Distant Retrograde Orbit Research Articles

Family of 2:1 resonant quasi-periodic distant retrograde orbits in cislunar space

Given the current enthusiasm for lunar exploration, the 2:1 resonant distant retrograde orbit (DRO) in Earth-Moon space is of interest. To gain an in-depth understanding of the complex dynamic environment in cislunar space and provide more options for parking orbits, this paper investigates the existence of quasi-periodic orbits near the 2:1 resonant DRO in the circular restricted three-body problem (CR3BP). Firstly, the numerical computation approach, continuation strategy, and stability analysis method of quasi-periodic orbits are introduced. Then, addressing the primary challenges in the continuation progress, we have developed an adaptive continuation algorithm with automatic adjustment of the step size and the number of discrete points that characterize the invariant torus. Finally, two types of 2D quasi-DROs and their linear stability properties are explored. Using Poincaré sections, we investigated the boundaries of the maximum extent attainable by both 2D quasi-DRO families in the CR3BP at a specific Jacobi energy, confirming that both types of quasi-periodic families have reached their respective boundaries. The algorithm described in this paper is beneficial for facilitating the computation of quasi-periodic families and aids in discovering additional potential dynamical structures.

Trajectory optimization of near-Earth asteroids exploration by using reusable probes from cislunar space

Implementing the flyby to Near-Earth Asteroids (NEAs) with the potential impact risks to the Earth allows for obtaining detailed physical parameters, thereby supporting the high-precision orbit prediction and planetary defense strategy. Different from those conducted asteroid flyby missions, in the 12th China Trajectory Optimization Competition (CTOC-12), a NEAs flyby trajectory design problem using reusable probes that depart from a Lunar Distant Retrograde Orbit (DRO) station in the cislunar space was released. The objective was flyby to as many NEAs as possible using up to 20 probes within a total of 10 years. The ∑ team proposed a solution that can explore 47 NEAs using 11 probes, ranking the first in the competition. In this paper, the methods and results from the winning team are introduced, including mission analysis and preliminary design, and low-energy transfer trajectory optimization. In particular, a round-trip trajectory is divided into three phases: deep space transfer, indirect transfer between the Earth to DRO, and DRO phasing and rendezvous. With the combination of global optimization and local optimization algorithms, the required velocity increments to change the orbital planes are effectively reduced, thus increasing the number of the explored NEAs. The final solution of our team is presented and the results are compared with those of the top three teams. The competition demonstrates that the regularization of flyby missions from the cislunar space to explore NEAs with the potential impact risks to the Earth is the feasible and promising.

Trajectory Design of Potentially Hazardous Asteroid Exploration with Reusable Probes from Cislunar Space

This article presents a trajectory design problem concerning the exploration of potentially hazardous near-Earth asteroids (PHAs) with reusable probes from cislunar space. A total of 20 probes, making round trips departing from and returning to a service space station in a lunar distant retrograde orbit, are expected to explore as many PHAs as possible by means of close flyby within a 10-year time window. The trajectory design problem was released in the 12th edition of China’s Trajectory Optimization Competition on 20 August 2022, and a total of 10 sets of trajectory solutions were submitted. As the authors who proposed the competition problem, we present in this article the problem descriptions, trajectory analysis, and design, as well as an impressive trajectory solution in which a total of 105 PHAs are explored. It is concluded that taking advantage of reusable probes from cislunar space is a promising option to efficiently explore large numbers of PHAs.

Distant retrograde orbit baseline generation considering solar eclipse mitigation

Mitigating solar eclipses presents a formidable challenge in the design of spacecraft orbits, particularly in the case of a distant retrograde orbit (DRO), which is susceptible to significant solar eclipse threats. This paper undertakes a comprehensive analysis of the occurrence characteristics and patterns of both Moon and Earth eclipses on a DRO. The proposed approach involves a two-stage design procedure, encompassing initial orbit selection and orbit extension. The initial orbit selection method primarily focuses on mitigating Earth eclipses by employing the out-of-plane motion inherent in a DRO. The study meticulously explores the influence of three pivotal elements — amplitude, period, and initial phase — on the efficacy of Earth eclipse avoidance. Concurrently, when faced with unavoidable solar eclipses of the initial orbit, a series of tiny maneuvers are systematically applied to extend the baseline orbit. The parameter design space is discretized, and a tree search method is employed to identify viable maneuver sequences. The research successfully achieves the long-term stabilization of the baseline DRO, ensuring that solar eclipses do not exceed 2 h in 10 years. The proposed method’s robustness and applicability are substantiated through validation under the ephemeris model.

Orbit determination of Earth-Moon libration point navigation constellation based on Inter-satellite links

Earth-Moon libration point navigation constellation has a merit of fully covering the cislunar space and providing navigation services with merely a small number of satellites. Furthermore, this type of constellation itself can achieve orbit determination by using only its Inter-satellite links (ISL) owing to the well-known gravitational asymmetry near the libration points. This paper adopts a representative four-satellite navigation constellation including three satellites located near the libration point L3, L4, L5, and an extra one in Distant Retrograde Orbit (DRO), and studies the orbit determination accuracy of the constellation under two conditions: establishing ISLs within itself (called Solely libration point satellites) and establishing additional ISLs with BeiDou Navigation Satellite System (BDS) (called Libration + BeiDou satellites). The simulation results indicate that, for the Solely libration point satellites scenario with the 1 m range error and solar radiation pressure (SRP) error with the level of 10% deviation between ball model and macro model, the final orbit accuracies for L3, L4, L5, and DRO satellites can respectively achieve 11.3 m, 12.7 m, 12.6 m, and 7.3 m. Reducing the link interval can significantly shorten the arc length to achieve final accuracy, whileas it has less impact on the final orbital accuracy. When the link interval is set as 240, 60, 10, and 2 min, the arc lengths at the final accuracy of better than 15 m are about 35, 29, 23, and 20 days, respectively. To balance the communication burden and the orbit determination arc length, the recommended ISL building interval is 10 min. Errors coming from range measurement model and dynamic model, in addition, are key factors in orbit determination, which can result in meters to tens of meters of orbital accuracy. For the Libration + BeiDou satellites scenario, the augmented ISLs to BDS can substantially improve constellation orbital accuracy and shorten the orbit determination arc length. When the DRO satellite attached to the Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites of BDS respectively, the improved accuracy are 37.1%, 61.2%, and 42.2%, while the shortened arc length are 20.1%, 28.3%, and 28.1%, respectively. The research findings presented in this paper can serve as a reference for the construction and assessment of navigation constellations in the Earth-Moon system.

Near-Earth Asteroids Orbit Determination by DRO Space-Based Optical Observations

In response to the problem that ground-based optical monitoring systems cannot monitor near-Earth asteroids which are in the direction too close to the Sun on the celestial sphere, we raise a method that tracks and determines the orbit of asteroids by Distant Retrograde Orbit (DRO) platforms with optical monitoring. Through data filtering by visibility analysis and the initial orbit information of the asteroids provided by Jet Propulsion Laboratory (JPL), the asteroids’ orbits are determined and compared with the reference orbit. Simulation results show that with a measurement accuracy of two arcseconds and an arc length of three years, the orbit determination accuracy of the DRO platform for near-Earth asteroids selected in the simulation example can reach tens of kilometers, especially the asteroids with Atira orbits to an accuracy of fewer than ten kilometers. In conclusion, the near-Earth asteroids monitoring systems based on DRO platforms are capable to provide sufficient monitoring effectiveness which enables precisely tracking of the target asteroids and forecast of their positions.

Utilizing the geometric mechanics framework to predict attitude in a full ephemeris model of the Cislunar region

Predicting the attitude of spacecraft traveling within the Cislunar region is crucial to ensure the success of future missions planned within that realm of space. To consider the coupled nature of translational and rotational motion, the circular restricted full three-body problem (CRF3BP), previously proposed by the authors, is utilized to obtain an initial guess for the orbit and attitude motion of the spacecraft. Then, that initial guess is used to transition the trajectory into a full ephemeris model, which considers the additional perturbations due to the Sun’s gravitational effect and the eccentricity of the Moon’s orbit. Orbit/attitude coupling is studied for multiple orbits obtained within the CRF3BP considering spacecraft of different sizes. The trajectories selected for analysis are an L2 Lyapunov orbit, a distant retrograde orbit, a northern halo orbit, and a Lunar transfer from low-Earth orbit. The efficacy of the CRF3BP is demonstrated by studying how spacecraft motion, notably its attitude, is predicted in the full ephemeris model using this formalism.

A Lunar-Orbiting Satellite Constellation for Wireless Energy Supply

The goal of this research is to define a lunar-orbiting system that provides power to the lunar surface through wireless power transmission. To meet the power demand of a lunar base, a constellation of satellites placed in stable orbits is used. Each satellite of this constellation consists of solar arrays and batteries that supply a power transmission system. This system is composed of a laser that transmits power to receivers on the lunar surface. The receivers are photonic power converters, photovoltaic cells optimized for the laser’s monochromatic light. The outputs of this work will cover the architecture of the system by studying different orbits, specifically analyzing some subsystems such as the laser, the battery pack and the receiver placed on the lunar ground. The study is conducted considering two different energy demands and thus two different receivers location: first, at the strategic location of the Artemis missions’ landing site, the Shackleton Crater near the lunar south pole; second, on the lunar equator, in anticipation of future and new explorations. The goal is to evaluate the possible configurations to satisfy the power required for a lunar base, estimated at approximately 100 kW. To do this, several cases were analyzed: three different orbits, one polar, one frozen and one equatorial (Earth–Moon distant retrograde orbit) with different numbers of satellites and different angles of the receiver’s cone of transmission. The main objective of this paper is to perform a comprehensive feasibility study of the aforementioned system, with specific emphasis placed on selected subsystems. While thermal control, laser targeting, and attitude control subsystems are briefly introduced and discussed, further investigation is required to delve deeper into these areas and gain a more comprehensive understanding of their implementation and performance within the system.

Trajectory Optimization and Control Applied to Landing Maneuvers on Phobos from Mars-Phobos Distant Retrograde Orbits

This paper presents research on the application of trajectory design, optimization, and control to an orbital transfer from Mars–Phobos Distant Retrograde Orbits to the surface of Phobos. Given a Distant Retrograde Orbit and a landing location on the surface of Phobos, landing trajectories for which total Δv for a direct 2-burn maneuver is minimized are computed. This is accomplished through the use of Particle Swarm Optimization in which the required Δv and time of flight are optimization parameters. The non-uniform gravitational environment of Phobos is considered in the computation. Results show how direct transfers can be achieved with Δv on the order of ∼30 m/s.

Multi-orbit lunar GNSS constellation design with distant retrograde orbit and Halo orbit combination

The Moon is the closest natural satellite to mankind, with valuable resources on it, and is an important base station for mankind to enter deep space. How to establish a reasonable lunar Global Navigation Satellite System (GNSS) to provide real-time positioning, navigation, and timing (PNT) services for Moon exploration and development has become a hot topic for many international scholars. Based on the special spatial configuration characteristics of Libration point orbits (LPOs), the coverage capability of Halo orbits and Distant Retrograde Orbit (DRO) in LPOs is discussed and analyzed in detail. It is concluded that the Halo orbit with a period of 8 days has a better coverage effect on the lunar polar regions and the DRO has a more stable coverage effect on the lunar equatorial regions, and the multi-orbital lunar GNSS constellation with the optimized combination of DRO and Halo orbits is proposed by combining the advantages of both. This multi-orbital constellation can make up for the fact that a single type of orbit requires a larger number of satellites to fully cover the Moon, using a smaller number of satellites for the purpose of providing PNT services to the entire lunar surface. We designed simulation experiments to test whether the multi-orbital constellations meet the full lunar surface positioning requirements, and compare the coverage, positioning, and occultation effects of the four constellation designs that pass the test, and finally obtain a set of well-performing lunar GNSS constellations. The results indicate that the multi-orbital lunar GNSS constellation combining DRO and Halo orbits can cover 100% of the Moon surface, provides there are more than 4 visible satellites at any time on the Moon surface, which meets the navigation and positioning requirements, and the Position Dilution of Precision (PDOP) value is stable within 2.0, which can meet the demand for higher precision Moon surface navigation and positioning.

Midcourse correction of Earth-Moon distant retrograde orbit transfer trajectories based on high-order state transition tensors

Midcourse correction of Earth-Moon distant retrograde orbit transfer trajectories based on high-order state transition tensors

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.

Phasing analysis on DRO with impulsive maneuver

The cis-lunar periodic orbit exhibits some unique dynamic characteristics. Among them is the distant retrograde orbit, which has long-term stability and is one of the ideal candidate deployment orbits for cis-lunar space stations and deep-space exploration transfer stations. Orbiting, rendezvous, and docking are among the flight operations involved in space station on-orbit construction, material supply, spacecraft monitoring, and other tasks. Suitable initial conditions can be created for these operations by shortening the relative distance between spacecraft through phasing. In this study, the characteristics of a two-impulse phasing orbit on a distant retrograde orbit (DRO) are summarized, and its phasing ability is globally analyzed. Based on these analyses, a phasing optimization problem was presented and solved. Using DRO’s dynamic characteristics, a DRO multi-impulse phasing rolling solution method is presented. For accuracy purposes, the orbit determination error is also considered in this method. The simulation analysis was performed using the circular restricted three-body problem (CR3BP) dynamic model and the ephemeris model. Compared with the results of two-impulse phasing, this method reduces the offset of the end position of the DRO phasing orbit from hundreds to tens of kilometers. This result satisfies the relative distance requirements for subsequent spacecraft operations. The total pulse requirement of this phasing method for the two models was within a reasonable and feasible range.

In Situ Propellant Alternatives for a Lunar Ascent/Descent Vehicle

Recently, NASA has pushed for returning humans to the moon sustainably with in situ resource utilization as the central focus. The moon has an abundance of water that is proposed to be electrolyzed into hydrogen and oxygen to be used as propellant. Other volatiles such as ammonia, carbon dioxide, and methane are also present. A mission architecture for a lunar ascent/descent vehicle (LADV) from the Polytechnic University of Turin and nuclear thermal propulsion (NTP) engine models from the University of Alabama in Huntsville were used to compare in-situ-derived propellants for a LADV. This study considered a LADV originating from the lunar surface, delivering a payload in the lunar distant retrograde orbit, and returning to the lunar surface for retanking. This research analyzed the impacts on this mission of using hydrogen NTP, water/ammonia NTP, liquid-oxygen augmented nuclear thermal rocket, and Aeon 1 methane–oxygen engines using the selected architecture and tools. The results were compared to the reference hydrogen–oxygen RL10 engine. The propulsion system comparison analysis showed that combustion engines will offer better overall performance than NTP-based engines due to a 50% decrease in propellant volume, a 20% decrease in dry mass, and a lower propellant mass than the water and ammonia NTP systems. Both the hydrogen–oxygen and methane–oxygen propulsion systems will have similar propellant masses when compared to other systems. This is due to the order of magnitude higher mass of the NTP engines, with the highest mass contribution coming from the reactor. However, both water and ammonia alternative propellant NTP engines can still be viable candidates for the usage of these minimally processed propellants to satisfy this mission.

Differential algebra methods applied to continuous abacus generation and bifurcation detection: application to periodic families of the Earth–Moon system

The return of human space missions to the Moon puts the Earth–Moon system (EMS) at the center of attention. Hence, studying the periodic solutions to the circular restricted three-body problem (CR3BP) is crucial to ease transfer computations, find new solutions, or to better understand these orbits. This work proposes a novel continuation method of periodic families using differential algebra (DA) mapping. We exploit DA with automatic control of the truncation error to represent each family of periodic orbits as a set 2D Taylor polynomial maps. These maps guarantee the access to any point of the family without any numerical propagation, providing a continuous abacus. When applied to the halo family at $$L_1$$ and $$L_2$$ , the planar Lyapunov at $$L_1$$ and $$L_2$$ , the distant retrograde orbit (DRO) family, and the butterfly family, we show that the DA-based 2D mapping is asymptotically more efficient than point-wise methods by at least two orders of magnitude, with controlled accuracy. To assist the computation of family of periodic orbits, we propose a novel DA-based automatic bifurcation detection algorithm that enables the continuous mapping of the family’s bifurcation criteria. A bifurcation study on the halo $$L_2$$ shows identical results as point-wise methods while highlighting two undocumented bifurcations.

Optimal design of Mars immigration by using reusable transporters from the Earth–Moon system

In the 2016 International Astronautical Congress, SpaceX’s Mars immigration plan was first formally proposed alongside a fully-reusable transportation infrastructure. In the 12th edition of the China Trajectory Optimization Competition (CTOC-12) held in 2022, a Mars transportation trajectory design problem using reusable transporters from a parking distant retrograde orbit (DRO) in the Earth–Moon system was released. It is expected to transport as many immigrants as possible using a maximum of 50 transporters within a total of 20 years. The BIT-DFH-BJUT team reported a solution that can deliver 9080 immigrants to Mars, which ranked first in the competition. In this paper, the methods and results from the winning team are presented, primarily including an overall analysis, underlying round-trip trajectory design, and top-level scheduling. Specifically, a round-trip is divided into four phases, leaving the DRO to man-boarding at the perigee, Earth–Mars interplanetary transfer, Mars’s return to the Earth, and return to the DRO. An overall optimization framework is constructed by synthesizing techniques such as data set creation and patching, differential evolution, nonlinear programming, greedy algorithm, and mixed-integer programming. Finally, we outline the final solution of our team and compare the results with those from the top five teams. This competition demonstrates that a large-scale Mars immigration plan is possible by using reusable transporters from the Earth–Moon system.

Propulsion Alternatives for Mars Transportation Architectures

Recently, NASA has pushed for returning humans to the moon, with in-situ resource utilization being the key capability to provide sustainability. One of the potential future developments could be a propellant depot in lunar distant retrograde orbit. Using Aerojet Rocketdyne Mars mission architectures and University of Alabama in Huntsville Nuclear Thermal Propulsion (NTP) engine models, this research analyzed the impacts of using chemical and engines as well as the liquid-oxygen (LOX) Augmented Nuclear Thermal Rocket (LANTR) engines for these missions and compared their performances to the reference hydrogen-based NTP (H-NTP) engines all the while assuming a propellant depot at lunar distant retrograde orbit. For a human mission to Mars originating in the lunar distant retrograde parking orbit, the LANTR engines will offer better overall performance than H-NTP engines with a predicted 55.6% decrease in propellant volume, 39% decrease in vehicle dry mass, and 50% decrease in the number of aggregation launches. This is due to LANTR’s 22% higher specific impulse than conventional chemical propulsion systems, three times higher density than pure hydrogen, and 440% higher thrust than the baseline H-NTP engines. However, these benefits come at the cost of the propellant mass, which is 32.4% higher for the conjunction class mission and 106.7% higher for the opposition class mission than the baseline H-NTP system.

Impacts of In Situ Alternative Propellant on Nuclear Thermal Propulsion Mars Vehicle Architectures

Recently, NASA has pushed for returning humans to the moon sustainably with In situ resource utilization being the central focus. In its permanently shadowed regions, the moon has an abundance of water and ammonia, which are two potential alternative propellants to hydrogen in nuclear thermal propulsion (NTP) engines. Using Aerojet Rocketdyne Mars mission architectures and University of Alabama in Huntsville NTP engine models, this research analyzed the impacts of using water or ammonia as propellants on mission architectures. For a human mission to Mars originating in the lunar distant retrograde parking orbit, when comparing the baseline hydrogen vehicles to vehicles using water or ammonia, the effects of increased propellant density by an order of magnitude despite a 62% decrease in specific impulse will still require an average of 53% of the launches for vehicle assembly, 59% of the dry mass, 25% of the propellant volume for the conjunction-class mission, and 50% of the propellant volume for the opposition-class mission when comparing against the baseline hydrogen vehicle. Due to the oxidative nature of water, which results in 29% of the engine life compared with that of hydrogen and ammonia, ammonia outperforms water in terms of the total number of missions per engine block by an average factor of 6.8. Because ammonia’s specific impulse is 40.6% that of hydrogen, the propellant mass is increased by a factor of 2.9 and longer burn times result in an average of a 10% decrease in the total number of missions that the hydrogen system can achieve. Since the changes to the vehicle architecture are more extreme and in favor of ammonia than the total mission capability, for reusable vehicles using NTP technology ferrying humans to Mars while utilizing in situ propellants from the moon, this research recommends ammonia as the propellant of choice.

Autonomous orbit determination and timekeeping in lunar distant retrograde orbits by observing X‐ray pulsars

<h3>Abstract</h3> A server satellite that is parked in a stable distant retrograde orbit (DRO) in the vicinity of the Moon can provide navigation service for satellites in the Earth– Moon system. In this study, X-ray pulsar navigation (XPNAV) is investigated to determine the server’s orbital position and velocity, and maintain its onboard timing autonomously to ensure the autonomy of the server. First, the feasibility and potential advantages of XPNAV in DRO are analyzed qualitatively based on the unique properties of DRO: long-term orbital stability and short-term, nearly uniform-velocity rectilinear motion. Second, high-fidelity X-ray photon timestamps are simulated to serve as the original measurements for XPNAV. A classical extended Kalman filter is used to estimate the orbital states (i.e., position and velocity) and the clock timing of the satellite in DRO, wherein the pulse phase and Doppler frequency are estimated as intermediate measurements. Finally, Monte Carlo simulations are conducted to assess the variation in the XPNAV performance with the DRO orbital period, clock noise, and detector effective area. The simulation results show that XPNAV in DRO can achieve considerably improved position accuracy than that in low Earth orbit using the same hardware while maintaining the long-term stability of the satellite onboard clock, thus demonstrating the capability of XPNAV to be used in an operational spaceflight mission around or beyond the Moon.

Strategies to capture asteroids to distant retrograde orbits in the Sun–Earth system

Capturing near-Earth asteroids would be of great significance for future space missions. Due to its stability, distant retrograde orbit (DRO) around the Earth has the potential to be an ideal destination for the captured asteroids. In this paper, we propose three strategies to capture asteroids to DROs in the model of the circular restricted three-body problem in the Sun–Earth system. In the manifold-assisted strategy, Lyapunov orbits that are tangential to DROs are calculated, and then stable manifolds are employed to design transfers for capturing asteroids. The non-coplanar Hohmann transfer is used to guess the total cost of capturing an asteroid, and candidate asteroids are thus selected. The second strategy of asteroid capture is defined as direct capture to increase opportunities of capturing asteroids with low cost. The captured asteroid can be inserted into the target DRO with a maneuver at any position along the DRO. Then optimal results are obtained after analyzing the capture conditions. Finally, a strategy of using a flyby of the Earth is proposed as the power Earth-flyby capture, and an additional maneuver is imposed on an asteroid at the perigee of the transfer trajectory. Results show that the direct and powered Earth-flyby asteroid capture strategies potentially need fewer velocity increments than the manifold-assist strategy. Furthermore, 2020SO can be captured into DROs with lower energy than the other candidate asteroids in three capture strategies, and the minimum cost is approximately 189.93 m/s.