arXiv subjects

Antonio F. B. A. Prado

Publications and source records attributed to Antonio F. B. A. Prado.

10 recordsLinked to original sources

arXiv2026

Designing 3D transfers: application to Earth-Moon

Three dimensional Earth-Moon transfers usually consume more fuel than planar ones, but are needed depending on the latitude of the launch site and the desired inclination of the final lunar orbit. A systematic search of the optimal 3D transfers represents a true challenge due the dimension of the parameter set to span. In this paper, we propose a new method to design 3D transfers using a tangential velocity constraint for the burns, modeled using the overdetermined constraints technique based on the Theory of Functional Connections for an optimal search of solutions in a numerically efficient way. The developed method is applied here for a systematic study of optimal 3D Earth-Moon transfers, but could be used to design any type of 3D maneuvers.

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arXiv2026

GravDyn: A Python Framework for Gravitational Modeling of Irregular Celestial Bodies Using Polyhedral, mascon, and Series Expansion Methods

GravDyn is an open-source Python package for computing gravitational potentials and accelerations around irregular celestial bodies. It implements three approaches within the same workflow: the constant-density polyhedral method, a layered mascon approximation based on tetrahedral decomposition, and the Potential Series Expansion Method (PSEM). The package handles shape-model preprocessing, builds the selected gravity representation, and evaluates potentials and accelerations efficiently. The three implemented methods serve different regimes: the polyhedral model provides a reference solution near the surface, the mascon model supports layered internal density structures, and PSEM offers fast evaluation outside the Brillouin sphere once the polynomial coefficients have been generated. Validation tests against the polyhedral solution show that the mascon and PSEM models reproduce the reference potential with small relative errors while reducing evaluation costs. GravDyn is intended for mission design and studies of spacecraft motion, orbital stability, and gravitational modeling around asteroids and other small bodies.

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arXiv2025

Analytical modeling of the gravitational potential of irregularly shaped celestial bodies considering three distinct internal structures: application to (21) Lutetia

The classical polyhedral model is one of the most accurate methods currently used to represent the gravitational field of irregularly shaped bodies. However, it assumes a homogeneous density distribution, which may not accurately reflect the internal composition of real objects. This study aims to analyze the effects of the internal structure of asteroid (21) Lutetia on gravitational potential modeling by considering a three-layered composition with distinct densities. The gravitational approach adopted in this study is the Potential Series Expansion Method (PSEM), represents models the body as a polyhedron and decomposes it into tetrahedral elements to estimate of the total potential around the asteroid. This estimation involves summing the contributions of each tetrahedron using a direct triple integral over its volume. Although this method does not achieve the same level of accuracy as the classical polyhedral approach, it offers a reasonable degree of precision, expresses the potential in analytical form, significantly reduces computational time, and, due to the simplified algebraic manipulation of the potential, facilitates the analysis of the asteroid's internal structural composition.

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arXiv2025

Potential series expansion method applied in Analytical Modeling of Gravitational field of Irregularly Shaped Celestial Bodies

This study aims to establish an analytical model that reproduces the gravitational field around non-spherical bodies with constant density. Due to the non-spherical geometry of such bodies, their gravitational potential is disturbed relative to a central field. By considering the body as a polyhedron and decomposing it into tetrahedral elements, we use the Series Potential Expansion Method (PSEM) to approximate the total potential by summing the potentials of each tetrahedron. While this model does not offer higher accuracy than the classical polyhedral approach, it achieves relative errors below 0.1\% for points outside the body when developed to higher orders (e.g., orders 11 and 12), and significantly reduces execution time. To validate this approach, we apply our model to asteroids (87) Sylvia, (101955) Bennu, (99942) Apophis, and (25143) Itokawa. We determine equilibrium points, analyze stability, investigate zero-velocity planes, and calculate the relative errors between the gravitational field modeled by PSEM and the results obtained using both the classical polyhedral method by Tsoulis and Petrovic and the mass concentration method. Our results highlight the computational efficiency of PSEM in modeling the gravitational potential of irregularly shaped bodies. This efficiency stems from expressing the gravitational potential through a homogeneous analytical function that is easy to manipulate algebraically, enabling explicit determination of the acceleration vector. Our model provides a robust framework for more complex analyses, such as studying periodic orbits around non-spherical celestial bodies, assessing their stability, and planning the smooth landing trajectories of spacecraft.

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arXiv2023

Orbit transfer using Theory of Functional Connections via change of variables

This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections (TFC) mathematical framework by a specific change of coordinates. In these problems, the constraints are initially written in non-linear and coupled mathematical forms using classical rectangular coordinates. The symmetries of the constrained problem are used to select a new system of coordinates that transforms the non-linear constraints into linear. This change of coordinates is also used to isolate the components of the constraints. This way the TFC technique can be used to solve the ordinary differential equations governing orbit transfer problems subject to mission constraints. Specifically, this paper shows how to apply the change of coordinates method to the perturbed Hohmann-type and the one-tangent burn transfer problems.

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arXiv2023

Suppression of Chaotic Motion of Tethered Satellite Systems Using Tether Length Control

This study focuses on attitude and control motion of two bodies (a base-satellite and a sub-satellite) connected by an inextensible and massless tether in a circular orbit under the influence of the Earths gravitational force. The base-satellite is assumed to be far more heavier than the sub-satellite. In such cases, the base-satellite is regarded as the reference spacecraft. Because of the complexity of the problem, no thrusters on the sub-satellite are considered, and the effect of atmospheric drag, Earths oblateness, and electrodynamic force on the spacecraft are neglected.

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arXiv2023

Theory of Functional Connections and Nelder-Mead optimization methods applied in satellite characterization

The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, we propose and analyze the application of two optimization procedures to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder-Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. In this paper, we propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second procedure proposed in this research takes advantage of the Nealder-Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.

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arXiv2023

Using Upgraded Versions Of Close Approach Maneuvers As Transportation Solutions For Deep Space Missions

Gravity-Assisted maneuvers have been used as a technique to reduce fuel consumption in deep space missions for several decades now. It opened the doors of the exterior solar system. The literature shows those results, as well as new versions of this maneuver, which includes: the use of propulsion combined with the close approach, both high or low thrust; the passage by the atmosphere of a planet to help to change the trajectory of the spacecraft; the use of tethers to increase the changes in the velocity of the spacecraft. All those new versions have the goal of increasing the variations of energy given by the maneuver, making possible missions that would not be possible without this technique.

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arXiv2021

A Particle-Linkage Model for Elongated Asteroids with Three-Dimensional Mass Distribution

The goal of the present paper is to develop a simplified model to describe the gravitational fields of elongated asteroids. The proposed model consists of representing an elongated asteroid using a triple-particle-linkage system distributed in the three-dimensional space. It is an extension of previous models that focused only on planar models. A non-linear optimization method is used to determine the parameters of our model, minimizing the errors of all the external equilibrium points with respect to the solutions calculated with a more realistic model, the polyhedron model, which are assumed to be the real values of the system. The model considered in this article is then applied to three real irregular asteroids 1620 Geographos, 433 Eros and 243, Ida. The results show that the current triple-particle-linkage three-dimensional model gives better accuracy when compared to the axisymmetric triple-particle-linkage model available in the literature, and provides an advantage in terms of accuracy over the mass point model, while keeping computational time low. Also, this model is used to carry out simulations to characterize regions with solutions that remain bounded or that escape from around each asteroid under analysis. We investigated an initial inclination of 0 degree (direct orbits) and 180 degrees (retrograde orbits). We considered the gravitational field of the asteroid, the gravitational attraction of the Sun, and the solar radiation pressure Our results are then compared to the results obtained using the Mascon gravitational model based on the polyhedral shape source. We found good agreement between the two models.

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arXiv2016

The dynamical environment of asteroid 21 Lutetia according to different internal models

One of the most accurate models currently used to represent the gravity field of irregular bodies is the polyhedral approach. In this model, the mass of the body is assumed to be homogeneous, which may not be true for a real object. The main goal of the present paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layers) of asteroid (21) Lutetia, an object that recent results from space probe suggest being at least partially differentiated. The Mascon gravity approach used in the present work, consists of dividing each tetrahedron into eight parts to calculate the gravitational field around the asteroid. The zero-velocity curves show that the greatest displacement of the equilibrium points occurs in the position of the E4 point for the four-layers structure and the smallest one occurs in the position of the E3 point for the three-layers structure. Moreover, stability against impact shows that the planar limit gets slightly closer to the body with the four-layered structure. We then investigated the stability of orbital motion in the equatorial plane of (21) Lutetia and propose numerical stability criteria to map the region of stable motions. Layered structures could stabilize orbits that were unstable in the homogeneous model.

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