Halo Orbit Research Articles

A 62-minute orbital period black widow binary in a wide hierarchical triple

Over a dozen millisecond pulsars are ablating low-mass companions in close binary systems. In the original 'black widow', the eight-hour orbital period eclipsing pulsar PSR J1959+2048 (PSR B1957+20)1, high-energy emission originating from the pulsar2 is irradiating and may eventually destroy3 a low-mass companion. These systems are not only physical laboratories that reveal the interesting results of exposing a close companion star to the relativistic energy output of a pulsar, but are also believed to harbour some of the most massive neutron stars4, allowing for robust tests of the neutron star equation of state. Here we report observations of ZTF J1406+1222, a wide hierarchical triple hosting a 62-minute orbital period black widow candidate, the optical flux of which varies by a factor of more than ten. ZTF J1406+1222 pushes the boundaries of evolutionary models5, falling below the 80-minute minimum orbital period of hydrogen-rich systems. The wide tertiary companion is a rare low-metallicity cool subdwarf star, and the system has a Galactic halo orbit consistent with passing near the Galactic Centre, making it a probe of formation channels, neutron star kick physics6 and binary evolution.

Stochastic optimization for stationkeeping of periodic orbits using a high-order Target Point Approach

Periodic orbits in the Restricted Three-Body Problem are widely adopted as nominal trajectories by different missions. To maintain periodic orbits in a three-body regime, a stationkeeping strategy based on a high-order Target Point Approach (TPA) is proposed, where fuel-optimal and error-robust TPA parameters are acquired from stochastic global optimization. Accurate TPA maneuvers are calculated in a high-order fashion enabled by Differential Algebra techniques. Orbit determination epoch is selected using a sensitivity analysis based on the convergence radius of a stroboscopic map. Stochasticity is handled by incorporating Monte Carlo simulations in the process of optimization and the evaluation of high-order ODE expansions is employed to supplant the time-consuming numerical integration. Two specific types of periodic orbits, Near Rectilinear Halo Orbits and Quasi-Satellite Orbits, are investigated to demonstrate the validity and efficiency of the strategy.

Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines

Generation of Artificial Halo Orbits in Near-Moon Space Using Low-Thrust Engines

Study of Matter Density Distributions, Elastic Electron Scattering Form factors and Root Mean Square Radii of 9C, 12N, 23Al, 11Be and 15C Exotic Nuclei

The ground state densities of neutron-rich (11Be,15C) and proton-rich (9C,12N,23Al) exotic nuclei are investigated using a two-body nucleon density distribution (2BNDD) with two frequency shells model (TFSM). The structure of the valence one-neutron of 11Be is in pure (1p1/2) and of 15C in pure (1d5/2) configuration, while the structure of valence one-proton configuration is in 9C,12N are to be in a pure (1p1/2) and 23Al in a pure (2s1/2) . For our studied nuclei, an efficient (2BNDD) operator for point nucleon system folded with two-body correlation operator's functions is used to investigate nuclear matter density distributions, elastic electron scattering form factors, and root-mean square (rms) radii. The effect of the strong tensor force (TC) in nucleon-nucleon forces is taken into account in the correlation. The wave functions of a single particle harmonic oscillator are used with two different oscillator size parameters, βc and βv, the former for core (inner) orbits and the latter for valence (halo) orbits. The measured matter density distributions of these nuclei clearly show the long tail results. The plane wave born approximation (PWBA) is used to investigate the elastic electron scattering form factors for these exotic nuclei.

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.

LUMIO: A CubeSat for observing and characterizing micro-meteoroid impacts on the Lunar far side

The Earth-Moon system is constantly bombarded by meteoroids of different size and impact speed. Observation of the impacts on the Moon can enable thorough characterization of the Lunar meteoroid flux, which is similar to that of the Earth. While Earth-based Lunar observations are restricted by weather, geometric and illumination conditions, a Lunar-based observation campaign can improve the detection rate and, when observing the Lunar far side, complement in both space and time the observations taken from Earth.The Lunar Meteoroid Impact Observer (LUMIO), one of the two winning concepts of the ESA SysNova Lunar CubeSats for Exploration challenge, is a mission designed to observe, quantify, and characterize the micro-meteoroid impacts on the Lunar far side. It is based on a 12U CubeSat that carries the LUMIO-Cam, a custom-designed optical instrument capable of detecting light flashes in the visible spectrum. The spacecraft is placed on a halo orbit about the Earth–Moon L2 point, where permanent full-disk observation of the Lunar far side can be performed with excellent quality, given the absence of Earth background noise. After passing Phase 0 and an independent feasibility study in the ESA Concurrent Design Facility, the mission has successfully completed its Phase A in March 2021. Although the Phase 0 design of the LUMIO spacecraft was assessed as feasible by the ESA CDF study, a number of critical issues were identified, which have been tackled by the Phase A design.The paper presents the outcome of this Phase A design effort for the LUMIO spacecraft. Particularly relevant changes or updates in the spacecraft design include: a consolidated design of the LUMIO-Cam, with longer baffle for straylight protection; a set of ADCS sensors and actuators with increased redundancy; a combination of Direct-to-Earth communication and inter-satellite link with a mothership in Lunar orbit; use of Earth ranging to complement and validate the current innovative autonomous navigation strategy based on optical observations of the Moon by means of the LUMIO-Cam; re-assessment of the COTS components selection for the power and propulsion systems.

Optimal Control of Transfer to Vertical Orbits from Lyapunov Orbits Using Low-Thrust Engine

There are many different families of periodic orbits in the Earth-Moon system, such as Lyapunov orbits, halo orbits, vertical orbits, etc. The establishment of a lunar space station requires a spacecraft to be able to transfer among these orbits. Lyapunov orbits have been used by some missions and are well-studied orbits, while periodic vertical orbits can provide large amplitudes of spacecraft motion outside the plane of the Moon’s motion, which makes it possible to avoid shadowing of the orbits and use them as relay satellite in cislunar space. Modern researchers mainly consider the use of high-thrust engines for transfer. With the development of electric propulsion technology, the use of low, but long-acting thrust for deep space exploration has become especially relevant. This is due to the high specific characteristics of the propulsion systems of this type. In this article, an algorithm has been developed for determining the optimal control with a low-thrust engine for a transfer from Lyapunov orbit to a vertical orbit. The minimum time of flight or the minimum costs of the working body are used as criteria for optimality. In the calculation for solving the two-point boundary value problem of the optimal control theory, the parameter continuation algorithm is used, which allows to gradually get the transfer from some simple results to the final transfer trajectory. The results obtained make it possible to assert that the use of intermediate axial orbits allows the use of propulsion systems with lower thrust levels. In this case, the duration of the flight increases slightly with an almost unchanged consumption of the working body. Moreover, the homotopy method makes it possible to reduce the consumption of working body, while the control of the engine throttling becomes discrete. The results of this study and the algorithms proposed in this article can be used to determine the optimal program control and ballistic design of lunar missions.

An adaptive surrogate model-based fast planning for swarm safe migration along halo orbit

Taken the optimal assignment, trajectory optimization and collision avoidance into consideration, this research focuses on the fast-planning method for swarm safe-migration along Halo orbit. The swarm safe-migration planning problem is an inherently high-dimensional nonlinear problem. Repeatedly solving the bottom layer’s collision-free trajectory optimization problem causes heavy computation burden in the traditional two-layer optimization framework. To reduce the computation cost and keep the optimization performance, an adaptive surrogate model-based swarm safe-migration planning method is developed in this paper. The surrogates fitted to the collision-avoidance constraints are investigated and the input variables of the surrogates are analyzed and selected for improved efficiency. In particular, a classifier-based surrogate management strategy is designed for the swarm safe-migration problems to improve the optimization capability of the proposed algorithm. Finally, the proposed method is applied to two real-world swarm migration problems, i.e., a reconfiguration problem with geometric constraint and an assignment optimization problem. Numerical results indicate that, compared with the optimal result from the widely-used Genetic Algorithm method, our method could obtain a similar solution within only about 4% of the computational time.

Size-Optimal Network-Coded Bundle Aggregation for Earth–Lunar Disruption-Tolerant Network via Markov Decision

In recent years, a disruption-tolerant network (DTN) has attracted significant attention regarding lunar exploration, as they can be employed in various relay spacecraft, such as lunar orbiters, due to their excellent constant all-time coverage capability. An exclusive relay satellite with limited storage capacity and downlink communication bandwidth to Earth could be congested with huge amounts of return data from multiple sources on the lunar surface, resulting in low efficiency in the backhaul link. To address this issue, a network-coded forwarding scheme employing a Markov-decision-assisted bundle aggregation for a Halo-orbit Earth–lunar DTN is proposed in this article. Specifically, a network-coding-enabled store-and-forward scheme is designed for the downlink relay delivery in the L2-point Halo orbit using a two-priority bundle-aggregation mechanism. A size-optimal bundle slicing-aggregation algorithm is developed for the two-source network coding scheme using the Markov decision algorithm. Simulation results demonstrate that the proposed mechanism exhibits better performance than existing delivery schemes in reducing end-to-end delivery latency. Thus, the throughput can be improved, and the arrival rate of high-priority bundles can be guaranteed.

Closed Loop Guidance During Close Range Rendezvous in a Three Body Problem

The paper presents a novel application of the State Dependent Riccati Equation (SDRE) guidance approach with state constraints for a chaser spacecraft in the close proximity of a passive target. The dynamics are described by full 6 degree of freedom rigid-body relative motion. The final trajectory is defined by a passively safe approaching cone, which acts as path constraint and follows the attitude motion of target. A Near Rectilinear Halo Orbit in the Earth-Moon system is the selected rendezvous scenario to fully validate the proposed solution, even though the parameters related to the constraints and weighting functions are kept as general as possible, thus applicable to other similar missions.

Low-Thrust Trajectory Design with Successive Convex Optimization for Libration Point Orbits

In space missions, numerical techniques for minimizing the fuel consumption of spacecraft using low-thrust propulsion are desirable. Among various nonlinear optimization methods, convex optimization has been attracting attention because it allows optimal solutions to emerge robustly and requires short computation times. In particular, trajectory design in the three-body problem near the Lagrange points involves instability and nonlinearity. Hence, this study considers the application of convex optimization to trajectory design with low-thrust propulsion in cislunar space and verifies that this technique performs well, even for sensitive and highly nonlinear dynamics. Specifically, the convex optimization scheme is applied in the transfer from a halo orbit to a near-rectilinear halo orbit where both are periodic as defined in the circular restricted three-body problem. As a further step, the transfer problem is transitioned to an ephemeris model. In addition, extensive investigations of the dependence on various parameters used in convex optimization are conducted, and a trajectory corrections maneuver method is constructed combined with the convex optimization process. This investigation provides valuable insight into the convex optimization technique in the three-body problem and facilitates the estimation of low-thrust trajectory designs for complex space missions.

In‐Orbit Performance Analysis of Solar Array for Chang'e‐4 Relay Satellite in an Earth–Moon Lagrangian Point 2 Halo Orbit

Herein, the in‐orbit performance of the solar array for Chang'e‐4 Relay Satellite in an Earth–Moon Lagrangian point 2 (EML2) Halo orbit is analyzed. The daily degradation coefficient of the photovoltaic current is calculated to be 0.99989 independent of whether the relay antenna outspreads, indicating an annual degradation coefficient of 3.94%. However, due to the shading effect of the antenna and the electrical performance degradation, the output voltage of the solar array dissatisfies the requirement of the power controller on around the 700th day, resulting in an abrupt decrease of the photovoltaic current. In addition, the in‐orbit working temperature of the solar array for Chang'e‐4 Relay Satellite is also studied. The working temperature mainly ranges from 52.3 to 76.8 °C, while the working temperature decreases to the range of 0–25 °C once the relay antenna outspreads. The present work is helpful to a deepen the understanding of EML2 Halo orbit and provide reference to the solar array design for a deep space exploration aircraft.

Comparison of Autonomous Orbit Determination for Satellite Pairs in Lunar Halo and Distant Retrograde Orbits

<h3>Summary</h3> A comprehensive study on the autonomous orbit determination (AOD) performance of satellite pairs in halo orbits and distant retrograde orbits (DROs) is carried out. A factor called <i>dynamic and geometric dilution of precision</i> (DAGDOP) is proposed to simultaneously incorporate influences from the dynamics and geometry of satellite pairs. Based on the DAGDOP, the effect of different observation arcs on the AOD accuracy is investigated. Next, the AOD accuracy of three different types of satellite pairs—halo+halo, DRO+DRO, and halo+DRO—is systematically analyzed. The hybrid halo+DRO type shows the best overall accuracy. Finally, the AOD performance of the hybrid type is verified in a realistic model. Our studies find that the average AOD accuracy of the halo orbit is about 170 meters, and that of the DRO is about 190 meters. The relative time synchronization error of two satellites is less than 30 nanoseconds.

Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits

Near Rectilinear Halo Orbits (NRHOs) are stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA’s upcoming Gateway mission. The spacecraft, however, incurs continuous deviations due to unmodeled forces and orbit determination errors in this dynamically sensitive region. The current investigation focuses on an impulsive stationkeeping technique to maintain the spacecraft near a virtual reference orbit despite these uncertainties. The flow dynamics in the region are utilized to identify appropriate maneuver and target locations. The investigation reflects the impact of various factors on maneuver cost and efficacy. For orbits where position and velocity states are particularly sensitive to epoch time, an additional feedback control strategy is applied for phasing constraints.

ハロー軌道における宇宙機フォーメーションフライトのための周期軌道の設計

A formation flying around a halo orbit is discussed in this paper. We aim to form a natural and closed formation flying around a halo orbit to reduce fuel consumption. A method to form a periodic orbit using a monodromy matrix derived by linearizing the equation of motion of spacecraft is proposed, where the complex eigenvalues of the monodromy matrix and their corresponding eigenvectors are used to form multiple orbiting formations. Using the proposed method, it is confirmed that the formation in which a chief moves around the halo orbit a certain number of times and a deputy returns to its same relative position can be constructed with almost zero velocity increment. We also discuss the design of formation trajectories when adding velocity increments. The validity of the proposed method is confirmed by numerical calculations.

Mission Design of an Aperture-Synthetic Interferometer System for Space-Based Exoplanet Exploration

In recent years, exoplanet detection has become the technological frontier in the field of astronomy, because it provides evidence of the origin of life and the future human habitable exoplanet. Deploying several satellites to form an aperture-synthetic interferometer system in space may help discover “another Earth” via interferometry and midinfrared broadband spectroscopy. This paper analyzes a space-based exoplanet exploration mission in terms of the scientific background, mission profile, trajectory design, and orbital maintenance. First, the system architecture and working principle of the interferometer system are briefly introduced. Secondly, the mission orbit and corresponding transfer trajectories are discussed. The halo orbit near the Sun-Earth L2 (SEL2) orbit is chosen as the candidate mission orbit. The low-energy transfer via stable invariant manifold with multiple perigees is designed, and the proper launch windows are presented. A speed increment less than 10 m/s is imposed for each transfer to achieve the insertion of the halo orbit. Finally, the tangent targeting method (TTM) is applied for high-precision formation maintenance with the whole velocity increments of less than 5 × 1 0 − 4 m / s for each spacecraft when the error bound is 0.1 m. The overall fuel budget during the mission period is evaluated and compared. The design in this paper will provide technical support and reliable reference for future exoplanet exploration missions.

Halo Orbit Maintenance around L1 Point of the Sun-Earth System Using Optimal Control and Lyapunov Stability Theory

AbstractThis paper addresses the maintenance of a halo orbit around the L1 point of the Sun-Earth system in a circular restricted three-body problem. To this effect, a trajectory tracking problem i...

Three-maneuver transfers from the cislunar L2 halo orbits to low lunar orbits

In this paper, a three-maneuver strategy is presented to study the transfer from a cislunar L 2 halo orbit to a low lunar orbit (LLO). Both the cislunar L 2 point orbits and lunar orbits are generally considered as habitats for space vehicles of various missions, so a transfer strategy between these orbits that combines flexibility with minimal fuel consumption is worth considering for future complex space applications in the Earth-Moon system. In terms of the three-maneuver transfer method, the first maneuver is carried out along the direction of the unstable invariant manifold toward the moon, and each point in the halo orbit can be a departure position of the transfer. Then, the spacecraft is allowed to drift for a period of time, but in the meantime we are constantly searching the window for the second maneuver that towards the target LLO and figuring out the transfer trajectory for optimal maneuver cost. The third maneuver is a deceleration into the target LLO. The transfer procedure is first established in the circular restricted three-body problem (CRTBP) model, with a feasibility analysis of not constraining orbital inclination of LLOs. After that, the results of the transfer to both polar and equatorial LLOs in the CRTBP model are used as initial solutions for the design procedure of transfer trajectories in the ephemeris model. Finally, optimized results of transfer window of up to 180 days with corresponding overall maneuver costs in the ephemeris model are given for a quasi-halo orbit, which demonstrate the flexibility and reliability of the three-maneuver transfer strategy.

Study of the matter density distributions of halo nuclei 6He and 16C using the binary cluster model

The harmonic oscillator (HO) and Gaussian (GS) wave functions within the binary cluster model (BCM) have been employ to investigate the ground state neutron, proton and matter densities as well as the elastic form factors of two-neutron 6He and 16C halo nuclei. The long tail is a property that is clearly revealed in the density of the neutrons since it is found in halo orbits. The existence of a long tail in the neutron density distributions of 6He and 16C indicating that these nuclei have a neutron halo structure. Moreover, the matter rms radii and the reaction cross section (σr) of these nuclei have been calculated using the Glauber model.

Transfers from the Earth to L_2\xa0Halo orbits in the Earth\u2013Moon bicircular problem

This paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.