Perturbing Forces Research Articles

Optimal design of the long-term LEO almanac by considering the atmosphere drag effects

ABSTRACT Almanac is an elegant design to help Global Navigation Satellite Systems (GNSS) signal acquisition, which has been adopted by all global satellite navigation systems. For the future low Earth orbit (LEO) navigation constellation, the almanac will be more critical due to larger constellation and signal Doppler variation, while the LEO orbit prediction is more challenging due to complex perturbation forces, especially atmospheric drag. This study introduces a novel 9-parameter almanac model for LEO constellation, leveraging the Empirical Mode Decomposition (EMD) method. Our innovative approach uniquely balances almanac accuracy and simplicity by considering the atmosphere drag effects, addressing a critical gap in existing models. The proposed almanac model is validated with four in-orbit LEO satellites at various altitudes. For the LEO with a 600 km orbit or lower, our model achieves a 50% improvement in 23-day orbit prediction accuracy compared to the classical GPS almanac model. This significant enhancement extends to visibility prediction and signal acquisition performance. Our design limits the maximum elevation angle error to less than 1.5 degrees, efficiently excluding invisible satellites during LEO navigation signal acquisition. Furthermore, for visible satellite, the proposed LEO almanac reduces the signal frequency searching range by about 20 times during acquisition, with Doppler prediction errors better than 0.5 kHz/0.3 kHz for 95% of cases. These advancements represent a substantial leap in LEO navigation technology, offering improved efficiency and accuracy for future satellite systems.

Perturbing and Oblateness's Impact on the Generalized Photogravitational Restricted Three-Body Problem

In this research work, the effects of perturbing and oblateness on the generalised photogravitational restricted three body problem (RTBP) are examined when the primary are regarded as radiation sources and oblate spheroid. The perturbing forces were included in the equations of motion that we developed for the system. The triangular libration points were derived in terms of the perturbing parameters using linear approximations, and their influence was seen. Applying Murray's criteria, we determined that the triangular libration points remained unstable due to the nature of the characteristics equation matching to the variational equations of motion of the system generated.

Decadal evolution of GPS, GLONASS, and Galileo mean orbital elements

We examine the decadal evolution of GPS, GLONASS, and Galileo satellite orbital elements, including the semi-major axis, inclination, eccentricity, right ascension of the ascending node, and the argument of perigee. We focus on the long-term changes in Keplerian elements by averaging them over several complete revolutions forming mean orbital elements giving an explanation of the main perturbing forces for each Keplerian parameter. The combined International GNSS Service (IGS) orbits are employed which were derived in the framework of IGS Repro3 for ITRF2020 preparation spanning eight years from 2013 to 2021. The semi-major axis for GPS satellites is affected by a strong resonance with Earth’s gravity field resulting in a long-period perturbation similar to a secular drift. The semi-major axes of Galileo and GLONASS do not show any large-scale rates, however, Galileo satellites are affected by the Y-bias resulting in semi-major axis drifts. A significant perturbations due to solar radiation pressure affect the semi-major axis, eccentricity, and the argument of perigee. Notably, for Galileo satellites in eccentric orbits, the signal with a one-draconitic year is evident in the semi-major axis. The evolution of the mean right ascension of the ascending node and argument of perigee is primarily characterized by nearly linear regression mainly due to even zonal harmonics of the Earth’s gravity field. The long-term evolution of eccentricity and inclination does not follow a linear trend but exhibits clear oscillations dependent on the secular drift of the right ascension of the ascending node (for inclination) or the argument of perigee (for eccentricity). Additionally, the long-term perturbation of inclination reaches its maximum when the absolute value of the Sun’s elevation angle above the orbital plane (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} angle) is at its minimum, while the eccentricity reaches its minimum simultaneously with the minimum of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} angle.

Less fuel strategies for space debris removal in Low Earth Orbit

This paper proposes less fuel strategies for space debris removal. To mitigate the risk of space debris cost-efficiently, multi-rendezvous missions are under development. On the other hand, multi-rendezvous missions often require changing orbital planes of removal satellites, which requires a huge amount of ΔV. Therefore, this study focuses on exploiting the J2 perturbation force as an auxiliary force and aims to establish maneuver rules that minimize ΔV consumption while maximizing the benefit of the J2 perturbation. The J2 perturbation equation is explored analytically, which clarifies whether the change in the semi-major axis or the inclination dominates the efficiency of the exploitation. A straightforward criterion is extracted which determines the efficient maneuver based on the initial inclination of the satellite.

Dissecting Allosteric Mutations for Antibiotic Resistance by Time-Dependent Linear Response Theory.

We report a new approach that combines molecular dynamics trajectories with time-dependent linear response theory to compute the time evolution of residue fluctuation responses to force perturbations exerted at functional sites. Applying this new approach to TEM-1 beta-lactamase, we observe that the time-resolved response profiles of allosteric sites to perturbations of TEM-1 active sites are distinct from those of non-allosteric residues. Using Fourier transformations, we convert the time domain response profiles to the frequency domain and demonstrate that the frequency space representation of the perturbation response can capture the mutational behavior of each site when applied to deep sequencing mutational data. Furthermore, we show that classification models built on perturbation responses can accurately identify distal positions that regulate antibiotic resistance. These findings provide insights into the contributions of specific residues to resistance-encoded in time-resolved perturbation response behavior and highlight the importance of this new approach in identifying allosteric mutations, opening avenues for the potential characterization of additional allosteric positions without extensive computational simulations.

Perturbation-based estimation of within-stride cycle metabolic cost

Metabolic cost greatly impacts trade-offs within a variety of human movements. Standard respiratory measurements only obtain the mean cost of a movement cycle, preventing understanding of the contributions of different phases in, for example, walking. We present a method that estimates the within-stride cost of walking by leveraging measurements under different force perturbations. The method reproduces time series with greater consistency (r = 0.55 and 0.80 in two datasets) than previous model-based estimations (r = 0.29). This perturbation-based method reveals how the cost of push-off (10%) is much smaller than would be expected from positive mechanical work (~ 70%). This work elucidates the costliest phases during walking, offering new targets for assistive devices and rehabilitation strategies.

The Trajectory Prediction of Spacecraft under the Influence of Gyroscopic Effect Generated during Non-Keplerian Motion

Due to perturbation forces and control forces, trajectories of spacecraft around the Earth are usually non-Keplerian orbits, which may result in a gyroscopic effect. To meet the complex demands of space operations in the future, the trajectory prediction of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion needs to be studied in depth. The paper investigated the trajectory of spacecraft under the gyroscopic effect generated during non-Keplerian motion. Firstly, according to the similarity between the spacecraft precession motion and the gyroscopic precession, as well as the definition of the “gyroscopic effect” of high-speed rotating bodies, the “gyroscopic effect” generated during the non-Keplerian motion of spacecraft around the earth was defined. Then, taking a continuous radial thrust orbit as an example, the dynamics equations of spacecraft under the influence of gyroscopic effect were deduced. Through theoretical analysis and numerical simulation, the trajectory of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion was investigated. Finally, the paper simulated the examples and tested the performance of the proposed method. Simulation results show that a large gyroscopic moment may be generated in some non-Keplerian motion of the spacecraft. The greater the rotational angular velocity of the orbital plane, the greater the gyroscopic moment. Due to the gyroscopic effect, there is a significant deviation in the orbit and the orbital elements compared to those without considering the gyroscopic effect, which indicates that the influence of the gyroscopic effect generated during non-Keplerian motion on the orbit of the spacecraft cannot be ignored. It can be seen from the simulation results that the gyroscopic effect has a significant influence on the trajectory of spacecraft. In some special cases, the gyroscopic effect can be utilized reasonably to save fuel and realize low-energy orbit maneuver control technology in actual space missions; but the control should be considered for the spacecraft to bring it back to the desired orbit in most cases. It is necessary to study the trajectory of spacecraft under the influence of gyroscopic effect. The method and conclusions proposed can provide a theoretical reference for spacecraft trajectory prediction and future large-scale fast orbital maneuvers to meet the needs of complex space operations.

Chaos synchronization of two coupled map lattice systems using safe reinforcement learning

When synchronizing two continuous typical chaotic systems, the state variables of the response system are usually bounded and satisfy the Lipschitz condition. This permits a universal synchronization method. In the synchronization of two high-dimensional discrete chaotic systems such as the coupled map lattice systems, the state variables of the response system often diverge, which makes it difficult to seek a universal synchronization method. To overcome this difficulty, bounded and hard constraints, which correspond to the concept of safety level III in reinforcement learning terms, on the state variables must be imposed, when the discrete response system is perturbed. We propose a universal method for synchronizing two discrete systems based on safe reinforcement learning (RL). In this method, the RL agent’s policy is used to reach the goal of synchronization and a safety layer added directly on top of the policy is used to satisfy safety level III. The safety layer consists of a one-step predictor for the perturbed response system and an action correction formulation. The one-step predictor, based on a next generation reservoir computing, is used to identify whether the next state of the perturbed system is within the chaotic domain, and if not, the action correction formula is activated to modify the corresponding perturbing force component to zero. In this way, the state of the perturbed system will remain in the bounded chaotic domain. We demonstrate that the proposed method succeeds in synchronization without divergence through a numerical example with two coupled map lattice systems, and the average synchronization time is 12.66 iteration steps over 1000 different initial conditions. The method works even when parameter mismatches and disturbances exist in the system. We compare the performance in both cases with and without the safety layer and find that successful synchronization is only possible in the former case, emphasizing the significance of the safety layer. The performance of the algorithm with optimal hyper-parameters obtained by Bayesian optimization is robust and stable.

Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system’s behavior and the extent to which it deviates from the unperturbed case.

Turbulent Gas-rich Disks at High Redshift: Bars and Bulges in a Radial Shear Flow

Recent observations of high-redshift galaxies (z ≲ 7) reveal that a substantial fraction have turbulent, gas-rich disks with well-ordered rotation and elevated levels of star formation. In some instances, disks show evidence of spiral arms, with bar-like structures. These remarkable observations have encouraged us to explore a new class of dynamically self-consistent models using our agama/Ramses hydrodynamic N-body simulation framework that mimic a plausible progenitor of the Milky Way at high redshift. We explore disk gas fractions of f gas = 0%, 20%, 40%, 60%, 80%, and 100% and track the creation of stars and metals. The high gas surface densities encourage vigorous star formation, which in turn couples with the gas to drive turbulence. We explore three distinct histories: (i) there is no ongoing accretion and the gas is used up by the star formation, (ii) the star-forming gas is replenished by cooling in the hot halo gas, and (iii) in a companion paper, we revisit these models in the presence of a strong perturbing force. At low f disk (≲0.3), where f disk is the baryon mass fraction of the disk relative to dark matter within 2.2 R disk, a bar does not form in a stellar disk; this remains true even when gas dominates the inner disk potential. For a dominant baryon disk (f disk ≳ 0.5) at all gas fractions, the turbulent gas forms a strong radial shear flow that leads to an intermittent star-forming bar within about 500 Myr; turbulent gas speeds up the formation of bars compared to gas-free models. For f gas ≲ 60%, all bars survive, but for higher gas fractions, the bar devolves into a central bulge after 1 Gyr. The star-forming bars are reminiscent of recent discoveries in high-redshift Atacama Large Millimeter/submillimeter Array observations of gaseous disks.

Orbit Determination of High Orbit Spacecraft based on BDS-3 using Extended Kalman Filter

The positioning of highly elliptical orbit (HEO) spacecraft is very important in deep space exploration and other missions. The Beidou Navigation Satellite System (BDS-3), which was completed in 2020, has put forward new ideas for using GNSS technology to make up for the lack of earth-based TT&C systems. At the same time, the selection of the gravity field order and the perturbation forces must be considered when using dynamical methods for HEO spacecraft positioning. In this paper, simulation experiments are carried out based on the Two-Line Orbital Element (TLE) data of BDS. Two HEO satellites with different semimajor-axis (67509.6 km, 212857.3 km) are selected as the target spacecraft orbits. The single point positioning (SPP) method and Extended Kalman Filter (EKF) method are used for HEO spacecrafts positioning respectively. The experiments show that a 20×20 order gravity field model can be chosen for the orbital integral of HEO spacecraft orbits, and the integration error caused by solar gravity and lunar gravity should be taken into account with the change of orbital altitude. Adding Geostationary Orbit (GEO) and Inclined GeoSynchronous Orbit (IGSO) navigation satellites improved the visibility of these two orbits by 19.45% and 16.64%, respectively, and improved the GDOP value by 14.1% and 3.8%, respectively, compared to observing MEO satellites only. The use of the EKF method can effectively improve the positioning accuracy of the HEO spacecraft compared to the SPP method. For the spacecraft in HEO-1, the RMS value of the positioning errors of the EKF method was 67.82 m, and the accuracy of each direction was improved by 44.28%, 38.85%, and 38.62%, respectively. For the spacecraft in HEO-2, the positioning errors in the x direction of EKF method was within 12 km and within 2 km in the y and z directions. The accuracy of these three directions was improved by 84.91%, 79.24%, and 58.64%, respectively.

An Analytical Method for Accuracy Analysis of Close Proximity Rendezvous in Space Based on an Improved C-W Equation under Perturbation Effects

In order to address the issue of quantitatively solving the impact of perturbation forces and initial errors on rendezvous accuracy, traditional analytical methods are not suitable, and the calculation steps for statistical methods based on Monte Carlo simulation analysis are complex and computationally time-consuming. To overcome these challenges, this paper proposes a method for analysing rendezvous accuracy based on an improved relative motion dynamics model. Describing the relative motion between a sub-spacecraft and a target spacecraft by an improved Clohessy-Wiltshire (C-W) equation. By employing the derived state transition matrix from the model, it is possible to calculate the error propagation during the rendezvous process and express the rendezvous accuracy analytically. Through simulation examples, the proposed method proves to be both accurate and efficient in analysing the influence of perturbation forces and random errors such as initial position and velocity on rendezvous accuracy. This study verifies the correctness and effectiveness of the approach.

A six degrees-of-freedom cable-driven robotic platform for head-neck movement.

This paper introduces a novel cable-driven robotic platform that enables six degrees-of-freedom (DoF) natural head-neck movements. Poor postural control of the head-neck can be a debilitating symptom of neurological disorders such as amyotrophic lateral sclerosis and cerebral palsy. Current treatments using static neck collars are inadequate, and there is a need to develop new devices to empower movements and facilitate physical rehabilitation of the head-neck. State-of-the-art neck exoskeletons using lower DoF mechanisms with rigid linkages are limited by their hard motion constraints imposed on head-neck movements. By contrast, the cable-driven robot presented in this paper does not constrain motion and enables wide-range, 6-DoF control of the head-neck. We present the mechatronic design, validation, and control implementations of this robot, as well as a human experiment to demonstrate a potential use case of this versatile robot for rehabilitation. Participants were engaged in a target reaching task while the robot applied both assistive and resistive moments on the head during the task. Our results show that neck muscle activation increased by 19% when moving the head against resistance and decreased by 28-43% when assisted by the robot. Overall, these results provide a scientific justification for further research in enabling movement and identifying personalized rehabilitation for motor training. Beyond rehabilitation, other applications such as applying force perturbations on the head to study sensory integration and applying traction to achieve pain relief may benefit from the innovation of this robotic platform which is capable of applying controlled 6-DoF forces/moments on the head.

Evidence of apsidal motion and a possible co-moving companion star detected in the WASP-19 system

Context. Love numbers measure the reaction of a celestial body to perturbing forces, such as the centrifugal force caused by rotation, or tidal forces resulting from the interaction with a companion body. These parameters are related to the interior density profile. The non-point mass nature of the host star and a planet orbiting around each other contributes to the periastron precession. The rate of this precession is characterized mainly by the second-order Love number, which offers an opportunity to determine its value. When it is known, the planetary interior structure can be studied with one additional constraint beyond the mass, radius, and orbital parameters. Aims. We aim to re-determine the orbital period, eccentricity, and argument of the periastron for WASP-19Ab, along with a study of its periastron precession rate. We calculated the planetary Love number from the observed periastron precession rate, based on the assumption of the stellar Love number from stellar evolutionary models. Methods. We collected all available radial velocity (RV) data, along with the transit and occultation times from the previous investigations of the system. We supplemented the data set with 19 new RV data points of the host star WASP-19A obtained by HARPS. Here, we summarize the technique for modeling the RV observations and the photometric transit timing variations (TTVs) to determine the rate of periastron precession in this system for the first time. Results. We excluded the presence of a second possible planet up to a period of ~4200 d and with a radial velocity amplitude bigger than ≃ 1 m s−1. We show that a constant period is not able to reproduce the observed radial velocities. We also investigated and excluded the possibility of tidal decay and long-term acceleration in the system. However, the inclusion of a small periastron precession term did indeed improve the quality of the fit. We measured the periastron precession rate to be 233−35+25″d−1. By assuming synchronous rotation for the planet, it indicates a k2 Love number of 0.20−0.03+0.02 for WASP-19Ab. Conclusions. The derived k2,p value of the planet has the same order of magnitude as the estimated fluid Love number of other Jupiter-sized exoplanets (WASP-18Ab, WASP-103b, and WASP-121b). A low value of k2,p indicates a higher concentration of mass toward the planetary nucleus.

A metagenomics pipeline reveals insertion sequence-driven evolution of the microbiota

Insertion sequence (IS) elements are mobile genetic elements in bacterial genomes that support adaptation. We developed a database of IS elements coupled to a computational pipeline that identifies IS element insertions in the microbiota. We discovered that diverse IS elements insert into the genomes of intestinal bacteria regardless of human host lifestyle. These insertions target bacterial accessory genes that aid in their adaptation to unique environmental conditions. Using IS expansion in Bacteroides, we show that IS activity leads to the insertion of "hot spots" in accessory genes. We show that IS insertions are stable and can be transferred between humans. Extreme environmental perturbations force IS elements to fall out of the microbiota, and many fail to rebound following homeostasis. Our work shows that IS elements drive bacterial genome diversification within the microbiota and establishes a framework for understanding how strain-level variation within the microbiota impacts human health.

On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations

On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations

Periodicity and lifetime of orbits around elongated asteroids

This paper presents dynamics and control of orbits around an asteroid that is modelled as a uniformly rotating homogeneous rectangular parallelepiped (HRP). Aside from the non-uniform gravitational field of the asteroid, we include the solar radiation pressure (SRP) as a perturbing force. A simple model based on the polyhedral method is employed for calculating the gravity around the HRP. First, circular periodic orbits are identified both in the presence and absence of solar radiation pressure. Then, families of general non-circular periodic orbits in the presence of SRP are determined and subsequently analysed for stability. Next, for a general orbit in the equatorial plane, its stability against a catastrophic impact of an orbiting spacecraft onto the asteroid’s surface is checked in the presence of SRP. Orbits, where the solar radiation pressure is less/more dominant over the central body’s gravity, are identified with the aim of finding the best orbits for parking a spacecraft. Then, for long-period orbits, SRP is averaged and the time averaged evolution of the orbital elements is obtained. For a special set of initial condition, a closed form solution for the evolution of the orbital eccentricity is obtained. Using this solution, a lower limit for the life-time of a spacecraft that is left uncontrolled is derived in a closed form. Finally, active control strategies are developed for orbit-keeping ofspacecraft for any choice of orbital parameters. A linear-quadratic regulator (LQR) is designed to track a given Keplerian orbit with minimum fuel expenditure. Fuel expenditure on various orbits are calculated and compared to determine the orbits of cheapest operation. The work presented is applicable to small body (asteroids and comets) exploration missions which require online cancellation of the perturbing forces with minimal knowledge of the accurate shape, size, and composition of the small body prior to the mission.

Impact of Earth Radiation Pressure Physical Analytical Model on Satellite Laser Ranging Orbit Determination

SLR (Satellite Laser Ranging) is a kind of important space geodesy technique for the establishment of a Terrestrial Reference Frame (TRF) and determination of EOP (Earth Orientation Parameters). It determines the origin and scale factor of TRF. The accuracy of future TRF is 1 mm. This requires improving the SLR data processing accuracy and importing higher accuracy SLR satellite data. The Earth Radiation Pressure (ERP) is an important perturbation force for SLR satellites. The traditional Earth radiation pressure model for SLR satellites is the simple Cannon Ball model. This paper establishes the Box-Wing physical Earth radiation pressure model for SLR satellites and takes Lageos-1 as an example to evaluate the physical analytical model. The Lageos-1 is divided into two blocks: metal shell and corner reflectors. The area and optical characteristics of each block are analyzed according to the requirements of three kinds of Earth albedo and emissivity models of point source, experience and grid models. The results show that after importing the physical analytical Earth radiation pressure model, the empirical force acceleration in the T direction is significantly reduced and the orbit overlap arc precision is about 3 mm smaller than that of the original model. The orbit prediction results show that the prediction accuracy of the new Earth radiation pressure model has generally improved significantly. The maximum improvement percentage of the physical analytical model is 12%, 16%, 28% and 25% respectively in the prediction arc length of 1 day, 3 days, 5 days and 7 days. The physical grid model performs the best with the increase of prediction arc length.

A pilot study: effect of somatosensory loss on motor corrections in response to unknown loads in a reaching task by chronic stroke survivors.

Despite recent studies indicating a significant correlation between somatosensory deficits and rehabilitation outcomes, how prevailing somatosensory deficits affect stroke survivors' ability to correct their movements and recover overall remains unclear. To explore how major deficits in somatosensory systems impede stroke survivors' motor correction to various external loads, we conducted a study with 13 chronic stroke survivors who had hemiparesis. An inertial, elastic, or viscous load, which was designed to impose perturbing forces with various force profiles, was introduced unexpectedly during the reaching task using a programmable haptic robot. Participants' proprioception and cutaneous sensation were also assessed using passive movement detection, finger-to-nose, mirror, repositioning, and Weinstein pressure tests. These measures were then analyzed to determine whether the somatosensory measures significantly correlated with the estimated reaching performance parameters, such as initial directional error, positional deviation, velocity deviations, and speed of motor correction were measured.Of 13 participants, 5 had impaired proprioception, as they could not recognize the passive movement of their elbow joint, and they kept showing larger initial directional errors even after the familiarization block. Such continuously found inaccurate initial movement direction might be correlated with the inability to develop the spatial body map especially for calculating the initial joint torques when starting the reaching movement. Regardless of whether proprioception was impaired or not, all participants could show the stabilized, constant reaching movement trajectories. This highlights the role of proprioception especially in the execution of a planned movement at the early stage of reaching movement.

Analysis of albedo and disc effects in the generalized restricted four-body problem

This manuscript explores the Generalized Restricted Four-Body Problem within the context of radiation pressure, the albedo effect, oblateness, and a disc-like structure that orbits around the primary bodies. We have considered that one of the primaries is a bigger primary, and the rest of the two smaller primaries are of equal masses, in which one of the smaller primaries is considered as a black body. Moreover, the perturbing forces by the effect of radiation pressure and oblateness are considered in the bigger primary. The effect of albedo and oblateness due to the second smaller primary is also taken into count. This study yields nine equilibrium points corresponding to various parameter values, including three collinear and six non-collinear equilibria. We conduct an analysis of the equilibrium points, their linear stability, and the motion around them. In the context of the considered parameter set, certain collinear equilibrium points exhibit stability, while others are unstable. Additionally, most of the non-collinear equilibrium points display linear stability. We also investigate variations in Jacobi’s constant and the positions of existing equilibrium points caused by the albedo and disc effects. It is found that the value of Jacobi constant CLj decreases with an increase in the mass parameter μ at the collinear points, which results in an expansion in the prohibited region. The inhibited zone of motion of the infinitesimal body is shown for different sets of parameters.