arXiv subjects

A. F. B. A. Prado

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

14 recordsLinked to original sources

arXiv2026

A generalized dipole-segment model for the gravitational field of elongated bodies

Context. Various simplified models have been investigated to understand the complex dynamical environment near irregular asteroids. We propose a generalized dipole-segment model (GDSM) to describe the gravitational fields of elongated bodies. The proposed model extends the dipole-segment model (DSM) by including variable pole masses and a connecting rod while also accounting for the spheroidal shape of the poles instead of assuming point masses. Methods. A nonlinear optimization method was employed to determine the model parameters, which minimizes the errors between the equilibrium points predicted by the GDSM and those obtained using a more realistic approach, such as the polyhedron model, which is assumed to provide the accurate values of the system. The model was applied to three real irregular bodies: the Kuiper belt objects Arrokoth, Kleopatra, and comet 103P/Hartley. Results. The results show that the GDSM represents the gravitational field more accurately than the DSM and significantly reduces computational time and effort when compared with the polyhedron model. This reduction in computational complexity does not come at the cost of efficiency. This makes the GDSM a valuable tool for practical applications. The model was further employed to compute heteroclinic orbits that connect the unstable triangular equilibrium points of the system. These trajectories, obtained from the intersections of the stable and unstable manifolds, represent natural pathways that enable transfers between equilibrium regions without continuous propulsion. The results for Arrokoth, Kleopatra, and 103P/Hartley are consistent and validate the GDSM as an accurate and computationally efficient framework for studying the dynamical environment and transfer mechanisms around irregular small bodies.

astro-ph.EP↗

arXiv2025

Investigation of optimal transfers to retrograde co-orbital orbits in the Earth-Moon system

Recent findings on retrograde co-orbital mean-motion resonances in the Earth-Moon system, highlight the potential use of spacecraft in retrograde resonances. Based on these discoveries, this study investigates retrograde co-orbital resonances within the Earth-Moon system, focusing on both optimal and sub-optimal orbital transfers to such configurations. The paper provides a comprehensive analysis of retrograde co-orbital resonances, optimization techniques to evaluate and enhance the performance of bi-impulsive transfers to these configurations. The results reveal the feasibility of low-cost transfers, which could support a range of future missions, including space exploration and satellite deployment. Combining advanced optimization processes, we obtained solutions for orbital transfers for different arrival points in retrograde co-orbitals improving mission efficiency and offering a cost-effective approach to interplanetary exploration.

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arXiv2024

Tangent Velocity constraint for orbital maneuvers with Theory of Functional Connections

Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modelling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform rendezvous maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.

astro-ph.IM↗

arXiv2023

Analysis of the dynamics of a spacecraft in the vicinity of an asteroid binary system with equal masses

In this work, we performed a dynamical analysis of a spacecraft around a nearly equal-mass binary near-Earth asteroid with application to the asteroid 2017 YE5, which is also a possible dormant Jupiter-family comet. Thus, we investigated the motion of a particle around this binary system using the circular restricted three-body problem. We calculated the locations of the Lagrangian points of the system and their Jacobi constant. Through numerical simulations, using the Poincaré Surface of Sections, it was possible to find several prograde and retrograde periodic orbits around each binary system's primary, some exhibiting significantly-sized higher-order behavior. We also calculated the stability of these orbits. After finding the periodic orbits, we investigated the influence of solar radiation pressure on these orbits. For this analysis, we considered that the area-to-mass ratio equals 0.01 and 0.1. We also performed a spacecraft lifetime analysis considering the physical and orbital characteristics of the 2017YE5 system and investigated the behavior of a spacecraft in the vicinity of this system. We analyzed direct and retrograde orbits for different values of Jacobi's constant. This study investigated orbits that survive for at least six months, not colliding or escaping the system during that time. We also analyze the initial conditions that cause the spacecraft to collide with $M_1$ or $M_2$, or escape from the system. In this work, we take into account the gravitational forces of the binary asteroid system and the solar radiation pressure (SRP). Finally, we calculated optimal bi-impulsive orbital maneuvers between the collinear Lagrangian points. We found a family of possible orbital transfers considering times of flight between 0.1 and 1 day.

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arXiv2023

Dynamics Around an Asteroid Modeled as a Mass Tripole

The orbital dynamics of a spacecraft orbiting around irregular small celestial bodies is a challenging problem. Difficulties to model the gravity field of these bodies arise from the poor knowledge of the exact shape as observed from the Earth. In order to understand the complex dynamical environment in the vicinity of irregular asteroids, several studies have been conducted using simplified models. In this work, we investigate the qualitative dynamics in the vicinity of an asteroid with an arched shape using a tripole model based on the existence of three mass points linked to each other by rods with given lengths and negligible masses. We applied our results to some real systems, namely, asteroids 8567, 243 Ida and 433 Eros and also Phobos, one of the natural satellites of Mars.

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arXiv2023

Numerical investigations of the orbital dynamics around a synchronous binary system of asteroids

In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio of the system and the size of the secondary. We assume that the gravitational fields of the bodies are modeled assuming the primary as a mass point and the secondary as a rotating mass dipole. This model allows to compute families of planar and halo periodic orbits that emanate from the equilibrium points $ L_1 $ and $L_2$. The stability and bifurcations of these families are analyzed and the results are compared with the results obtained with the Restricted Three-Body Problem (RTBP). The results provide an overview of the dynamical behavior in the vicinity of a binary asteroid system.

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arXiv2023

Strategies For Non-Planar Configurations Of Geostationary Tethered Collecting Solar Power Satellite Systems

To collect additional solar energy during the hours of darkness and to overcome the limited Terrestrial solar power due to the diurnal day night cycle, the concept of a Geostationary Tethered Collecting Solar Power Satellite System has been proposed by several authors in the last years. This tethered system consists of a long tether used to link two bodies: a single large panel with a capability of collecting solar energy, and an Earth-pointing microwave transmitting satellite. In this manner, the solar energy would be collected directly from the space and beamed back down to any point on Earth. Planar configurations, when the panel and the microwave transmitting satellite are placed on geostationary orbits, have been usually investigated to maintain the tethered system around the Earth. However, this configuration implies that the panel and the microwave transmitting satellite must to orbit the Earth in exactly the same orbital plane of all geostationary satellites.

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arXiv2023

Machine learning to predict the solar flux and geomagnetic indices to model density and Drag in Satellites

In recent years (2000-2021), human-space activities have been increasing faster than ever. More than 36000 Earth' orbiting objects, all larger than 10 cm, in orbit around the Earth, are currently tracked by the European Space Agency (ESA). Around 70\% of all cataloged objects are in Low-Earth Orbit (LEO). Aerodynamic drag provides one of the main sources of perturbations in this population, gradually decreasing the semi-major axis and period of the LEO satellites. Usually, an empirical atmosphere model as a function of solar radio flux and geomagnetic data is used to calculate the orbital decay and lifetimes of LEO satellites. In this respect, a good forecast for the space weather data could be a key tool to improve the model of drag. In this work, we propose using Time Series Forecasting Model to predict the future behavior of the solar flux and to calculate the atmospheric density, to improve the analytical models and reduce the drag uncertainty.

physics.space-ph↗

arXiv2021

Influence of Apophis' spin axis variations on a spacecraft during the 2029 close approach with Earth

Tumbling asteroids belong to a small group of objects, whose angular velocity vector is unaligned with any of its principal axes of inertia. This leads to challenging efforts to model the trajectory of any spacecraft designed to orbit these bodies. In this work, we deepen a previous study on this topic, concerning the asteroid (99942) Apophis during its close encounter with the Earth in 2029. We analyze the orbital behaviour of a spacecraft orbiting the asteroid during this event, by including the effects of the changes of orientation of the spin axis of the asteroid, depending on two sets of initial conditions. The global dynamics of the spacecraft around the target are analyzed using three approaches, MEGNO, PMap, and Time-Series prediction. We confirm that no spacecraft with natural orbits could survive the high perturbations caused by the close encounter with our planet.

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arXiv2020

First approximation for spacecraft motion relative to (99942) Apophis

We aim at providing a preliminary approach on the dynamics of a spacecraft in orbit about the asteroid (99942) Apophis during its Earth close approach. The physical properties from the polyhedral shape of the target are derived assigning each tetrahedron to a point mass in its center. That considerably reduces the computation processing time compared to previous methods to evaluate the gravitational potential. The surfaces of section close to Apophis are build considering or not the gravitational perturbations of the Sun, the planets, and the SRP. The Earth is the one that most affects the invisticated region making the vast majority of the orbits to collide or escape from the system. Moreover, from numerical analysis of orbits started on March 1, 2029, the less perturbed region is characterized by the variation of the semimajor axis of 40-days orbits, which do not exceed 2 km very close to the central body ($a < 4$ km, $e < 0.4$). However, no regions investigated could be a possible option for inserting a spacecraft into natural orbits around Apophis during the close approach with our planet. Finally, to solve the stabilization problem in the system, we apply a robust path following control law to control the orbital geometry of a spacecraft. At last, we present an example of successful operation of our orbit control with a total $\bigtriangleup v$ of 0.495 m/s for 60 days. All our results are gathered in the CPM-ASTEROID database, which will be regularly updated by considering other asteroids.

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arXiv2017

Mapping stable direct and retrograde orbits around the triple system of asteroids (45) Eugenia

It is well accepted that knowing the composition and the orbital evolution of asteroids may help us to understand the process of formation of the Solar System. It is also known that asteroids can represent a threat to our planet. Such important role made space missions to asteroids a very popular topic in the current astrodynamics and astronomy studies. By taking into account the increasingly interest in space missions to asteroids, especially to multiple systems, we present a study aimed to characterize the stable and unstable regions around the triple system of asteroids (45) Eugenia. The goal is to characterize unstable and stable regions of this system and compare with the system 2001 SN263 - the target of the ASTER mission. Besides, Prado (2014) used a new concept for mapping orbits considering the disturbance received by the spacecraft from all the perturbing forces individually. This method was also applied to (45) Eugenia. We present the stable and unstable regions for particles with relative inclination between 0 and 180 degrees. We found that (45) Eugenia presents larger stable regions for both, prograde and retrograde cases. This is mainly because the satellites of this system are small when compared to the primary body, and because they are not so close to each other. We also present a comparison between those two triple systems, and a discussion on how these results may guide us in the planning of future missions.

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arXiv2017

Dynamics in the vicinity of (101955) Bennu: Solar radiation pressure effects in equatorial orbits

Here we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the sun gravity effects. We calculate the solar radiation pressure at the perihelion, semi-major axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the solar radiation pressure in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into ten equal layers seems to be the most suitable for this problem. We can highlight that the centre point $E$8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude $ψ_0 = -180^o$, starting with the spacecraft longitude $λ= 0$, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to $ψ_0 = -135^o$, the orbits with initial longitude $λ= 90^0 $ appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of solar radiation pressure are softened, and we find more stable orbits.

physics.space-ph↗

arXiv2015

Stable retrograde orbits around the triple system 2001 SN263

The NEA 2001 SN263 is the target of the ASTER MISSION - First Brazilian Deep Space Mission. Araujo et al. (2012), characterized the stable regions around the components of the triple system for the planar and prograde cases. Knowing that the retrograde orbits are expected to be more stable, here we present a complementary study. We now considered particles orbiting the components of the system, in the internal and external regions, with relative inclinations between $90^{\circ}< I \leqslant180^{\circ}$, i.e., particles with retrograde orbits. Our goal is to characterize the stable regions of the system for retrograde orbits, and then detach a preferred region to place the space probe. For a space mission, the most interesting regions would be those that are unstable for the prograde cases, but stable for the retrograde cases. Such configuration provide a stable region to place the mission probe with a relative retrograde orbit, and, at the same time, guarantees a region free of debris since they are expected to have prograde orbits. We found that in fact the internal and external stable regions significantly increase when compared to the prograde case. For particles with $e=0$ and $I=180^{\circ}$, we found that nearly the whole region around Alpha and Beta remain stable. We then identified three internal regions and one external region that are very interesting to place the space probe. We present the stable regions found for the retrograde case and a discussion on those preferred regions. We also discuss the effects of resonances of the particles with Beta and Gamma, and the role of the Kozai mechanism in this scenario. These results help us understand and characterize the stability of the triple system 2001 SN263 when retrograde orbits are considered, and provide important parameters to the design of the ASTER mission.

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arXiv2012

Stability Regions Around the Components of the Triple System 2001 SN263

The NEAs (Near-Earth Asteroids) are good targets for spatial missions, since they periodically approach the orbit of the Earth. Recently, the NEA (153591) 2001 SN263 was chosen as the target of the ASTER MISSION- First Brazilian Deep Space Mission, planned to be launched in 2015. In February 2008, the radio astronomers from Arecibo-Puerto Rico concluded that (153591) 2001 SN263 is actually a triple system (Nolan et al., 2008). The announcement of the ASTER MISSION has motivated the development of the present work, whose goal is to characterize regions of stability and instability of the triple system (153591) 2001 SN263. The method adopted consisted in dividing the region around the system into four distinct regions. We have performed numerical integrations of systems composed by seven bodies: Sun, Earth, Mars, Jupiter and the three components of the system, and by thousands of particles randomly distributed within the demarcated regions, for the planar and inclined prograde cases. The results are diagrams of semi-major axis versus eccentricity, where it is shown the percentage of particles that survive for each set of initial conditions. The regions where 100% of the particles survive is defined as stable regions. We found that the stable regions are in the neighborhood of Alpha and Beta, and in the external region. It was identified resonant motion of the particles with Beta and Gamma in the internal regions, which lead to instability. For particles with I>45° in the internal region, where I is the inclination with respect to Alpha's equator, there is no stable region, except for the particles placed really close to Alpha. The stability in the external region is not affected by the variation of inclination. We also present a discussion on the long-term stability in the internal region, for the planar and circular cases, with comparisons with the short-term stability.

astro-ph.EP↗