Orbit Maintenance Research Articles

Achieving solar sail orbital maintenance with adjustable ballast masses in the ERTBP

An innovative method for orbital maintenance in the Sun-Earth Elliptic Restricted Three-Body Problem (ERTBP) is introduced. The concept arose from observing that Natural Periodic (NP) orbits in the ERTBP exhibit deviations from their periodic behavior over time. These NP orbits are derived solely from accurately specified initial orbital conditions. Hence, a strategy for orbital maintenance becomes essential for these missions. This approach utilizes NP orbits as the designated reference trajectory to be tracked by the spacecraft. It assumes a solar sail equipped with two ballast masses and suggests a Fully Coupled Orbit-Attitude (FCOA) model. In this comprehensive model, both orbital and attitude states mutually influence each other, enabling orbital adjustments through attitude control. Therefore, the first step involves developing the governing equations for this FCOA model incorporating two ballast masses within the ERTBP. The strategy includes dividing the NP orbit period into τ equal time intervals. During each interval, adjusting the velocity of the ballast mass using a 7-mode electrical motor facilitates precise attitude control, establishing a framework for orbital maintenance. Maintaining constant velocity within each interval simplifies achieving the desired ballast mass positions. The adjustment of ballast mass velocity is proposed to be conducted using a hybrid meta-heuristic Invasive Weed Optimization/Particle Swarm Optimization (IWO/PSO). The analysis examines how increasing the mass of the ballast masses enhances tracking performance, underscoring the critical role of mass in optimizing tracking capabilities. This highlights the significance of meticulous structural design in achieving superior outcomes for orbital maintenance missions.

On-orbit mission overview of the low power hall thruster propulsion system aboard venμs satellite

Venμs is a satellite launched in 2017, for super-spectral Earth imaging and Electric Propulsion System (EPS) demonstration. In this paper we overview EPS design and operation throughout all five mission phases, from open/closed-loop orbit control, through orbit descent (720 → 410 km), orbit maintenance under high drag environment, to orbit raising (410 → 560 km). The EPS consisted of two throttleable Hall thrusters, PPU, Propellant Management Assembly (PMA), and a 9 L propellant tank carrying 16 kg of Xenon. Both thrusters operated in the 300–550 W power range, generated a combined total impulse of 158.1 kN-sec and consumed all propellant. Two methods are described to compute the remaining propellant mass – “Bookkeeping” and “PTV” methods. The advantages and disadvantages of each method are discussed in light of the Venµs mission. Thruster performance was measured on-orbit using the “Orbit Determination” method and compared to laboratory experiments conducted on the ground with identical thrusters. The measured performance on-orbit was found to agree within the error bars with the performance measured on the ground. Lastly, we present several repeating events in which the propulsion system suffered from sudden beam-outs or ignition difficulties. We present the methods used to construct a solution and implement it.

Multi-objective design optimization and physics-based sensitivity analysis of field emission electric propulsion for CubeSat platforms

Field-emission electric propulsion is an electrostatic space electric propulsion technology that offers various advantageous features including efficient design, high specific impulse, and versatile thrust capabilities ranging from micro-Newton to milli-Newton levels. These characteristics make this type of propulsion a promising technology for small satellite platforms, enabling precise attitude control, orbit maintenance, and de-orbiting through ionization and acceleration of a liquid metal propellant. The growing demand for small propulsion systems in CubeSat platforms has spurred significant progress in modeling and characterizing field emission electric propulsion thrusters to enhance their overall performance. However, little study has been conducted to investigate the effect of geometric configurations on electric fields or expelled ion trajectories for design optimization. In this study, multi-objective design optimization is performed by incorporating electrostatic simulation coupled with an analytical performance model into evolutionary algorithms based on prediction from surrogate modeling, aiming to optimize the thruster emission design to maximize thruster performance. Physical insights into the key design factors influencing the performance of field emission electric propulsion have been gained by probing into the interaction between ion particles and electric field behavior within the thruster. It has been found that the length of the emitter tip has a significant effect on plume divergence, i.e., a longer emitter tip under the influence of electric field at higher emitter current tends to result in lower initial acceleration of emitted ions and subsequently wider spread or divergence of the ion beam. A shorter emitter tip, on the other hand, generates a sharper E-field gradient, resulting in a more focused and narrower ion beam. Additionally, sensitivity analysis has identified the mass flow rate and potential distributions as the most influential design factors on performance due to the active roles they play in the performance generation process.

Optimal design and current control strategies of an electrodynamic tape for ISS station-keeping

This study analyzes the performance of a tape-like bare electrodynamic tether as a promising propellant-free technology for the International Space Station (ISS) station-keeping, supporting the concept that the technology can provide significant mission benefits by reducing the ISS reliance on costly refueling operations for orbit maintenance. Convenient control laws for managing the electrical power supplied to the tether are proposed, exploring two distinct scenarios. The first involves using the electrodynamic tether continuously to counteract aerodynamic drag. The second adopts a cyclic approach, alternating between boosting the station with the tether and allowing for periods of natural decay. Optimal tether geometry, aimed at maximizing system efficiency, is also detailed. The study specifies an electrodynamic tether configuration featuring a 6-kilometer-long aluminum ribbon, 5 cm wide and 50 μm thick, capable of overcoming aerodynamic drag ranging from 0.40 N to 0.80 N. Additionally, numerical simulations assess the tether performance under real environmental conditions. Furthermore, the study briefly introduces the potential of a photovoltaic tether as a fully autonomous system capable of supplying the necessary input power.

Maneuver strategies of Starlink satellite based on SpaceX-released ephemeris

In the face of huge collision risks posed by the Starlink mega-constellation, the detection of unpredictable orbital maneuvers of Starlink satellites emerges as an important topic of Space Situational Awareness (SSA). The ephemerides released by the SpaceX company on the Space-track website provide a timely and valuable opportunity for addressing this problem. Based on the mean orbital elements extracted from Starlink ephemerides released at the end of 2023, the maneuver strategies, including maneuver frequency and characteristics of Starlink satellites in different orbital phases, are discussed, and the start time and end time with error ranges of confirmed maneuvers are acquired. It is found that operational satellites in Shell 1 perform an orbit maintenance maneuver approximately every 2 days, while those in Shells 2–5 execute a maneuver roughly once a day. Moreover, the parking satellites maneuver approximately every 0.25 days on average. As for satellites in the climbing orbit and the deorbiting orbit, they maneuver around every 0.1 days. The maneuver strategies of Starlink summarized in this paper can contribute to optimizing the observation plan of the Starlink constellation.

Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

A novel station-keeping strategy leveraging periodic revolutions of homeomorphic orbits in the Elliptic Restricted Three-Body Problem within the pulsating frame is presented. A systemic approach founded on arc-length continuation is presented for the discovery, computation, and classification of periodic revolutions that morph from their traditional circular restricted three-body counterparts to build an a priori dataset. The dataset is comprehensive in covering all possible geometric architectures of the restricted problem. Shape similarity is quantified using Hausdorff distance and works as a filter for the station-keeping algorithm in relation to appropriate target conditions. Finally, an efficient scheme to quantify impulsive orbit maintenance maneuvers that minimize the total fuel cost is presented. The proposed approach is salient in its generic applicability across any elliptic three-body system and any periodic orbit family. Finally, average annual station-keeping costs using the described methodology are quantified for selected “orbits of interest” in the cis-lunar and the Sun–Earth systems. The robustness and efficacy of the approach instill confidence in its applicability for realistic mission design scenarios.

Orbital Tolerance and Intrinsic Orbital Capacity for Electric Propulsion Constellations

Large constellations are typically designed using sets of periodic orbits and satellite control boxes sized to ensure compatible phasing between coorbital constellation planes to prevent conjunction events. This work investigates how the control action for orbit maintenance influences feasible intrashell and intershell distances in a satellite constellation. Two-dimensional lattice flower constellations are simulated in an environment inclusive of orbital perturbations, with onboard sensors and an electric propulsion system constituting the satellite guidance, navigation, and control system. An analysis to define estimates for minimum separation distances is performed as a function of control, propulsion, orbit, environmental, and spacecraft characteristics. An estimate of the intrinsic (geometric) orbital capacity is proposed, based on current and advanced technologies, in order to quantify the number of admissible spacecraft and orbital shells in a selected altitude range. Simulation results are used to improve the fidelity of intrinsic orbital capacity estimates and to understand factors that influence the number of admissible satellite locations in low Earth orbit.

The communication and measurement architecture of BDS-3 global operations and services

This study introduces the third-generation BeiDou Navigation Satellite System (BDS-3) system’s creative global operation and service architecture based on regional stations and Ka-band inter-satellite links (ISLs). The architecture’s contributions to BDS-3 include not only combined orbit determination and time synchronization but also autonomous orbit determination and time synchronization, global operations and services. The BDS-3 on-orbit operation results are being presented in the paper to verify the designed capabilities. Compared with BDS-2, the orbit determination accuracy is improving from 0.6 m to 0.15 m, and the time synchronization accuracy is improving from 6.67 ns to 1.16 ns. Under autonomous orbit determination and time synchronization, the 30-day orbit maintenance accuracy reaches 16 m, and the time synchronization accuracy reaches 3.74 ns. The success rate of data transmission reaches 99%, and the delay is better than 12.9 s. In the future, laser ISLs will be used to enhance the system structure and further improve global operation and service capabilities.

Stable Orbiting Around Small Moons Using J2-Perturbed Elliptic Restricted Problem

Confirmed small-body missions Martian Moons eXploration (MMX) and Hera are set to explore Martian moons and the binary asteroid Didymos’s moon Dimorphos, respectively. Orbital dynamics around these small moons differ substantially from those around previously visited targets. Simplified models, such as the circular-restricted three-body problem, cannot yield accurate predictions for orbits and their stability in real-world operations. To be specific, the orbit of the small moon and its vicinity are significantly perturbed by the oblateness of the planet and their relative positions. Realistic control constraints and the unstable 3:1 resonance of retrograde orbits further complicate orbit maintenance around a small moon. Therefore, minimizing the dynamical perturbation on baseline orbits resulting from model mismatches is crucial. This paper introduces the J2-ER3BP+GH model dedicated to describing the orbital dynamics around the small moon. It incorporates the J2 perturbation of the planet on the elliptic-restricted three-body problem and can accommodate a nonspherical gravity field of the moon. Bounded orbits can still be identified without much effort in this sophisticated model. Baseline orbits around Phobos and Dimorphos from the J2-ER3BP+GH model become much easier to maintain, as verified in the high-fidelity dynamic and control environments.

Utilizing a control technique for orbital maintenance near [formula omitted] point and Lyapunov exponents

In present article, we have explored the orbit maintenance strategy around an artificial equilibrium point in the Sun–Jupiter system. Two control strategies, proportional control and proportional derivative control laws are discussed for orbit maintenance. The maximum Lyapunov exponent is used to check the chaotic behavior of planetary orbit. We anticipate that the recently established Lyapunov exponent criteria may be used to study motion of planets in generalized stellar binary systems. This research is being guided by the conclusions of recent observations as well as those that are expected from existing and upcoming planet search missions.

Elliptical Orbit Design Based on Air-Breathing Electric Propulsion Technology in Very-Low Earth Orbit Space

Very-low Earth orbit (VLEO) space below 200 km is essential for high-quality communications and near-Earth space environment detection. Due to the significant atmospheric drag, orbital maintenance is required for spacecraft staying here. Based on air-breathing electric propulsion (ABEP) technology, this paper analyzed the orbital boundary conditions of the spacecraft under the constraints of parameters including slenderness ratio, thrust-to-power ratio, drag coefficient, and effective specific impulse. The energy balance is the key constraint for low VLEO orbits, which is determined by the drag coefficient, slenderness ratio, and thrust-to-power ratio. Under the existing technical conditions, the lowest circular orbit (along the terminator) is about 170 km. An elliptical orbital flight scheme is also analyzed to reach a 150 km perigee. A half-period control method was proposed based on the on–off control method for the elliptical orbit, which could enable the spacecraft to maintain a stable 150–250 km elliptical orbit.

Numerical simulation of thermo-throttle for iodine flow rate control in multidirectional plasma thruster

Background: Recently, a new direction in the field of electric propulsion has emerged – the multidirectional plasma thrusters. These thrusters are capable of producing propulsive forces in multiple directions. The thrusters are proposed to be used for orbit maintenance and alterations, formation flights, and interplanetary flights of space artificial objects ranging in size from CubeSats to fusion-powered interplanetary spacecraft. In this paper, the results of numerical simulation of the iodine propellant supply system for the multidirectional plasma thruster are presented. Methods: The geometry and temperature parameters of propellant supply system various elements are varied to determine the stable modes of iodine propellant ejection into the gas discharge chamber of the thruster. The temperatures of the thermo throttle and filter are found to ensure iodine mass flow rate in the range of 0.1 to 1.5 mg/s. The thermo throttle and filter temperatures are altered in the range of 65 to 200 °C and 65 to 100 °C, correspondingly. Results: The mass flow rate is critically dependent on the filter temperature and iodine saturated vapor pressure, as well as the filter and throttle geometries. The required values of iodine flow rate have been achieved by using the throttle with a diameter of 0.5 mm and a length of 60 mm and a filter with 56 holes, each hole diameter is 0.2 mm, and temperature from 90 C to 200 C. Conclusions: According to the data obtained, the iodine storage and supply system is preferably equipped with a thermos throttle, which provides precise control of the flow rate, as well as reduces sharp jumps of the flow rate when the temperature of the filter changes. Preferred filter geometry: 56 holes, each hole 0.2 mm in diameter.

Maintenance Strategy for Elliptical Orbit Satellite With Air-Breathing Electric Propulsion

Owing to the strong perturbation caused by atmospheric drag, it is inevitable to consume a significant amount of fuel for the orbital maintenance of ultralow Earth orbit (ULEO) satellites. Air-breathing electric propulsion (ABEP) has emerged at the right time, which makes use of the atmosphere to provide propulsion. Aiming to adopt an elliptical orbit, an ABEP-based satellite can collect the atmosphere near its perigee, which can be applied for propulsion to maintain the orbit shape. However, to guarantee propulsive efficiency, the thrusters should not work during the intake process, that is, near the perigee. This causes difficulties in orbital control methods because propulsion near the perigee is the most effective for simultaneous increasing the semi-major axis and eccentricity. To overcome this problem, this study proposes the “in-orbit balance” strategy, wherein the orbit maintenance can be achieved in closed orbits. Some of these orbits are used for air intake, while others are applied for propulsion near perigee. Considering the requirements regarding working gas, electric power, maneuverability and temperature, the constraints are analyzed for systematic parameter design. Using equivalent treatments, feasible satellite layout schemes can be searched for, and a constrained optimization problem is constructed to determine the solutions that satisfy the specific engineering requirements. Furthermore, optimal control for a continuous system is applied to allocate the thrust. The simulations verified the efficiency of the parameter design and confirmed that the ULEO can be controlled using the proposed strategy without resulting in extra fuel consumption.

Adaptive closed-loop maneuver planning for low-thrust spacecraft using reinforcement learning

Autonomy is an increasingly essential component of future space missions, and new technologies are necessary to accommodate off-nominal occurrences onboard that may pose risks to mission success. Identifying a suitable maneuver plan for onboard, low-thrust mission applications in cislunar space remains challenging, particularly in the case of unanticipated events. This investigation addresses this challenge by demonstrating artificial neural networks as promising tools for accurately estimating startup solutions for a conventional targeting-based iterative guidance and control algorithm. This blended approach produces a robust ‘hybrid’ architecture that simultaneously benefits from the computational simplicity of neural networks and the robustness of differential corrections to satisfy mission requirements. In this paradigm, a multiple shooting scheme is incorporated directly into a reinforcement learning process, tasking the resulting neural network controller with convergence basin identification for trajectory recovery. Rapid low-thrust maneuver planning is demonstrated in a ‘runaway’ spacecraft scenario, where deviation over time from a planned near rectilinear halo orbit path renders stationkeeping ineffective and demands an alternative approach to determine an effective recovery plan. The proposed Neural Network-Initialized Targeting (NNIT) algorithm significantly extends the recovery window compared to a crossing-control orbit maintenance approach and exhibits promising results in identifying both the timing and control components for low-thrust maneuver plans.

Formation flying along artificial halo orbit around Sun–Earth L2 point for interferometric observations

This paper proposes a method of using multiple spacecraft flying in formation in an artificially reduced halo orbit around the 2nd Lagrange point in the Sun–Earth system (SEL2) to make interferometric observations. One of the requirements for interferometric observations is to collect baseline vectors between telescopes or antennas. A shape-based approach is introduced to design a formation flight orbit that spirally spreads to satisfy this requirement. In this approach, orbits are designed on the basis of a linear theory. However, the formation orbits based on the linear theory quickly diverge because of the unstable dynamics around the SEL2. Therefore, the state-dependent Riccati equation, which allows for nonlinear control, is applied to orbit maintenance. The control system consists of two components: one for maintaining the reference orbit around the SEL2 and the other for controlling the relative position between the multiple spacecraft. The performance of the developed formation flight system is verified through a numerical simulation, confirming that the position accuracy requirement of the infrared interferometer is satisfied. It is also shown that both controls can be achieved with a low-thrust magnitude by using an electric propulsion system.

Design of an Elliptical Orbit for High-Resolution Optical Observation at a Very Low Altitude over the Korean Peninsula

Surveillance and reconnaissance intelligence in the space domain will become increasingly important in future battlefield environments. Moreover, to assimilate the military provocations and trends of hostile countries, imagery intelligence of the highest possible resolution is required. There are many methods for improving the resolution of optical satellites when observing the ground, such as designing satellite optical systems with a larger diameter and lowering the operating altitude. In this paper, we propose a method for improving ground observation resolution by using an optical system for a previously designed low orbit satellite and lowering the operating altitude of the satellite. When the altitude of a satellite is reduced in a circular orbit, a large amount of thrust fuel is required to maintain altitude because the satellite’s altitude can decrease rapidly due to atmospheric drag. However, by using the critical inclination, which can fix the position of the perigee in an elliptical orbit to the observation area, the operating altitude of the satellite can be reduced using less fuel compared to a circular orbit. This method makes it possible to obtain a similar observational resolution of a medium-sized satellite with the same weight and volume as a small satellite. In addition, this method has the advantage of reducing development and launch costs to that of a small-sized satellite. As a result, we designed an elliptical orbit. The perigee of the orbit is 300 km, the apogee is 8,366.52 km, and the critical inclination is 116.56°. This orbit remains at its lowest altitude to the Korean peninsula constantly with much less orbit maintenance fuel compared to the 300 km circular orbit.

Design of Ganymede-Synchronous Frozen Orbit around Europa

A Ganymede-synchronous frozen orbit around Europa provides a stable spatial geometry between a Europa probe and a Ganymede lander, which facilitates the observation of Ganymede and data transmission between probes. However, the third-body gravitation perturbation of Ganymede continues to accumulate and affect the long-term evolution of the Europa probe. In this paper, the relative orbit of Ganymede with respect to Europa is considered to accurately capture the perturbation potential. The orbital evolution behaviors of the Europa probe under the non-spherical gravitation of Europa and the third-body gravitation of Jupiter and Ganymede are studied based on a double-averaging framework. Then, the initial orbital conditions of the Ganymede-synchronous frozen orbit are developed. A station-keeping maneuver was performed to maintain the orbital elements to achieve the Ganymede-synchronous and frozen behaviors. A numerical simulation showed that the consumption for orbital maintenance is acceptable.

Analysis of Initial Deployment Strategy for Low-Orbit Large-Scale Constellations

With the development of commercial space technology, low-orbit large-scale satellite constellation has shown great development potential in communication services and military applications due to its advantages of low delay, strong signal, high coverage rate, fast communication rate, and low cost of mass production. It has become an urgent problem in the field of satellite constellations to study the perturbation evolution law of low-orbit large-scale constellation initialization and orbit maintenance, and how to maintain and control the deployment and initialization of low-orbit satellite constellations efficiently, economically, and stably. In this paper, the satellite motion law, constellation configuration evolution characteristics, and constellation initialization control strategy are analyzed considering the perturbation of earth’s nonspherical gravity and atmospheric drag under the orbit deviation of satellite orbit elements. Firstly, MonteCarlo simulation was used to simulate the deviation of satellite initial orbit elements, and the evolution law of ascending ascension point and phase angle of different constellations was analyzed and, secondly, establish the initialization phase constellation deployment and the ascending node right ascension deployment of mathematical equations, using Starlink constellation (V1.0-L3, 8) satellite TLE data; initialization of Leo constellation orbit plane is analyzed, by considering the orbit bias satellite simulation data; the same orbital plane satellite initialization phase deployment method is analyzed; finally, this paper provides some suggestions for the future deployment and maintenance control strategy of low-orbit constellation.

A machine learning method for the orbit state classification of large LEO constellation satellites

Recently, large LEO constellation satellites have received much attention from the aspect of Space Domain Awareness (SDA) due to their significant number and relatively complex orbit states. Low-thrust propulsion system technologies are widely used during the lifetime of such satellites, making it difficult for the work of TLE (Two Line Element) based maneuver detection. This study proposes a machine learning method for orbit state classification based on TLE data, considering the concept of the Auto-Encoder (AE) network and Decision Tree (DT). In this manuscript, the orbit states were classified into four categories: non-maneuver, controlled orbit raising, controlled orbit lowering, and controlled orbit maintenance. First, historical TLE data of multiple satellites of the STARLINK constellation system and uncontrolled objects in a similar orbital area was analyzed using an Auto Encoder network to identify nonlinear features. Second, the extracted feature was sent to the DT network for the training of the supervised classification model, which could classify the input into four categories of orbit states. Finally, extra targets that had not been considered during the modeling process were used to test the applicability of the proposed method on satellites of the same constellation system. The results suggest that the method we presented here was applicable for orbit state classification with a macro precision of 93.8% and a macro F1-score of 93.7%, according to our numerical experiments. Once set up, the proposed method presented a feasible orbit state classifier for satellites of the same constellation system, operating at a similar altitude.

Onboard Estimation of Mean Orbital Elements Extended to State Jumping Case

Mean orbital elements play a significant role in constellation guidance, orbital maintenance, and transfer strategy design. Hence, research on mean orbital elements estimation flourishes with the development of mega-constellation construction, for instance, the Starlink program. This paper investigates the autonomous on-orbit estimation problem of mean orbital elements under the consideration of real-time mean orbital elements acquisition, reliable mean orbital elements prediction, and extreme condition handling of state jumping caused by protective orbit transfer or nonfatal spacecraft collision. A novel mean orbital elements estimator based on the Savitzky–Golay filter (“Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Analytical Chemistry, Vol. 36, No. 8, 1964, pp. 1627–1639) with adaptive frame size, maneuvering detector, and multimode switching mechanism is proposed. Adaptive frame size according to the orbital period for completing the Savitzky–Golay process guarantees the estimation efficiency and accuracy of mean orbital elements estimation and prediction. Then, the prediction value is employed to generate the mean orbital elements difference compared with the estimation. Finally, the mean orbital elements difference is adopted to govern the satellite state detector for mode switching. Comparison simulations for both with and without state jumping are conducted, and the results demonstrate the superiority of the mean orbital elements estimator over the direct mapping method and the Savitzky–Golay filter in estimation efficiency, accuracy, and range of application.