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In this paper, optimal gliding trajectories are analyzed, formulating an optimal control problem to be solved computationally via nonlinear programming. A multi-objective terminal cost function that minimizes the velocity, altitude, horizontal flight path angle, and the error of a desired terminal point is formulated. The results are validated via Monte Carlo simulations, analyzing the influence of the variations in the lift-to-drag ratios in the atmospheric entry. The results show feasible solutions for minimizing the distance to the desired final point, which have significant practical implications for the controlled gliding entry of a spaceplane on Mars. In this sense, the results also show that the longitudes of the landing points do not change too much for almost all trajectories, while the latitude of these points is in the interval of about 4 degrees for the majority of the trajectories. This suggests that it is possible to implement an optimal control approach with reasonable accuracy for the controlled gliding entry of a spaceplane on Mars, even in the presence of some uncertainties regarding the aerodynamic performance of the spacecraft, such as the lift-to-drag ratio. [ABSTRACT FROM AUTHOR]

This work is the third in a series on point mascon lunar gravity models. Point mascon models are computationally-efficient replacements for the standard spherical harmonics gravity models used in astrodynamics applications. Weighted cubed-sphere mascon gravity models are introduced as runtime-efficient alternatives to the spherical harmonics representation that do not impose the extreme memory costs imposed by other interpolated gravity modeling schemes. Localized models for the lunar gravity field are generated using sets of point-mass potentials and referenced to a cubed-sphere grid. Adjacent localized point mascon gravity models are combined using Junkins weighting functions to form a smooth global model. Three demonstration models are generated that reproduce the GRGM1200A lunar gravity model with equivalent fidelity to degree 70, 300, and 550 spherical harmonics truncation levels. The weighted cubed-sphere models are benchmarked for runtime and memory cost against the standard spherical harmonics models and two recently-introduced types of globally-defined mascon models. The benchmarking results show that the weighted cubed-sphere mascon models enable significant runtime improvements with reasonable memory costs, especially when using OpenMP parallelization. Comparing acceleration runtime with spherical harmonics, the degree 300 equivalent weighted cubed-sphere model shows up to a 30-fold speedup with an 89 megabyte memory footprint and the degree 550 equivalent model shows up to a 90-fold speedup with a 170 megabyte memory footprint. Order of magnitude speedups are demonstrated without parallelization. The runtime models and driver code are available online. [ABSTRACT FROM AUTHOR]

• Variable stiffness design for a 3-legged asteroid probe. • Landing dynamics for soft landing on the 2016HO3 asteroid is modeled. • Response surface surrogate model is established for optimization. • Variable stiffness leg and pressing force are optimized. China plans to launch a probe to detect and sampling on the near-Earth asteroid 2016HO3 around 2025. In view of this, this paper discusses an alternative landing strategy with passive variable stiffness landing gears, which help to land the probe stably on the asteroid for sufficient sampling time. First, a three-legged lander is introduced, following which, a four-bar-linkage-based variable stiffness leg is designed considering the design constraint of landing clearance. Then, a numerical model of the probe for landing simulation is established. Moreover, a surrogate model is obtained using the second-order response surface method (RSM) to improve computational efficiency. Based on the surrogate, the variable stiffness leg and the pressing force are optimized to reduce the impact forces at touchdown and the landing time. Finally, the optimal solution is validated using the dynamics analysis model. [ABSTRACT FROM AUTHOR]

The problem is considered to find the time-optimal control that transfers a fourth-order system that consists of a double integrator and a harmonic oscillator, coupled by one control channel, between two arbitrary states. That fourth-order system is equivalent to the Hill-Clohessy-Wiltshire model of the relative dynamics of an orbiting spacecraft in proximity of a second spacecraft on a circular reference orbit, subjected to a thrust parallel to the orbital velocity vector and having time-continuous amplitude. A new method is here introduced to determine the time-optimal control problem stated above. This method combines two previously discovered optimal control synthesis methods: the method by Romano and Curti (2020), that enables to find (analytically, in some case) the optimal control transferring a general Linear Time Invariant Normal system between two arbitrary states; and, the method by Belousova and Zarkh (1996), that enables to find the optimal control transferring a fourth-order system consisting of a double integrator and a harmonic oscillator, coupled by one control channel, from an arbitrary initial state to the origin of the state space, if the optimal control is a priori known, that transfers the same system from a reference state to the origin. The here proposed combined method utilizes two phases. During the first phase, a number of reference minimum-time controls are obtained that transfer the system from specific reference states to the state space origin; this is achieved by exploiting Pontryagin's principle together with back-propagation from the origin of the state space. During the second phase, a search is run along a particular curve in the state space (named extremal search path) that depends on the boundary states of the problem at hand. In particular, a minimum-time control problem is iteratively solved to find the optimal control history that steers the system from a state on that curve to the origin, by exploiting Belousova and Zarkh method, until a particular state is found which satisfies an equivalency condition that, as demonstrated by Romano and Curti, guarantees that the optimal control history pertaining to the problem of transferring the system from that state to the origin is the same optimal control history that transfers the system between the arbitrarily set initial and final states. The new results, substantiated by numerical experiments, have both a theoretical and a practical value, as they could be applied for the optimal guidance of spacecraft performing autonomous proximity maneuvers. [ABSTRACT FROM AUTHOR]

A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation under Newtonian conditions and is a more accurate tool for astrodynamics than the traditional equation. Preliminary simulation results demonstrate the application potential of the modified vis-viva equation for more complex n-body systems. Spherical symmetry is assumed in this approach; however, this limitation could be removed in future research. This study is a pivotal step toward bridging classical and relativistic mechanics and thus makes an important contribution to the field of celestial dynamics. [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]

The KIAM Astrodynamics Toolbox, a new software library for designing spacecraft orbital motion, is introduced. The toolbox is developed at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences in Fortran and Python languages and, therefore, combines computational speed and program design flexibility. The library can be useful for space flight mechanics specialists, as well as for students in relevant educational programs. [ABSTRACT FROM AUTHOR]

The growing population of man-made objects with the build up of mega-constellations and the multiplication of space debris not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but also poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, the applications of two optimization procedures are proposed and analyzed 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. 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 proposed procedure takes advantage of the Nelder–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. • Retrieving physical parameters of a satellite from the observational data. • Application of the Nelder–Mead optimization method for satellite characterization. • Application of the Theory of Functional Connections for satellite characterization. [ABSTRACT FROM AUTHOR]

Asteroid families consist of swarms of fragments generated after energetic interasteroidal collisions in the distant past that resulted in the breakup of their progenitors. They are recognized by searching for clusters in the three-dimensional space of "proper elements"; parameters characterizing the asteroid orbits that are very close to fundamental invariants of motion, and thus keep a dynamical record of the initial proximity of the orbits generated by a catastrophic fragmentation event. In the circumterrestrial context, proper elements have recently been applied to the dynamical taxonomy of resident space objects (RSO) for the association of debris from breakup into its "parent" satellite. Here, we clarify, adapt, and extend this fundamental concept to space situational awareness for on-orbit maneuver/anomaly detection. RSO proper elements, being linked to the underlying dynamical structure of orbits, can provide a more robust metric within existing maneuver-detection algorithms, through assessment of the induced changes in these quasi invariants of the motion. We highlight the deeper connection of proper elements to classical frozen orbits in Earth-satellite dynamics and to secular elements in artificial satellite theories based on canonical perturbation theory and showcase several techniques for their numerical computation, including a newly proposed Ptolemy method; applicable to both the asteroid and space-debris domains. We apply a Bayesian online changepoint-detection (BOCD) algorithm in both mean- and proper-element space and compare their performances for orbit-maneuver detection. [ABSTRACT FROM AUTHOR]

In this paper, optimal gliding trajectories are analyzed, formulating an optimal control problem to be solved computationally via nonlinear programming. A multi-objective terminal cost function that minimizes the velocity, altitude, horizontal flight path angle, and the error of a desired terminal point is formulated. The results are validated via Monte Carlo simulations, analyzing the influence of the variations in the lift-to-drag ratios in the atmospheric entry. The results show feasible solutions for minimizing the distance to the desired final point, which have significant practical implications for the controlled gliding entry of a spaceplane on Mars. In this sense, the results also show that the longitudes of the landing points do not change too much for almost all trajectories, while the latitude of these points is in the interval of about 4 degrees for the majority of the trajectories. This suggests that it is possible to implement an optimal control approach with reasonable accuracy for the controlled gliding entry of a spaceplane on Mars, even in the presence of some uncertainties regarding the aerodynamic performance of the spacecraft, such as the lift-to-drag ratio.

In Jupiter missions, single-satellite-aided capture employs the gravity assist of one of the Galilean moons, which could decrease the required Δ v to capture a spacecraft into a nominal orbit around Jupiter. Previous studies on single-satellite-aided capture mainly focused on Jovicentric orbits. In this paper, an optimization that focuses on Jovicentric orbits and considers the planetary segment and the nominal orbit around Jupiter was proposed. We use Jupiter arrival excess velocity and arrival time as the link between these two segments, which clearly illustrates single-satellite-aided capturing. VEGA and VEEGA sequences (both planetary gravity assist sequences) are tested in the numerical simulation. The result, with the complete orbits of the mission, indicates the reliability and good convergence of the method. It also turns out that Io and Ganymede are the best options for satellite-aided capture. [ABSTRACT FROM AUTHOR]

Time scales in Celestial Mechanics and Astrodynamics vary considerably, from a few hours for the motion of Earth's artificial satellites to millions of years for planetary dynamics. Hence, the time scales on which one needs to investigate the stability of celestial objects are different. Therefore, the methods of study are themselves different and might lead to specific definitions of stability, either in the sense of bounds on the initial conditions or rather in the sense of confinement in a given region of the phase space. In this work we concentrate on three different methods: perturbation theory, Nekhoroshev's theorem, KAM theory. All theories are constructive in the sense that they provide explicit algorithms to give estimates on the parameters of the system and on the stability time. Perturbation theory gives results on finite time scales, Nekhoroshev's theorem provides stability results on exponentially long times, KAM theory ensures the confinement between invariant tori in low-dimensional systems. We recall the basic ingredients of each theory, starting with KAM theory, then presenting Nekhoroshev's theorem and finally introducing perturbation theory. We provide examples of stability results for some objects of the Solar system. Precisely, we consider the stability of the rotational motion of the Moon (or other planetary satellites) within the spin-orbit model by means of KAM theory, we analyze the stability of asteroids, also in the triangular equilibrium Lagrangian points, using Nekhoroshev's theorem, we study the Earth's satellite dynamics through perturbation theory. [ABSTRACT FROM AUTHOR]

We propose a closed-form (i.e., without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the primary perturber. Starting with a multipole expansion of the barycentric (Jacobi-reduced) Hamiltonian, we carry out a sequence of normalizations in Delaunay variables by Lie series, leading to a secular Hamiltonian model without use of relegation. To this end, we introduce a book-keeping analogous to the one proposed in Cavallari and Efthymiopoulos (Celest Mech Dyn Astron 134(2):1–36, 2022) for test particle orbits interior to the one of the primary perturber, but here adapted, instead, to the case of exterior orbits. We give numerical examples of the performance of the method in both the planar circular and the spatial elliptic restricted three-body problem, for parameters pertinent to the Sun-Jupiter system. In particular, we demonstrate the method's accuracy in terms of reproducibility of the orbital elements' variations far from mean-motion resonances. As a basic outcome of the method, we show how, using as criterion the size of the series' remainder, we reach to obtain an accurate semi-analytical estimate of the boundary (in the space of orbital elements) where the secular Hamiltonian model arrived at after eliminating the particle's fast degree of freedom provides a valid approximation of the true dynamics. [ABSTRACT FROM AUTHOR]

We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman & Hut for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most-massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least-massive bodies (for wide binaries) or the most- plus least-massive bodies (for hard binaries). 3BBF overwhelmingly favors wide-binary formation with superthermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard-binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively as a ^3 for hard and slightly wider binaries. Although mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars—more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low-velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB.

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is the most relevant perturbation for objects in orbit around the Earth with a high area-to-mass ratio ( A / m ). We consider the single-averaged SRP model with the Sun in an elliptical and inclined orbit. In addition to the SRP effect, the orbital evolution of space debris is analyzed considering the perturbations due to the Earth's flattening and third-body perturbations in the dynamical system. The idea is to use the solar sail as a propulsion system using the Sun itself as a clean and abundant energy source so that it can remove space debris from the geostationary orbit and also contribute to the sustainability of space exploration. Using averaged dynamical maps as a tool, the numerical simulations show that the solar sail contributes strongly to exciting the eccentricity of the space debris, causing its reentry into Earth's atmosphere. To perform the numerical simulations, we consider data from real space debris. We also show that the solar sail can be used to remove space debris for a graveyard orbit. In this way, the solar sail can work as a clean and sustainable space-debris-removal mechanism. Finally, we show that the convenient choice of the argument of perigee and the longitude of the ascending node might contribute to amplify the growth of eccentricity. It is also shown that solar radiation pressure destroys the symmetry of the orbits that can be observed in keplerian orbits, so all the orbits will be asymmetric when considering the presence of this force. [ABSTRACT FROM AUTHOR]

In the next future, space agencies are planning to return to the Moon. The objective is to assemble an orbiting space station, called Gateway, on a Near Rectilinear Halo Orbit around the Moon as a base for future Moon and deep space missions. Within this framework, multiple side missions will be planned to sustain the Gateway (Artemis mission). The proposed work is thought in framework of the preliminary design of future cargo missions, in particular on the design of an efficient phasing trajectory, under the Circular Restricted Three body problem hypotheses, to bring a cargo vehicle from the end of the Earth-Moon transfer to the beginning of the proximity operations such as rendezvous and docking with the space station. The work aims covering the lack of literature in phasing trajectories with the NRHO by proposing three different strategies to connect the Earth-Moon transfer trajectory with the proximity operations. The three strategies are classified based on the choice of the parking orbits or the choice of the manifolds. Two strategies use butterfly and Halo orbits to park the vehicle before transferring to the target orbit. The third strategy, instead, uses manifolds to allow a direct phasing. In the paper, the three innovative strategies are designed and compare in a specific scenario. [ABSTRACT FROM AUTHOR]

The present research performs numerical studies to search for the best maneuvers, from the point of view of minimum time, to make adjustments in the semi-major axis, eccentricity and inclination of a spacecraft traveling around the Earth. For those maneuvers, low thrust propulsion is used under optimal and sub-optimal assumptions, to verify the main differences in terms of transfer time. In addition, solar sail dynamics is used. The spacecraft is assumed to have a propulsion with a fixed magnitude and that the control is based on choosing the direction of the propulsion. It is found that optimal control gives the minimum transfer time, while sub-optimal control restricted the control to follow a predescribed function, which is assumed to be a constant or linear function in time. Finally, solar sails present themselves as an option where fuel is a critical factor, given their much longer maneuver duration, but with a zero fuel consumption. The numerical-analytical modeling of optimization methods developed in this study can break any type of symmetry in the solutions. In turn, they can increase their energetic efficiency. The present research compares those results in detail, in particular looking at the transfer time in all cases studied. [ABSTRACT FROM AUTHOR]

The Gaia mission has detected many white dwarfs (WDs) in binary and triple configurations, and while observations suggest that triple-stellar systems are common in our Galaxy, not much attention was devoted to WDs in triples. For stability reasons, these triples must have hierarchical configurations, i.e., two stars are on a tight orbit (the inner binary), with the third companion on a wider orbit about the inner binary. In such a system, the two orbits torque each other via the eccentric Kozai–Lidov mechanism, which can alter the orbital configuration of the inner binary. We simulate thousands of triple-stellar systems for over 10 Gyr, tracking gravitational interactions, tides, general relativity, and stellar evolution up to their WD fate. As demonstrated here, three-body dynamics coupled with stellar evolution is a critical channel to form tight WD binaries or merge a WD binary. Among these triples, we explore their manifestations as cataclysmic variables, Type Ia supernovae, and gravitational-wave events. The simulated systems are then compared to a sample of WD triples selected from the Gaia catalog. We find that including the effect of mass-loss-induced kicks is crucial for producing a distribution of the inner binary–tertiary separations that is consistent with Gaia observations. Lastly, we leverage this consistency to estimate that, at minimum, 30% of solar-type stars in the local 200 pc were born in triples.

The development of large constellations of satellites (i.e., so-called megaconstellations or satcons) is poised to increase the number of LEO satellites by more than an order of magnitude in the coming decades. Such a rapid growth of satellite numbers makes the consequences of major fragmentation events ever more problematic. In this study, we investigate the collisional risk to on-orbit infrastructure from kinetic anti-satellite (ASAT) weapon tests, using the 2019 Indian test as a model. We find that the probability of one or more collisions occurring over the lifetime of ASAT fragments increases significantly in a satcon environment compared with the orbital environment in 2019. For the case of 65,000 satellites in LEO, we find that the chance of one or more satellites being struck by ASAT fragments of size 1 cm or larger is more than 25% for a single test. Including sizes down to 3 mm in our models suggests that impacts will occur for any such event. Finally, we apply our methods to examine the November 2021 Russian ASAT test, also finding a significant collision probability over the lifetime of the fragments. The heavy commercialization of LEO demands a commitment to avoiding debris-generating ASAT tests. [ABSTRACT FROM AUTHOR]

The physics-informed neural network (PINN) gravity model offers a novel and efficient way to represent high-fidelity gravity fields. PINNs leverage modern deep learning strategies to generate custom basis functions capable of modeling idiosyncratic features of a celestial body’s gravity field, bypassing the inefficiencies encumbered by gravity models which prescribe geometries like spherical harmonics. Prior research on the PINN gravity model focuses on its ability to represent the gravity fields of large, near-spherical celestial bodies with highly discontinuous surface features. This research extends the investigation of the PINN gravity model to the small-body regime. Specifically, the results demonstrate that the PINN gravity model is capable of solving the additional challenges associated with modeling small-body gravity fields such as divergence within the Brillouin sphere, cumbersome computational requirements, and sample-inefficient regression. Further, this paper investigates strategies to improve network gravity modeling performance—demonstrating how additional physics constraints in network cost function can increase robustness to noise in the training data and how introducing transformer-inspired changes to the network architecture can offer order-of-magnitude improvements in modeling accuracy. [ABSTRACT FROM AUTHOR]

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We present the Kustaanheimo–Stiefel (KS) regularization of the elliptic restricted three-body problem (ER3BP) at the secondary body P 2 , and discuss its use to study a category of transits through its Hill's sphere (fast close encounters). Starting from the Hamiltonian representation of the problem using the synodic rotating–pulsating reference frame and the true anomaly of P 2 as independent variable, we perform the regularization at the secondary body analogous to the circular case by applying the classical KS transformation and the iso-energetic reduction in an extended 10-dimensional phase-space; this translates into an efficient algorithm that can be readily implemented to numerically integrate the equations of motion. Using such a regularized Hamiltonian we recover a definition of fast close encounters in the ER3BP for small values of the mass parameter μ (while we do not require a smallness condition on the eccentricity of the primaries), and we show that for these encounters the solutions of the variational equations are characterized by an exponential growth during the fast transits through the Hill's sphere. Thus, for small μ , we justify the effectiveness of the regularized fast Lyapunov indicators (RFLIs) to detect orbits with multiple fast close encounters. Finally, we provide numerical demonstrations and show the benefits of the regularization in terms of the computational cost. • A KS regularization of the ER3BP is formulated in the synodic frame. • The KS regularization is implemented to integrate the equations of motion. • The KS regularization characterizes fast close encounters and their hyperbolicity. • KS-FLIs are used to detect initial conditions leading to multiple fast encounters. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to search for orbits that can be used in the Brazilian proposed Aster mission. This mission is under study and its objective is to use a spacecraft to observe the system 2001SN263, which is a triple asteroid system. With respect to the two-body problem (spacecraft and the main asteroid), the symmetries of the orbits are broken by the oblateness of the main body of the system, the solar radiation pressure, and the gravitational attraction of the two moons of the main body. Additionally, the masses of these two moons have errors associated with their predicted values, which reinforce the asymmetry and require extra effort to maintain the observational objectives of the mission. The idea is to find orbits that remain for some time observing the three bodies of that system, even if the physical parameters of the bodies are not the ones expected from observations made from the Earth. This is accomplished by studying the effects of errors in all the physical properties of the three asteroids in the trajectories described by a spacecraft that is orbiting this system. Several important and useful trajectories are found, which are the ones that can observe the desired bodies, even if the physical parameters are not the expected ones. To express our results, we built time histories of the relative distances between each of the asteroids and the spacecraft. They are used to select the trajectories according to the amount of time that we need to observe each body of the system. In this way, the first objective of this research is to search for trajectories to keep the spacecraft close to the three bodies of the system as long as possible, without requiring orbital maneuvers. The errors for the masses of the two smaller and lesser known bodies are taken into consideration, while the mass of the most massive one is assumed to be known, because it was determined with higher precision by observations. [ABSTRACT FROM AUTHOR]

The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a "gravity assisted" maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the gravity of this body to change its trajectory. This approach trajectory has symmetry with respect to the periapsis line when observed from a reference frame fixed in the approached body. There is also a more complex maneuver, when the passage by the celestial body is combined with the application of propulsion, either to give extra energy to the spacecraft or to help to satisfy other constraints required by the mission, like passing by a giving point or region in space. The main object of this study is to measure the efficiency of the application of a continuous thrust combined with the "gravity assisted" maneuver. The effect of this combination is analyzed using maps that give the energy variation of the spacecraft as function of the parameters related to the maneuver. This analysis is made from the point of view of the variation of energy of the spacecraft with respect to the main body of the system. The continuous thrust is applied in the different regions of the trajectory to evaluate the effects of the locations of the thrusting arcs in the variations of energy. The effects of the variations of the direction of the thrust are also studied. This type of combined maneuver may be used to give extra energy to the spacecraft and keeping control of the trajectory during the close approach to better position the spacecraft to complete the mission. [ABSTRACT FROM AUTHOR]

• It is presented a review of the AGAM, showing the classifications and proposed configurations of AGAMs and PAGAMs. • It is studied the effect of low Lift-to-Drag ratios in high altitude AGAM and PAGAM. • It is explored the use of continuum propulsion to null the Drag, improving the gains of energy when compared to GAM. The Gravity Assisted Maneuver has been applied in lots of space missions, to change the spacecraft heliocentric velocity vector and the geometry of the orbit, after the close approach to a celestial body, saving propellant consumption. It is possible to take advantage of additional forces to improve the maneuver, like the forces generated by the spacecraft-atmosphere interaction and/or propulsion systems; reducing the time of flight and the need for multiple passages around secondary bodies. However, these applications require improvements in critical subsystems, which are necessary to accomplish the mission. In this paper, a few combinations of the Gravity-Assist were classified, including maneuvers with thrust and aerodynamic forces; presenting the advantages and limitations of these variations. There are analyzed the effects of implementing low Lift-to-Drag ratios at high altitudes for Aero-gravity Assist maneuvers, with and without propulsion. The maneuvers were simulated for Venus and Mars, due to their relevance in interplanetary missions, the interest in exploration, and the knowledge about their atmospheres. The Aero-gravity Assist maneuver with low Lift-to-Drag ratios at high altitudes shows an increase of more than 10° in the turn angle for Venus and 2.5° for Mars. The maneuvers increase the energy gains by more than 15% when compared to the Gravity-Assist. From the Technology Readiness Levels, it was observed that the current level of development of the space technology makes feasible the application of Aero-gravity Assisted Maneuvers at high altitudes in short term. [ABSTRACT FROM AUTHOR]

The deflection of potentially dangerous asteroids has been treated with great intensity and has gained more and more attention in scientific research. Different techniques are developed over the years. Among these techniques, we found the kinetic impact deflection technique to be the most viable at the moment. In this work we address the kinetic impact deflection technique, but in a scenario where we have a short time to deflect an asteroid that will collide with Earth. For this, we also use a maneuver similar to a powered gravity-assisted maneuver with Earth in a previous passage to change the trajectory of the asteroid to avoid the collision. We apply this technique in three scenarios: (i) impulse before the close encounter, (ii) impulse during the close encounter, and (iii) impulse after the close encounter. We observe that some trajectories are symmetric with respect to the line Sun–Earth, and others are asymmetric. We show that, using this technique, it is possible to change the trajectory of the asteroid, even in a short period, to avoid the collision without using a large variation of velocity in the orbit of the asteroid. [ABSTRACT FROM AUTHOR]

We present a novel approach for the detection of events in systems of ordinary differential equations. The new method combines the unique features of Taylor integrators with state-of-the-art polynomial root finding techniques to yield a novel algorithm, ensuring strong event detection guarantees at a modest computational overhead. Detailed tests and benchmarks focused on problems in astrodynamics and celestial mechanics (such as collisional N -body systems, spacecraft dynamics around irregular bodies accounting for eclipses, computation of Poincaré sections, etc.) show how our approach is superior in both performance and detection accuracy to strategies commonly employed in modern numerical integration works. The new algorithm is available in our open source Taylor integration package heyoka. [ABSTRACT FROM AUTHOR]

As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural satellites Europa and Ganymede. This natural satellite is a good candidate to be visited by future missions. In this sense, the present work has the goal of studying and mapping the best initial orbital conditions for orbits around Io, considering the symmetrical or asymmetical perturbative effects of a third body (Jupiter) and the J 2 term from the mass configuration of Io. The initial orbital parameters of the probe were investigated through a set of numerical simulations. The results showed that although most orbits around Io have lifetimes of less than 6 months, some regions were found where the initial conditions of the orbits provided satisfactory times for the accomplishment of future missions around Io. [ABSTRACT FROM AUTHOR]