a two-satellite constellation deployed in these orbits are compared with that in a near rectilinear halo orbit (NRHO). Numerical results show that the constellation of axial orbits can provide longer contact duration to the lunar equator and southern hemisphere than that of the NRHO. Finally, a station-keeping strategy and a transfer design of cislunar L4 and L5 axial orbits are developed, and their fuel costs are studied.

Optimization, guidance, and control of low-thrust transfers from the Lunar Gateway to low lunar orbit

The Lunar Gateway will represent a primary space system useful for the Artemis program, Earth–Moon transportation, and deep space exploration. It is expected to serve as a staging location and logistic outpost on the way to the lunar surface. This study focuses on low-thrust transfer dynamics, from the Near-Rectilinear Halo Orbit traveled by Gateway to a specified Low-altitude Lunar Orbit (LLO). More specifically, this research addresses two closely-related problems: (i) determination of the minimum-time low-thrust trajectory and (ii) design, implementation, and testing of a guidance and control architecture, for a space vehicle that travels from Gateway to LLO. Orbit dynamics is described in terms of modified equinoctial elements, with the inclusion of all the relevant perturbations, in the context of a high-fidelity multibody ephemeris model. The minimum-time trajectory from Gateway to a specified lunar orbit is detected through an indirect heuristic approach, which uses the analytical conditions arising in optimal control theory in conjunction with a heuristic technique. However, future missions will pursue a growing level of autonomy, and this circumstance implies the mandatory design and implementation of an efficient feedback guidance scheme, capable of compensating for nonnominal flight conditions. This research proposes nonlinear orbit control as a viable and effective option for autonomous explicit guidance of low-thrust transfers from Gateway to LLO. This approach allows defining a feedback law that enjoys quasi-global stability properties without requiring any offline reference trajectory. The overall spacecraft dynamics is modeled and simulated, including attitude control and actuation. The latter is demanded to an array of reaction wheels, arranged in a pyramidal configuration. Guidance, attitude control, and actuation are implemented in an iterative scheme. Monte Carlo simulations demonstrate that the guidance and control architecture at hand is effective in nonnominal flight conditions, i.e. with random starting point from Gateway as well as in case of temporary unavailability of the propulsion system. The numerical results also point out that only a modest propellant penalty is associated with the use of feedback guidance and control in comparison to the minimum-time optimal trajectory.

The Moon as an effective propellant source: A comprehensive exergy analysis from extraction to depot

Establishing a permanent lunar base has gained increasing attention since it offers opportunities for international cooperation and the commercialization of space, forming the foundation and testing ground for a human existence independent from Earth. Essential to future missions beyond cislunar space is the exploration and in situ processing of the Moon's resources, especially the sustainable production of energetic resources and propellants. Utilizing in situ generated propellants can dramatically reduce transportation costs by removing the need to source propellants from Earth. Resources on the Moon are limited, and the extraction of available resources are energy-intensive processes demanding advanced techniques and technologies. Consequently, one of the biggest challenges lies in developing process architectures with a positive energy balance, for which comprehensive analyses are still missing. The focus currently lies on the extraction of water ice from lunar regolith and the production of hydrogen and oxygen through water electrolysis. However, alternative fuel and process options may reduce the energy cost while providing equivalent energetic revenue. In the scope of this research, the infrastructure and technologies required for extraction, refining, and storing are assumed to exist in cislunar space; therefore, only the operating cost is considered. Exergy analyses of in situ extraction methods are conducted to investigate whether the required energetic budget allows sustainable implementation. The analysis includes extraction methods and propellant options to reveal the extent to which alternatives to hydrogen are feasible. Exergy analyses determine thermodynamic losses of energy flows giving the ground for process optimization. The exergy destructed represents the margin of improvement within the process architecture and thus reflects the process's thermodynamic and economic value while allowing a more distinct examination of energy use. Assuming the availability of water and carbon dioxide ice in permanently shadowed regions, the analysis shows that choosing methane instead of hydrogen in combination with oxygen as propellants can reduce the required exergy input by up to a third. An example mission allows to directly compare the operating cost of the extraction processes for the different propellant options. The mission entails a spacecraft propelled by a liquid bipropellant engine utilizing the extracted propellant and transporting a payload of the same propellant to a depot located in lunar near-rectilinear halo orbit (NRHO). Although abundant in space, the results suggest that hydrogen may not be the only or even energetically cost-effective resource for developing cislunar and Martian space infrastructures. Likewise, sustainable extraction of propellants suitable for current and future propulsion systems will foster humanity's reach further into the solar system.

Solar Absorptivity Degradation of Spacecraft Materials Due to UV and Charged Particles in the Gateway Environment

Gateway will be an outpost in cislunar space designed to survive a 15-year mission to support human Moon landings and future deep space exploration. The Gateway Passive Thermal Control System (PTCS) Group has identified charged particle and UV degradation of potential Gateway materials as a knowledge gap for the Near Rectilinear Halo Orbit (NRHO) and transit environment, especially the slow spiral transit planned for the first two modules. Solar absorptivity degradation is important to quantify because the end-of-life absorptivity impacts thermal performance of the system. To address this, ground testing has been completed at NASA Goddard Space Flight Center in which potential Gateway materials, including radiators, multi-layer insulation (MLI), and structural materials are subjected to the expected transit plus 15-year on-orbit charged particle fluence (9.86x1015 protons/cm2 at 2.5 keV and 3.1x1016 electrons/cm2 at 10 keV) and 5093 Equivalent Solar Hours (ESH). Reflectivity of a single sample of each material was measured in atmosphere and in vacuum inside the chamber after exposure to incremental levels of ESH and charged particle fluence. Increase in absorptivity of most samples were seen throughout the test including large differences in absorptivity of materials of the same category. Future planned testing will validate these results and include additional materials of interest.

Rendezvous in cislunar halo orbits: Hardware-in-the-loop simulation with coupled orbit and attitude dynamics

Space missions to Near Rectilinear Halo Orbits (NRHOs) in the Earth–Moon system are upcoming. A rendezvous technique in cislunar space is proposed in this investigation, one that leverages coupled orbit and attitude dynamics in the Circular Restricted Three-body Problem (CR3BP). An autonomous Guidance, Navigation and Control (GNC) technique is demonstrated in which a chaser spacecraft approaches a target spacecraft in a sample southern 9:2 synodic-resonant L2 NRHO, one that currently serves as the baseline for NASA’s Gateway. A two-layer guidance and control approach is contemplated. First, a nonlinear optimal controller identifies an appropriate baseline rendezvous path for guidance, both in position and orientation. As the spacecraft progresses along the pre-computed baseline path, navigation is performed through optical sensors that measure the relative pose of the chaser relative to the target. A Kalman filter processes these observations and offers state estimates. A linear controller compensates for any deviations identified from the predetermined rendezvous path. The efficacy of the GNC technique is tested by considering a complex scenario in which the rendezvous operation is conducted with an uncontrolled tumbling target. Hardware-in-the-loop laboratory experiments are conducted as a proof-of-concept to validate the guidance algorithm, with observations supplemented by optical navigation techniques.

Transfer from Lunar Gateway to Sun-Earth Halo Orbits Using Solar Sails

To extend the usability of solar sails in the sun–Earth–moon system, we analyze the transfer trajectories from the 9:2 Earth–moon near-rectilinear halo orbit (NRHO) to halo orbits around the sun–Earth L1 and L2 points under the assumption of a future mission for a solar sail spacecraft equipped with a solar electric propulsion (SEP) system deployed from the Lunar Orbital Platform-Gateway. The dynamics are modeled using the bicircular restricted four-body problem, where the gravitational forces from the sun, Earth, and moon as well as solar radiation pressure (SRP) are considered. We propose a trajectory design method that utilizes both SRP and SEP. The method consists of initial guess generation and optimization steps. The initial guess generation comprises the forward propagation of the escape trajectory from the NRHO, the backward propagation of the stable manifold of the target halo orbits, and their apoapsis patching process. Optimization is conducted to minimize propellant consumption by effectively controlling SRP. We perform optimizations with various parameters, namely, the sail area-to-mass ratio (), specifications of SEP, target sun–Earth halo orbit, and departure direction. The results validate the proposed trajectory design method and verify that solar sail acceleration can reduce the necessary amount of propellant, which indicates that such missions can be realized by small CubeSats.

Analysis of accidental spacecraft break-up events in cislunar space

Fragmentation events are the most common source of artificial debris in space. Such events can happen for multiple reasons, ranging from collisions with active or inactive objects to propellant tanks or battery explosions. They are an inherent part of human activities in space, regardless of the location. At the same time, the interest in the Moon and the space around it increases. Multiple planned missions want to leverage the peculiar dynamics of the Earth-Moon system to build an infrastructure likely to support human exploration of space for centuries to come. The present research puts a step forward in the direction of Space Debris Mitigation techniques for future cislunar missions. After being tuned with novel implementation techniques, the NASA Standard Break-up Model has been employed to simulate explosion events in multiple locations in cislunar space. Notably, the Circular Restricted Three-Body Problem model has been employed to generate orbits, corrected in a higher-fidelity model to generate initial conditions for long-term propagations. Moreover, multiple starting positions along each orbit have been crossed with several possible event dates, providing a broader understanding of the aftermath of explosion events. Three case studies have been considered: an EML2 southern Near Rectilinear Halo Orbit (NRHO), candidate for the Gateway station, a larger Halo orbit of the same family, and a Distant Retrograde Orbit (DRO). These locations have been chosen to characterize dynamically different trajectories used in current applications. Results provided include the number, locations, and characteristics of collision with the Moon and the Earth, together with considerations on the interactions with Earth’s protected orbital regions of Low Earth Orbit (LEO) and Geostationary Orbit (GEO). A novel analysis is also introduced to determine the immediate danger for the Gateway station in the case of such an event. This research lays the foundation to develop a cislunar Space Debris Mitigation (SDM) framework in the hopes that awareness is raised when there is still time for proper implementation of guidelines.

Rendezvous trajectory design of logistics resupply missions to the lunar gateway in near-rectilinear halo orbit

Logistics resupply to the lunar Gateway is one of the candidates for the Japan's contribution to the Artemis program. The Japan Aerospace Exploration Agency (JAXA) is presently developing the HTV-X, a new unmanned spacecraft developed as the successor to the H-II Transfer Vehicle (HTV). The HTV-X will transport supplies to the International Space Station. JAXA is also investigating enhancements to the HTV-X for logistics resupply to the lunar Gateway. A Near-Rectilinear Halo Orbit (NRHO) of the L2 southern family was selected as the Gateway operational orbit. This paper proposes a trajectory design for missions to the Gateway in NRHO. The rendezvous scenario consists of a transfer from the Earth to NRHO, a rendezvous, and proximity operations in NRHO. Monte Carlo simulations are performed in all phases to identify the effects of navigation and control errors. In addition, the simulations evaluate the designed trajectory's fuel consumption, safety, and operational feasibility. This paper also identifies the GN&C requirements for rendezvous in NRHO determined by the study.

Launch parameters of a lunar ice payload traveling via electromagnetic mass accelerator

This paper describes a solution for procuring propellent needed for future space exploration missions based on the Lunar Electromagnetic Mass Accelerator (LEMMA) concept analyzed by McNab and McGlasson. This study examined the feasibility of using an electromagnetic launcher (EML) to transport raw materials used in propellent production from the lunar south pole to the National Aeronautics and Space Administration's (NASA) Lunar Gateway. The proposed Gateway space station, to be located in a lunar near-rectilinear halo orbit (NRHO), is a critical part of NASA's Artemis program. Cheaply and efficiently sourcing lunar hydrogen from surface ice to the Gateway would benefit the program's success and future exploration of the solar system. Our study of the launch requirements for a lunar EML payload are described here. AGI Inc's Systems Tool Kit (STK) was used to calculate the required launch azimuth, elevation, magnitude, epoch, and trip duration for a payload launched from the Moon to rendezvous with Gateway. The study shows that it is feasible to conduct a single launch from the lunar south pole that can intercept any point along the Gateway's orbit with variable launch conditions.

Semianalytical Measures of Nonlinearity Based on Tensor Eigenpairs

This paper proposes a semianalytical measure of nonlinearity (MoN) based on tensor eigenpairs. Approximating nonlinear dynamics via local linearization is a common practice that is used to enable analytical methods in dynamics, control, navigation, and uncertainty propagation. However, these linear approximations are only applicable near the linearization point, and the size and characteristics of the linear region are dependent on the system’s underlying degree of nonlinearity. This paper presents a novel MoN that is based on the eigenpairs of tensors that are derived from the higher-order terms in a Taylor series expansion, e.g., the local dynamics tensors and state transition tensors. Unlike existing MoN, the tensor eigenpair measure of nonlinearity (TEMoN) is semianalytical and its computation does not require empirical sampling or numerical optimization. TEMoN can be used to quantify nonlinearity, identify directions of strong nonlinearity, predict the size of a linear region, and justify the truncation order of a Taylor series expansion by distinguishing higher-order contributions to nonlinearity. The TEMoN method is demonstrated for equilibrium points in the circular restricted three-body problem, near-rectilinear halo orbits, and nonlinear parameter transformations.

Dim cislunar target tracking with GEO- and HEO-based optical sensors

This research considers the percentage of time that geosynchronous earth orbit (GEO)- and HEO-based optical sensors can track dim cislunar targets in L2 near-rectilinear Halo orbit (NRHO), taking into account observer constellation configuration—number of observer satellites and their orbits—as well as the sensors’ lunar exclusion angle (LEA). Simulations are created using systems tool kit (STK) to model the targets, observers, sensors, and all relevant orbits. Outputs of the simulations include target-sensor-Moon and target-sensor-Sun angles, as well as target signal-to-noise ratios (SNRs). Outputs are used for analyzing whether the observer constellation has access to the target (i.e., at least one sensor is not lunar- or solar-angle excluded), and the quality of the observation (i.e., the achieved SNR for every time step of the simulation). This research finds that LEA is the most significant variable influencing the extent to which tracking custody can be maintained over L2 NRHO and Halo targets. While utilizing larger OCCs does tend to increase the probability that targets will be trackable, this effect is insignificant relative to the impact of utilizing a smaller LEA. If a 1 deg LEA is implemented for these sensors, target tracking is successful through roughly 50% of the synodic period for targets in either orbit. Increasing the LEA beyond 3 deg decreases tracking uptime by a very significant margin for Halo targets, but not as significantly for NRHO targets.

Lunar Electromagnetic Mass Accelerator (LEMMA): An Initial Concept Assessment

National Aeronautics and Space Administration (NASA) plans to return to the Moon in 2025–2028 under the Artemis program, followed by establishment of a permanent lunar base by 2028–2032. This will be followed by future manned missions to Mars and exploration of the solar system. To support those objectives, the Gateway space station will be placed in a Near-Rectilinear Halo Orbit (NRHO) orbiting between the L2 Lagrange libration point beyond the Moon and the lunar south pole. The Gateway will be the intermediate supply station for future missions. Because of low lunar gravity, it should be much less expensive to supply lunar-derived water, fuel, and materials from the Moon to the Gateway than from the Earth. The lunar escape velocity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 2400$ </tex-math></inline-formula> m/s) is within the range achieved by the recent U.S. Navy railgun program. An initial evaluation of a lunar-based electromagnetic launcher (EML) railgun capable of delivering lunar-derived liquid hydrogen or lunar ice to the Gateway for fuel for a nuclear-reactor-powered Mars mission is provided here.

Continuous-Thrust Station-Keeping of Cis-Lunar Orbits Using Optimal Sliding Mode Control with Practical Constraints

The cis-lunar space has been more and more attractive for human beings, and different kinds of missions have been proposed. For cis-lunar missions with long durations, the stationing-keeping is a pivotal problem. In this paper, the station-keeping problem with continuous thrust for different cis-lunar orbits, including distant retrograde orbits (DROs), near rectilinear halo orbits (NRHOs), and halo orbits, are investigated in the ephemeris model. The optimal sliding mode control (OSMC) based on the linear quadrant regulator (LQR) control is designed for the station-keeping problem. Simulations only considering the initial insertion error are conducted first to show performances of the OSMC controller, and the Jupiter gravity and solar radiation pressure (SRP) are then included as unknown perturbations to test the controller’s robustness. Then, with considerations of more practical constraints caused by the navigation and propulsion systems, Monte-Carlo simulations are carried out to provide more realistic results, and station-keeping performances are compared and analyzed for different nominal orbits. The results can provide useful references for the selection of station-keeping strategy in future long-term lunar missions.

Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L2 southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.

Two and three impulses phasing strategy with a spacecraft orbiting on an Earth–Moon NRHO

The increasing interests in Moon exploration have led in recent years to international collaborations between space agencies aimed to assemble and operate the Gateway, an orbiting spaceport located on a Near Rectilinear Halo Orbit (NRHO) about the second libration point of the Earth–Moon system (EML-2). In this context, transfer strategies between the Earth and the spaceport cover a key role for both assembly and resupply missions. The presented work is thus focused on one leg of the transfer: the phasing maneuver. This work is conducted under the hypotheses of the Circular Restricted Three-Body problem (CR3BP) in which the Earth and the Moon are the only bodies that influence the spacecraft motion. The primaries are assumed to have a circular motion around their common barycenter. Under these hypotheses, is demonstrated the existence of periodic orbits, such as the Halo orbit family, that are exploited to design a proposed phasing maneuver. Two strategies are investigated: Halo parking orbit to NRHO two-impulses transfer and direct phasing with manifold exploitation. The first strategy is an optimal two-impulses transfer departing an EML-2 southern Halo and targeting the baseline NRHO. The second strategy considers the chaser already injected on the Gateway’s NRHO. Poincare maps are employed to identify unstable/stable manifolds intersections in search of low-energy phasing trajectories that leave the reference orbit along the unstable branch before re-entering it via the stable one. Three-impulses transfers with similar costs are found patching together these arcs. The two strategies are thus compared to highlight their advantages and disadvantages with the perspective of a real autonomous cargo mission around the Moon to refurnish the orbiting station.

Performance analysis of impulsive station-keeping strategies for cis-lunar orbits with the ephemeris model

Future long-term lunar missions, such as cis-lunar space stations and communication/navigation constellations, have been proposed by different space agencies. For such long-term missions, reliable station-keeping strategies are of great importance to counteract unfavourable effects of perturbations, navigation errors, etc. In this study, representative cis-lunar orbits with favourable characteristics, including near rectilinear halo orbits (NRHOs), distant retrograde orbits (DROs), and halo orbits, are considered as nominal orbits of long-term lunar missions for station-keeping analysis. Both the target point method and the discrete linear quadrant regulator (DLQR) control are applied to these nominal orbits in the ephemeris model. Under some practical constraints caused by the navigation and orbital control systems, Monte-Carlo simulations are carried out to evaluate performances of the station-keeping strategies. Then, effects of solar radiation pressure (SRP) and nonspherical lunar gravity on the station-keeping performances are demonstrated by Monte-Carlo simulations with low-fidelity nominal orbits constructed in ephemeris models without SRP or nonspherical lunar gravity. Finally, comparisons between different impulse intervals are made to find the balance between the station-keeping cost and position deviation. It is found that the stability index of the nominal orbit has no direct effect on the station-keeping cost, but plays an important role in the selection of the impulse interval. The DROs and NRHOs allow a much longer impulse interval than the unstable halo orbits. The results can provide useful references for selections of the nominal orbit and station-keeping strategy in future long-term lunar missions.

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

The near rectilinear halo orbit (NRHO) is a potential orbit for the establishment of lunar space station. This research is focused on the analysis of major orbital perturbations on NRHOs and the generation of nominal orbit using a low-thrust engine in the ephemeris model. First, the NRHO family is defined in the circular restricted three-body problem (CRTBP). Then, different perturbations are performed to integrate the spacecraft motion along the NRHOs; meanwhile, a modified momentum integral is employed to calculate the orbit deviation in the case of each perturbation examined independently. By this way, these perturbations are classified according to the magnitude of impact on NRHOs. Finally, combined with a fuel-optimal control, a target-point strategy generating the nominal-controlled NRHO in the real Earth–Moon system is proposed using low-thrust technology. By selecting a fixed point from the original NRHO, the spacecraft is forced to depart from this point and then return to it, thereby forming a controlled closed trajectory. This provides an alternative nominal orbit for the future application of the low-thrust engine to lunar exploration missions.