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The primary objective of this paper is to construct an analytical model for determining the total duration of eclipse events of satellites. The approach is based on the assumption that the trace formed in the orbital plane, cutting body's shadow under the classical conical shadow model, can be described as an ellipse. This allows for the derivation of its parameters through the use of classical orbital elements and solar position in the body's centric frame. Consequently, the problem of identifying satellite occultation events is simplified to searching for points of intersection between two ellipses: the satellite orbit and the shadow. The developed model has been demonstrated to be applicable for a wide range of inclinations, with the exception of cases where the orbital plane of the satellite's motion coincides with that of the sun's in the body-centric frame. It is shown that the shadow function constructed under the aforementioned assumptions can be simplified in the cylindrical shadow model. Several simplifications are provided in the research. The paper also considers the extension of the model to account for the non-spherical shape of celestial bodies and presents an algorithm for accounting for changes in eclipse duration caused by the heliocentric motion of celestial bodies. The model has been validated through numerous tests with a numerical algorithm and satellite real data, as well as with other analytical models. • An analytical method for calculating the total duration of satellite eclipses has been developed. • Developed approach can be applied to wide range of satellite orbits either hyperbolical or elliptical ones. • The equations that depend on the satellite's orbital elements and solar longitude to predict satellite eclipses are obtained. • Simplification of the problem in certain scenarios, allowing for rigorous and simple algebraic solutions are provided. [ABSTRACT FROM AUTHOR]

The regional coverage satellite constellations are in demand for fulfilling earth observation needs of specific user regions of interest as opposed to global coverage thus enhancing the revisit period for the area. In this paper, we present a few key mission aspects of the regional coverage constellation designed and operated by the Indian Space Research Organization (ISRO) in low earth orbit. ISRO developed three X-Band Synthetic Aperture Radar (SAR) Earth Observation satellites and placed them in three inclined orbit planes to enhance the Indian region's coverage. This is India's first inclined orbit constellation designed for remote sensing applications in low earth orbit. The satellites were built around a standard bus carrying a Synthetic Aperture Radar payload with a deployable Radial Rib Antenna (RRA). They were designed to achieve a high agility capability. As SAR sensors are capable of all-weather, day, and night imaging; thus, most suitable in inclined orbits where the illumination conditions vary continuously for imaging. Though the inclined orbits provide more revisit opportunities to the region of interest, their characteristics pose challenges in mission design and operations. Though the mission design and planning involved a host of elements, this paper brings out the details of a few key mission analysis elements, planning aspects and operations that were critical in the course of various mission phases. The mission analysis included mission-specific requirements like launch windows selection for the constellation and reference attitude generation specific to inclined orbit geometry. Mission planning had to take care of Radial Rib Antenna (RRA) deployment requirements which were very critical for the mission, apart from taking care of individual subsystem requirements. The SAR payload data product quality and targeting accuracy are very sensitive to the satellite image point range (vis-a-vis SAR operation data window). Extensive post-launch calibration activity was carried out to meet all these mission requirements and data product specifications. The challenge was in fixing the payload beam alignment and fixing the uncertainties in onboard and ground computations. The paper also describes the methods of fixing all possible error sources affecting the high-resolution SAR payload performance. • The regional coverage satellite constellations are in demand for area targets coverage. • Inclined orbit constellations are more suitable for regional coverage using SAR sensors. • Mission operations plans need to consider all the specific requirements of spacecraft systems. • Pre-launch and post -launch calibrations of sensors is mandatory for achieving system performance. [ABSTRACT FROM AUTHOR]

This paper examines the effect of shortening the post-mission disposal (PMD) orbit lifetime (remaining orbit lifetime after PMD) from 25 years to 5 or 1 year. Using NEODEEM, the debris evolutionary model developed by Kyushu University and JAXA, the change in the orbital environment at various altitude bands for long-term stability and short-term safety are discussed. It was confirmed that the PMD compliance rate is more important than shortening the orbit lifetime for improving the long-term stability of the orbital environment. In the short term, the 5- or 1-year rule reduced the collision rate and collision avoidance frequency at an altitude below 700 km, more than the 25-year rule, thus shortening the PMD orbit lifetime improves short-term safety, especially at low altitudes. The paper also evaluates the effect of large constellations (LCs) and it was shown that shortening the PMD orbit lifetime of LCs improves short-term safety, but the long-term impact is dominated by the number of LCs that remain at high operational altitudes due to PMD failure. It shows that the post-mission disposal lifetime and required compliance rate should be set according to the number and size of objects expected to be launched in the future. • The effect of shortening post-mission-disposal lifetime from 25 years are shown. • Short-term safety can be improved by 5-year rule or 1-year rule. • PMD compliance rate is more important for the long-term stability. • Difference between an elliptical and a circular orbit for PMD is shown. • PMD requirement changed according to the characteristics of the large constellation. [ABSTRACT FROM AUTHOR]

Low-thrust trajectory design in the context of the three-body problem, particularly in the vicinity of liberation points, is addressed in this paper with a focus on efficiency and accuracy. The Fourier series, previously successful in approximating near-coplanar low-thrust trajectories within two-body dynamics, is applied to the challenging landscape of the three-body problem, marked by instability and nonlinearity. This paper introduces a novel approach for constructing an initial guess trajectory, that combines coast arcs from periodic orbits and intermediate trajectory arcs from other natural dynamical structures. The resulting initial guess trajectory is instrumental in generating efficient initial estimates for the coefficients of the Fourier series. The study encompasses the analysis of homoclinic and heteroclinic transfers in both two-dimensional and three-dimensional scenarios. The approximated trajectories derived from this methodology serve as invaluable starting points for high-fidelity optimization solvers, offering promise for enhancing the precision and efficiency of low-thrust transfers in cislunar space. • The shape method based on Fourier series is applied to the initial design of the transfer trajectories between periodic orbits in cislunar space. • An innovative approach to construct a continuous initial guess trajectory is introduced to derive initial guess values for the coefficients of Fourier terms. • An accurate approximation of the optimal transfer trajectory can be rapidly obtained. [ABSTRACT FROM AUTHOR]

Comet Interceptor (Comet-I) was selected in June 2019 as the first ESA F-Class mission and aims to explore a pristine comet, which will visit the inner Solar System for the first time. Comet-I will hitch a ride to a Sun-Earth L2 quasi-halo orbit, as a co-passenger in ESA's M4 ARIEL's launch. At the time of writing, this is scheduled for 2029. It will then remain there awaiting the right departure conditions to leave definitively and intercept a newly discovered comet. Comet-I will be the first mission to be designed and launched without an already identified target. Given the latter, the Comet-I Target Identification Working Group is tasked with the continuous follow-up of newly discovered comets, to analyse their characteristics as virtual targets for Comet-I. The goal of the paper is to inform the decision-making process that will eventually be necessary to commit Comet-I spacecraft to its final target. Within this context, this paper presents a trajectory optimization process based on Primer Vector theory that considers intercept trajectories with multiple revolutions and multiple deep space manoeuvres (DSM). The process is applied to 21 long period comets, which were discovered since July 1, 2020 and whose characteristics are of interest for the Comet-I mission. In fact, one of the latest of these recently discovered comets, C/2023H2, is the most accessible virtual target discovered at the time of writing, with delta-V intercept costs well within Comet-I capabilities. A complete launch window analysis is thus presented for C/2023H2, which accounts not only for the most optimal delta-V intercept transfer, but also considers all launch options that satisfy all Comet-I's current boundary conditions and flyby constraints. A systematic launch window analysis is made possible by a grid search approach on which departure and fly-by dates are fixed and the remaining design variables, including the times for manoeuvres and their Δ v impulse vector, are optimized via Primer Vector theory. This allows to understand the latest possible departure date, but also the sensitivity to departure and arrival dates of key encounter characteristics such as relative fly-by speed, the solar aspect angle and the Earth distance. • A Primer Vector Theory-based trajectory optimization tool is shown, tailored for ESA's Comet Interceptor (Comet-I). • The method supports trajectories with multiple revolutions around the Sun and multiple impulses. • The method allows rapid grid search over the search space, finding the lowest cost trajectory and other notable solutions. • A novel analysis of the launch window is presented, contributing to the decision-making process of Comet-I. • A multi-manoeuvre strategy benefits Comet-I's trajectory design, lowering the delta-V cost and improving mission flexibility. [ABSTRACT FROM AUTHOR]

This paper analyzes the change in the heliocentric orbital elements due to the implementation of aerogravity and powered aerogravity assist maneuvers. Three cost functions were selected to maximize the planetocentric latitude, longitude, and velocity at the end of the atmospheric flight. An optimal control problem was solved to guide a spaceplane passing above the three inner planets: Venus, Earth, and Mars. The planets were selected because they have been relevant for gravity assists, and previous studies suggest that taking advantage of their atmospheres could increase the effects of the close approach. The research aims to analyze the variation in the heliocentric orbital elements of the trajectories after performing optimal aerogravity-assists and powered aerogravity-assisted maneuvers at high atmospheric altitudes. The trajectories were calculated via nonlinear programming to find the history of the control variables: angle of attack, bank angle, and thrust. Low-fidelity gravity and atmosphere models were implemented to evaluate this proof of concept. The optimization converged for all cases, and results show that maximization of the longitude increases the duration of the atmospheric flight, increasing the turning angle by almost twice the value of a single gravity assist. Furthermore, it reduces the energy and semimajor axis in half for approach angles between 20 and 90°, saving more than 10 km/s on propulsion. Maximizing the velocity with propulsion increases the semimajor axis by more than 1.1 times the semimajor axis of the respective planet, and the optimal latitude presents a change in inclination of more than 1.0°. This maneuver could be applied to collect atmospheric samples or increase the coverage above the planet of interest. Those kinds of applications are described at the end of this paper, including a brief discussion on the maturity of this technology. • Optimal control in aerogravity assists maneuvers at high atmospheric altitudes. • The maneuvers increase the values of the heliocentric orbital elements. • Multiple advantages over the gravity assist are observed. • Spaceplanes are feasible for performing those maneuvers. • Atmospheric passages at high altitudes reduce the risks associated with low altitudes. [ABSTRACT FROM AUTHOR]

Laser inter-satellite links (LISLs) are crucial for enabling rapid information exchange within low earth orbit (LEO) constellations. Previous research on laser link establishment often relied on the idealized probability density function (PDF) of the pointing uncertainty regions (PURs) when designing scan-and-capture methods, neglecting the impact of various practical uncertainties. To address the above issues, there is an urgent need to analyze the practical uncertainties to enhance the stability and reliability of LISL. This paper first provides a comprehensive introduction to the alignment process in LISL and mathematically formulates typical sources of uncertainty errors. Subsequently, a generalized system model (GSM) for laser link establishment was established at three stages: Orbit, Attitude, and Laser terminal. Finally, we integrate uncertainty models into the GSM and propose a PUR generating method to obtain precise PDFs. The research method proposed in this study can consider the influence of multiple uncertainties and generate the PDF for the PURs. Compared with traditional research, the PDF obtained by fitting the oscillation range considering dynamics is more detailed. By analyzing the PDF generated by typical uncertainty errors, it is observed that the orbit initial uncertainty may be the predominant factor influencing the PUR. • A generalized system model for the laser alignment process is established. • A method to generate the model for the pointing uncertainty region is proposed. • Envelope curve is used to describe the oscillation range for deviation samples. • The impact of different uncertainty errors on the uncertainty region is explored. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimizing minimum-time and minimum-propellant many-revolution low-thrust geocentric orbit-raising maneuvers to an arbitrary target. The proposed direct single-shooting technique utilizes the regularized h , e element set as well as analytical models for ephemeris, shadow geometry, and thrust magnitude for ease of the optimization procedure. Third body and J 2 effects are included for higher fidelity of the computed solution. The gradient information supplied through adjoint sensitivities facilitates the convergence of the numerical optimization scheme. We also propose a new automated, fast and robust initial guess generation methodology by solving a sequence of unconstrained optimization orbit-raising sub-problems. The performance of the developed algorithm is demonstrated for orbit-raising to a variety of targets: the geosynchronous equatorial orbit, the Molniya orbit, and a near-rectilinear halo orbit. • A new low-thrust trajectory algorithm is developed using adjoint sensitivities. • The sequentially generated initial guesses are fast and robust to calculate. • An end-to-end optimization formulation computes minimum-time and minimum-fuel transfers. [ABSTRACT FROM AUTHOR]

Satellite formation plays an important role in space missions such as on-orbit services and distributed space facilities. In these missions, hovering in a bounded range is one of the core tasks, but hovering technologies for the chief satellite in an elliptical orbit have been rarely investigated. Given the boundary constraints of relative motion between the chief and deputy satellites, this paper proposes two models for the design and control of hovering formation near an elliptical reference orbit through impulse: (1) the revisiting hovering formation model, which forces the deputy satellite to revisit the same relative position and maintains the formation via impulses; (2) the sequential-impulse-control hovering formation model, which uses a sequence of impulses to ensure the deputy satellite flies within the given boundary. Unlike the revisiting hovering formation model, this model does not require a fixed revisiting point, so the satellite's trajectory is more flexible. The geometrical properties, formation maintenance strategy, and impulse-control solution for both models are investigated in detail. Finally, numerical simulations are conducted to verify the advantages of the proposed methods over other conventional methods, suggesting their wide applications in practical space missions. • Two impulsive-control models are proposed for bounded hovering formation in elliptical orbit. • The proposed methods support in-plane, out-of-plane, and three-dimension hovering formations. • The in-plane and out-of-plane controls are decoupled to decrease control complexity and difficulty. • Different factors on the fuel cost are analyzed to provide a reference for practical engineering. [ABSTRACT FROM AUTHOR]

Lunisolar resonances shape the dynamics in the MEO region and have the effect of increasing an object's eccentricity possibly up to a value so high that the orbit's perigee reaches the atmosphere and friction determines the re-entry. The focus of this paper is the eccentricity growth phenomenon observed for navigation satellites. In particular, starting from a secular Hamiltonian model, analytical estimates for the maximum eccentricity reachable along an inclination-only dependent lunisolar resonance are derived as a function of the initial inclination. Also, trajectories that minimize an object's lifetime are studied, and analytical estimates for such a minimum lifetime are provided as a function of the initial eccentricity of the object. In addition, lifetime cartography maps are presented in the plane of the argument of perigee and the longitude of the ascending node. • Analytical estimates for the maximum eccentricity along lunisolar resonances. • Analytic formulae of minimum satellite lifetime at GPS and Galileo altitudes. • Litetime maps at GPS and Galileo altitudes in (ω)-(Ω) plane. [ABSTRACT FROM AUTHOR]

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. • Radiation perturbed periodic orbits around a parallelepiped-asteroid are obtained. • A boundary for stable non-crossing orbits is also analytically derived. • Closed form solutions for far-range orbits are obtained through Lagrange averaging. • Using the above, an analytical estimate for the lifetime of the orbit is presented. • A linear quadratic regulator (LQR) is employed to obtain ideal parking stations. [ABSTRACT FROM AUTHOR]

Separation and reconfiguration of stacked satellites in orbit is an effective method for constructing large space structures. This paper investigates the dynamics of a stacked satellite system (SSS) during the separation and reconfiguration process. Firstly, the dynamic model of the SSS is established via the natural coordinate formulation (NCF) to conveniently handle the time-varying constraints between satellites. Then, the separation and reconfiguration strategies are proposed for the SSS including the reconstruction step between two configurations. To ensure collision-free satellite assembly, a proportional differential (PD) controller combined with a potential function is introduced. Additionally, a docking mechanism is designed, considering collision force constraints during satellite docking assembly. Finally, several numerical simulations are conducted to demonstrate the effectiveness of the separation and assembly strategies. • An orbital dynamic model of a stacked satellite system (SSS) is established. • A collision detection algorithm for the docking mechanism is introduced. • A PD controller law for the collision-free assembly of satellites is designed. • The dynamics for reconfiguration and assembly of the SSS is studied. [ABSTRACT FROM AUTHOR]

Liquid crystal diffractive sails can generate controllable tangential radiation pressures, which have advantages in the Solar Polar Imager mission (SPI). This paper proposes a composite diffractive sail design consisting of an ideal passive diffraction grating sail and liquid crystal polarization gratings (LCPGs). The main diffractive grating sail generates thrust for orbital transfer with a sun-facing attitude. An optimal 3.8-year transfer trajectory is obtained by an improved direct method. Small-area LCPGs distributed around the edge are used for three-axis attitude control. The LCPGs can continuously modulate the force and torque by controlling the applied voltage based on the electro-optical characteristic of liquid crystal materials. A control strategy, including an adaptive attitude-tracking PD controller and a control allocation method, is designed to track the attitude profile generated by the transfer trajectory. Finally, the attitude-orbit coupling dynamics are used to simulate the whole process, and the results show that orbital insertion errors are minor. • A combined diffractive solar sail model using liquid crystal polarization gratings. • Independent and controllable three-axis attitude control of diffractive solar sails. • Optimizing transfer trajectory for solar polar mission based on the proposed sail. • An adaptive attitude-tracking PD controller and a control allocation method. [ABSTRACT FROM AUTHOR]

Controlled de-orbiting is crucial for a low earth orbiting (LEO) satellite or capsule intending to land in a desired location and to prevent damage to people and property on the ground caused by debris. Drag modulation is one possible mechanism to control de-orbiting, exploiting atmospheric drag variation to reduce the necessary orbital energy from the initial conditions to the re-entry interface. In this context, this paper proposes a novel targeted de-orbiting Artificial Neural Network (ANN) and drag-based guidance algorithm for a LEO artificial satellite. It relies on the combination of empirical and analytical relations with Deep Neural Networks (DNNs) to estimate the main parameters of the optimal control law in real time. The training set is composed of several optimal control solutions generated with a previously developed optimal control algorithm, exploiting the formulation in equinoctial modified orbital parameters to manage the large time scale of the problem and the computational cost. An innovative procedure for the training set generation led to the achievement of general results with a limited number of samples. The successful outcome of the guidance algorithm on over 1000 cases demonstrates its robustness and generalization of results. To conclude, a Linear Quadratic Regulator (LQR) feedback control is applied to one case to deal with a more realistic and uncertain density model. • Analytical optimal guidance for a satellite de-orbiting from Low Earth Orbit. • A novel approach based on Deep Neural Networks. • Prediction of the key parameters of the optimal control law in real time. • A Monte Carlo analysis showed the algorithm's robustness and generalization. • Successful feedback control thanks to a Linear Quadratic Regulator (LQR). [ABSTRACT FROM AUTHOR]

Orbiting solar reflectors (OSRs) are flat, thin and lightweight reflective structures that are proposed to enhance terrestrial solar energy generation by illuminating large terrestrial solar power plants locally around dawn/dusk and during night hours. The incorporation of OSRs into terrestrial energy systems may offset the daylight-only limitation of terrestrial solar energy. However, the quantity of solar energy delivered to the Earth's surface remains low due to short duration of orbital passes and the low density of the reflected solar power due to large slant ranges. To compensate for these, this paper proposes a constellation of multiple reflectors in low-Earth orbit for scalable enhancement of the quantity of energy delivered. Circular near-polar orbits of 1000 km altitude in the terminator region are considered in a Walker-type constellation for a preliminary analysis. Starting from a simplified approach, the equations of Walker constellations describing the distribution of the reflectors are first modified by introducing a phasing parameter to ensure repeating pass-geometry over solar power farms. This approach allows for a single groundtrack optimisation to define the constellation, which was carried out by a genetic algorithm for single and two reflectors per orbit with an objective function defined as the total quantity of energy delivered per day, to existing and hypothetical solar power projects around the Earth. When full-scale constellations are considered with a number of reflectors, the quantity of solar energy delivered is substantial in the broader context of global terrestrial solar energy generation. • Terrestrial solar energy enhancement by constellation of orbiting reflectors is proposed. • Scalable, predictable and continuous solar energy from space is aimed. • Walker constellation equations are modified for repeating reflector passes. • Groundtrack optimised by genetic algorithm to maximise daily energy delivery. • Quantity of daily solar energy delivered is considerable in the global context. [ABSTRACT FROM AUTHOR]

Space debris near the synchronous orbit poses significant collision risks to spacecraft in this area. Therefore, it is necessary to analyze the orbital dynamics of space debris in order to predict its orbital evolution and prevent it from colliding with the spacecraft. Due to the combined effect of the dissipative forces and Earth's 1:1 tesseral resonance, the space debris with high area-to-mass ratio near the synchronous orbit exhibits two special dynamical behaviors: resonance capture and resonance jump. By using a simplified model, this paper analyzes in detail the orbital evolution of the debris of the resonance capture and resonance jump, and explores the conditions for their occurrence. It is found that the dynamical behavior of space debris around the resonance capture or resonance jump is highly sensitive to its initial conditions. In addition, the long-term direct numerical integrations with the full dynamical model for the orbital evolution of the debris are performed. The difference between the phase space parameters of the resonance capture and resonance jump for space debris is discussed, and the pendulum-like oscillation of the resonant angle is also studied. • Resonance capture and resonance jump for space debris around the synchronous orbit. • Initial conditions of resonance capture and resonance jump of space debris are found. • Resonance capture and resonance jump of debris are sensitive to initial conditions. • Resonant angle of near-synchronous debris exhibits pendulum-like oscillation. [ABSTRACT FROM AUTHOR]

The rotating detonation rocket engine has certain advantages in propulsion performance and is expected to develop into a new type of attitude/orbit control power device. In this paper, an experimental investigation on the detonation propagation characteristics during the short-time pulse operating process of rotating detonation combustor (RDC) was performed. A 60-mm RDC was employed, and the H 2 and oxygen-rich air were used as the reactant. The results show that the experiment can successfully achieve rotating detonation mode when the RDC is operating with a 10-Hz pulse frequency. With the increase of oxidizer mass flow rate, the velocity and pressure of the detonation wave will increase. The average propagation frequency of the detonation wave shows a trend of first increasing and then slightly decreasing as increasing the equivalence ratio. There is a large velocity fluctuation in the RDC pulse operation, and the stability of the detonation wave is significantly affected by the equivalence ratio. The propagation velocity and stability of the detonation wave can be improved by increasing the supply mass flow rate or equivalence ratio with a certain condition. When the equivalence ratio is larger than 0.7, the establishment time of the detonation wave is less than 1 ms, which can meet the requirement of the fast response when the RDC is applied to attitude control engine. [ABSTRACT FROM AUTHOR]

This study introduces a new method to estimate the orbital parameters (inclination, nodal precession rate, and right ascension of the ascending node) of the broken-up object using in-situ debris measurements. To reduce collision probability with tiny debris generated from breakups of satellites, it is required to identify the origin of breakups and predict the orbit of debris. In general, small debris cannot be tracked from the ground, thus an in-situ measurement is an effective method to detect sub-millimeter-sized debris. Previous studies developed a method to identify the location of breakup origin from an in-situ measurement, however, it can be applied to an ideal situation where the detection occurs at the intersection of the orbit planes. This study introduces a new method to estimate the orbital parameters by fitting the model of geocentric declination to the measurement data. This method can be applied to practical situations that cannot be validated in previous studies. This paper also adopts iteratively reweighted least squares to improve estimation accuracy and mitigate initial value dependencies. [Display omitted] • A New method to estimate the orbital parameters of the broken-up object is derived. • Origin identification of breakup events in practical situations is simulated and validated. • Estimation accuracy is improved by adopting iteratively reweighted least squares. [ABSTRACT FROM AUTHOR]

Pseudo-arclength continuation is a scheme used to generate a set of solutions for nonlinear equations and has been applied in numerous fields. In continuation schemes, solutions are obtained by tracking a parameter associated with the system as it varies, thereby creating a solution path. Pseudo-arclength continuation employs the nullspace vector, which is tangent to the path, as an approximation of the arclength in order to determine the direction of variation at each point on the path. However, the nullspace vector has both positive and negative solutions that are equally valid, leading to uncertainty in the direction of travel along the path at each location. Selecting the wrong nullspace vector can result in returning to a previously located solution instead of continuing the mapping of the solution path. Techniques to ensure consistent path direction have been developed; however, their efficacy does not extend to all scenarios. This paper addresses this gap by introducing a "flipping condition" to track previously determined path directions and ensure continuous following of the same path direction. A clear description of the process used to incorporate the flipping condition into the pseudo-arclength continuation scheme, practical implementation of the scheme, and examples demonstrating its application to the nonlinear circular restricted three-body problem (CR3BP), is provided. The inclusion of the flipping condition ensures a consistent direction of travel along the solution path and allows for families of solutions to be developed. • Pseudo-arclength continuation develops solutions to nonlinear equations along a path. • Uncertainty in path direction comes from equally valid signs of the nullspace. • Previously-located solutions are repeatedly found without a consistent path direction. • Implementation process for pseudo-arclength continuation to track path direction. • Application to periodic orbits families in the circular restricted three-body problem. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network. • Uncertainty on the initial orbit determination is reduced using other sensor data. • Measurement outliers are detected and isolated. • Multifidelity methods are used for fast and accurate uncertainty propagation. • Robustness of batch orbit determination tools is improved. [ABSTRACT FROM AUTHOR]

In the exploration of celestial bodies, including planets, moons, and asteroids, it is useful to identify stable orbits in which the orbital elements remain, on average, constant (referred to as frozen orbits). This paper aims to investigate the feasibility of frozen orbits for a small body, such as a probe, orbiting a main body under the perturbation due to the gravitational attraction of an inner third-body, on a circular (or slightly eccentric) orbit coplanar with the main body equator, by means of an approach based on mean element theory. The disturbing potential has been developed in Legendre polynomials up to order l = 5 (triakontadipole level of approximation). Thus, the double-averaged potential function and the associated constants of motion have been determined up to the same order. Then, by applying the Lagrange Planetary Equations, the secular and long-term orbital element variations have been obtained. Therefore, frozen orbital solutions have been evaluated, and the effects on them of the addition of main body oblateness perturbation have been considered. Furthermore, the procedure has been repeated, and the frozen solutions are re-evaluated in the case of a disturbing body with small eccentricity up to order l = 4 (hexadecapole level of approximation). These solutions offer significant advantages in exploring bodies subject to a notable perturbation from an inner third-body, such as binary asteroid systems. • Frozen orbits for the inner third-body problem. • Inner circular planar third-body: Double-averaged potential up to triakontadipole. • Inner slightly eccentric planar third-body up to hexadecapole. • Orbital solutions for binary asteroid observation. [ABSTRACT FROM AUTHOR]