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We introduce six quantities that generalize the equinoctial orbital elements when some or all the perturbing forces that act on the propagated body are derived from a potential. Three of the elements define a non-osculating ellipse on the orbital plane, other two fix the orientation of the equinoctial reference frame, and the last allows us to determine the true longitude of the body. The Jacobian matrices of the transformations between the new elements and the position and velocity are explicitly given. As a possible application, we investigate their use in the propagation of Earth’s artificial satellites, showing a remarkable improvement compared to the equinoctial orbital elements.

This paper details the design of a guidance architecture, in the form of a layered, finite state machine, meant to enable safe and autonomous rendezvous operations. The onboard software uses relative state parametrization based on relative orbital elements which provide significant geometrical insight into the shape of the relative orbit. The development is structured in two main steps: first, novel closed-form impulsive control schemes, derived from the Gauss Variational Equations expressed in a velocity-aligned frame, are formulated. These complement available strategies from the literature and generalize them for arbitrarily eccentric reference orbits. Secondly, the definition of the guidance layer provides the chaser spacecraft with the capability to select, schedule, and execute the proper maneuvers to complete a given rendezvous scenario, ensuring operational safety and predictability. The functionality and performance of the implemented architecture are analyzed through numerical tests in a linear propagator and a high-fidelity non-linear simulator. The results provide validation of the developed maneuvers’ strategies, as well as demonstrating how the proposed guidance architecture can be used in a straightforward fashion across different target orbit scenarios, while guaranteeing the same level of passive safety.

The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years. This paper presents the development and analysis of a model predictive control based framework that is used with the D’Amico relative orbital elements (ROEs) to maintain the desired trajectories of a cluster of spacecraft while also allowing freedom to maneuver within some allowable bounds. Switching surfaces based on the ROE constraints contain the full state of the system, allowing for fuel reduction over other approaches that use the Hill—Clohessy—Wiltshire equations. The formation and boundary constraints are designed such that no two agents have overlapping regions, allowing the vehicles to maintain safety of fl ight without continually maintaining the trajectories of other agents. This framework allows for a scalable method that can support clusters of satellites to safely achieve mission objectives while minimizing fuel usage. This paper provides simulated results of the framework for a three spacecraft formation that demonstrates a 67% fuel reduction when compared to previous approaches.

The number of resident space objects (RSOs) has been steadily increasing over time, posing significant risks to the safe operation of on-orbit assets. The accurate prediction of potential collision events and implementation of effective and nonredundant avoidance maneuvers require the precise estimation of the orbit positions of objects of interest and propagation of their associated uncertainties. Previous research mainly focuses on striking a balance between accurate propagation and efficient computation. A recently proposed approach that integrates uncertainty propagation with different coordinate representations has the potential to achieve such a balance. This paper proposes combining the generalized equinoctial orbital elements (GEqOE) representation with an adaptive Gaussian mixture model (GMM) for uncertainty propagation. Specifically, we implement a reformulation for the orbital dynamics so that the underlying state and the moment feature of the GMM are propagated under the GEqOE coordinates. Starting from an initial Gaussian probability distribution function (PDF), the algorithm iteratively propagates the uncertainty distribution using a detection-splitting module. A differential entropy-based nonlinear detector and a splitting library are utilized to adjust the number of GMM components dynamically. Component splitting is triggered when a predefined threshold of differential entropy is violated, generating several GMM components. The final probability density function (PDF) is obtained by a weighted summation of the component distributions at the target time. Benefiting from the nonlinearity reduction caused by the GEqOE representation, the number of triggered events largely decreases, causing the necessary number of components to maintain uncertainty realism also to decrease, which enables the proposed approach to achieve good performance with much more efficiency. As demonstrated by the results of propagation in three scenarios with different degrees of complexity, compared with the Cartesian-based approach, the proposed approach achieves comparable accuracy to the Monte Carlo method while largely reducing the number of components generated during propagation. Our results confirm that a judicious choice of coordinate representation can significantly improve the performance of uncertainty propagation methods in terms of accuracy and computational efficiency.

Numerous methods exist for solving the Lambert problem, the two-point boundary value problem (BVP) governed by two-body dynamics. Many applications would benefit from a solution to a perturbed Lambert problem; a few studies have attempted to solve one. Establishing a larger pool of alternative solution methods gives practitioners greater latitude in choosing the solution that best suits their needs. To that end, a novel Lambert-type BVP is constructed in this work that includes oblateness by way of Vinti’s potential, rendering the problem mathematically unperturbed. This BVP is first defined and then converted to a system of equations that is amenable to an iterative solution. The formulation, which is valid for both the zero- and multiple-revolution problems, couples oblate spheroidal (OS) universal variables and OS equinoctial orbital elements together to sow robustness across all orbital regimes, only excepting orbits that are sufficiently rectilinear. For the first time, the solution space is broadly explored, exposing multiple new insights of significant practical use. Initial guess and root-solve techniques are offered to solve the system of equations. When assessed at Earth for robustness, accuracy, and computational efficiency, the zero-revolution algorithm excels across all three performance metrics, with runtimes averaging only about 15 times slower than a typical two-body Lambert solver. The multiple-revolution algorithm, while not yet evaluated as extensively, also exhibits high levels of performance, the formulation generally characterizing the existence of solutions around oblate bodies more accurately than its Keplerian counterpart.

Positional and multicolor photometric observations of near-Earth asteroids were carried out using the SBG telescope of the Kourovka Astronomical Observatory of Ural Federal University and the Zeiss-1000 telescope of the Simeiz Observatory of INASAN in 2022–2023. Based on the results of positional observations with the SBG telescope, improved orbital elements were obtained for seven asteroids. The periods of axial rotation of seven asteroids were estimated from photometric observations. Based on the results of photometric observations in the B , V , R , I filters, color indices were obtained for six asteroids.

To meet the growing complexity and demands of modern spacecraft missions, analytical solutions to initial value problems see continued use, typically supporting global searches of large trajectory design spaces. These efforts often employ universal two-body orbit propagators for their recognized speed and robustness, but many applications, like active space debris removal, would benefit from a comparable propagator with greater accuracy. Vinti propagators, which consider planetary oblateness, may serve this purpose, but existing Vinti solutions possess computational difficulties in certain orbital regimes. To mitigate these deficiencies, the present study develops and validates an analytical, third-order universal Vinti propagator free of computational difficulties by leveraging standard, oblate spheroidal (OS) universal variables and OS equinoctial orbital elements. Accuracy of the third-order approximation is assessed for multiple examples across an array of orbital regimes. Computational runtime is also evaluated, and performance is directly compared to the benchmark Vinti6 algorithm. On average, the Vinti propagator implemented in this work is only slower than a typical universal Kepler propagator by a factor of 4.0 and slower than Vinti6 by a factor of 1.8, but with greater robustness than the benchmark. The new form of the equations of motion also has favorable implications for the associated boundary value problem.

The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high.

Low Earth orbit (LEO) constellations have potentialities to augment global navigation satellite systems for better service performance. The prerequisite is to provide the broadcast ephemerides that meet the accuracy requirement for navigation and positioning. In this study, the Kepler ephemeris model is chosen as the basis of LEO broadcast ephemeris design for backward compatibility and simplicity. To eliminate the singularity caused by the smaller eccentricity of LEO satellites compared to MEO satellites, non-singular elements are introduced for curve fitting of parameters and then transformed to Kepler elements to assure the algorithm of ephemeris computation remains unchanged for the user. We analyze the variation characteristics of LEO orbital elements and establish suitable broadcast ephemeris models considering fit accuracy, number of parameters, fit interval, and orbital altitude. The results of the fit accuracy for different fit intervals and orbital altitudes suggest that the optimal parameter selections are \\[(Crs3,Crc3)\\], \\[(Crs3,Crc3, \\, a,n)\\] and \\[( Crs3,Crc3, \\, a,n, \\, i,a )\\], i.e., adding two, four or six parameters to the GPS 16-parameter ephemeris. When adding four parameters, the fit accuracy can be improved by about one order of magnitude compared to the GPS 16-parameter ephemeris model, and fit errors of less than 10 cm can be achieved with 20-min fit interval for a 400–1400 km orbital altitude. In addition, the effects of the number of parameters, fit interval, and orbit altitude on fit accuracy are discussed in detail. The validation with four LEO satellites in orbit also confirms the effectiveness of proposed models.

This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration technique. While previous studies show that Modified Chebyshev Picard Iteration (MCPI) is a powerful tool used to propagate position and velocity, the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required, which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity, and it also converges for > 5.5x as many revolutions using a single segment when compared with cartesian propagation. Results for the Classical Orbital Elements and the Modified Equinoctial Orbital Elements (the latter provides singularity-free solutions) show that state propagation using these variables is inherently well-suited to the propagation method chosen. Additional benefits are achieved using a segmentation scheme, while future expansion to the two-point boundary value problem is expected to increase the domain of convergence compared with the cartesian case. MCPI is an iterative numerical method used to solve linear and nonlinear, ordinary differential equations (ODEs). It is a fusion of orthogonal Chebyshev function approximation with Picard iteration that approximates a long-arc trajectory at every iteration. Previous studies have shown that it outperforms the state of the practice numerical integrators of ODEs in a serial computing environment; since MCPI is inherently massively parallelizable, this capability is expected to increase the computational efficiency of the method presented.