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The dynamics of the Solar system exhibit inherent chaos and instability. Mathematical tools, such as the maximum Lyapunov characteristic exponent (LCE) and Lyapunov time (T L), play a crucial role in providing a qualitative understanding of chaos within celestial objects, such as asteroids and moonlets. Celestial bodies with relatively small Lyapunov times have garnered significant research interest due to their stable orbits, a phenomenon referred to as stable or confined chaos. Notable examples include Saturn's satellites: Atlas, with a Lyapunov time on the order of 10 yr, Prometheus, and Pandora. This work aims to study the chaotic behaviour of the Atlas satellite and its relatively small T L. We present a three-dimensional model approach designed to isolate the radial contribution from the LCE and assess its influence within the LCE. Our investigation focuses on the Saturn system, comprising Saturn itself, along with its satellites Atlas, Prometheus, Pandora, and Mimas. To estimate the radial contribution of the LCE, we find the projection of the radial vector of a ghost Atlas (a slightly displaced Atlas) onto the Atlas radial vector, which allows us to calculate the difference between the radial vectors. This methodology enables us to estimate the radial contribution of the LCE and calculate the Lyapunov time. Remarkably, our results demonstrate that orbits remain confined even for integration times exceeding T L. Furthermore, we investigate the temporal behaviour of Atlas' angular position in its orbit, potentially shedding light on chaotic angular dynamics. [ABSTRACT FROM AUTHOR]

It is well known that the Near-Earth Objects population is sustained by bodies that migrate inwards from the main asteroid belt and outer regions of the Solar System. In this work, we aim to revisit the dynamic evolution of the NEO population inside the Solar System using a known debiased population of large objects. Therefore, we separate the phase space into five different regions: Near-Earth Objects (NEO), Main Asteroid Belt (MAB), Jupiter Family Comets (JFC), Centaurs (CEN), and Trans-Neptunian Objects. We performed numerical simulations for 985 NEOs for 100 Myrs and tracked their transferences between regions to determine the most common routes and fates for this population. The results show that solar thermal disruption is the most efficient mechanism to remove NEOs because 70% of the studied objects are led to this fate. Also, 13% of the objects are ejected from the Solar System, representing a significant contribution of interstellar minor bodies from the NEO population. We find that, during their dynamical evolution, more than half of the objects are first transferred to the JFC region and an even larger percentage of them make their way out from the Solar System through it. There is also a significant frequent exchange of bodies between NEO and MAB regions. Almost 30% of the bodies move to the MAB region, but less than 1% of them end their lives inside it, so it seems that for this sample of objects, MAB is a transitional region where escaped NEOs briefly pass through. We also found that only about 14% of the bodies never leave the NEO region. From those, about half of them collide with the terrestrial planets, while the remaining either survive for the whole integration of 100 Myrs or move to a low pericenter orbit. Additionally, we show that almost 10% of the studied sample can reach the CEN region and remain there for a substantial amount of time, telling a different side of the story for the NEO population. [ABSTRACT FROM AUTHOR]

We consider a simplified model to study some types of elongated asteroids with three protuberances, two at the ends and one in the middle. An example considered in this work is the asteroid Holiday. To model these bodies, we consider a tripolar system with a segment, which consists of a massive segment and three spheres, two at the ends of the segment and one between them, rotating around their center of mass with uniform angular velocity. In particular, we restrict our case to variations in masses and their positions, as well as variations in the mass of the segment or rod. For this problem, we obtain the potential and calculate families of symmetric periodic orbits, analyzing asymptotic points that may represent heteroclinic orbits as well as orbits that may represent possible collisions with the studied body. Furthermore, it was possible to obtain zero velocity curves and equilibrium points of the system. The analysis of symmetric periodic orbits can contribute to improve the efficiency of space missions, prolonging the useful life of satellites or spacecraft, in addition to collaborating for a better understanding of the dynamics of a satellite around an asteroid. The asteroid Holiday was chosen due to its degree of importance, both for its proximity to our planet and its periodicity, which led NASA to classify it as potentially dangerous. [ABSTRACT FROM AUTHOR]

The spin–orbit obliquity of a planetary system constraints its formation history. A large obliquity may either indicate a primordial misalignment between the star and its gaseous disc or reflect the effect of different mechanisms tilting planetary systems after formation. Observations and statistical analysis suggest that system of planets with sizes between 1 and 4 R⊕ has a wide range of obliquities (∼0–30○), and that single- and multiplanet transiting have statistically indistinguishable obliquity distributions. Here, we revisit the 'breaking the chains' formation model with focus in understanding the origin of spin–orbit obliquities. This model suggests that super-Earths and mini-Neptunes migrate close to their host stars via planet–disc gravitational interactions, forming chain of planets locked in mean-motion resonances. After gas-disc dispersal, about 90–99  per cent of these planetary systems experience dynamical instabilities, which spread the systems out. Using synthetic transit observations, we show that if planets are born in discs where the disc angular momentum is virtually aligned with the star's rotation spin, their final obliquity distributions peak at ∼5° or less, and the obliquity distributions of single- and multiplanet transiting systems are statistically distinct. By treating the star-disc alignment as a free-parameter, we show that the obliquity distributions of single- and multiplanet transiting systems only become statistically indistinguishable if planets are assumed to form in primordially misaligned natal discs with a tilt' distribution peaking at ≳10–20°. We discuss the origin of these misalignments in the context of star formation and potential implications of this scenario for formation models. [ABSTRACT FROM AUTHOR]

On August 19, 2020, at 13:18—UTC, a meteor event ended as a meteorite shower in Santa Filomena, a city in the Pernambuco State, northeast Brazil. The heliocentric orbital parameters resulting from images by cameras of the weather broadcasting system were semimajor axis a = 2.1 ± 0.1 au, eccentricity e = 0.55 ± 0.03, and inclination i = 0.15o ± 0.05. The data identified the body as an Apollo object, an Earth‐crossing object with a pericenter interior to the Earth's orbit. The chemical, mineralogical, and petrological evaluations, as well as the physical analysis, followed several traditional techniques. The meteorite was identified as a H5‐6 S4 W0 ordinary chondrite genomict breccia. The large amount of metal in the meteorite made a metallographic evaluation based on the opaque phases possible. The monocrystalline kamacite crystals suggest a higher petrological type and the distorted Neumann lines imply at least two different shock events. The absence of the plessite phase shows that the meteorite did not reach the highest shock levels S5 and S6. The well‐defined polycrystalline taenite is indicative of petrologic types 4 and 5 due to the conserved internal tetrataenite rim at the boundaries. The presence of polycrystalline taenites and the characteristics of the Agrell Effect suggest that the Santa Filomena meteorite did not reheat above 700°C. The absence of martensite confirms reheating temperatures <800°C and a slow cooling rate. The Ni contents and sizes of the zoned taenite particles indicate a slow cooling rate ranging from 1 to 10 K Myr−1. [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]

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]

Aerospace engineering is a relatively new topic in engineering. It deals with several aspects of activities related to space. It includes Astrodynamics, which is a field that studies the motion of spacecraft, like guidance and control, which studies different forms to guide the motion of a spacecraft, etc. All those fields started from the Celestial Mechanics, one of the first topics studied in Astronomy. The first studies had the goal to record and explain the motions of the stars, with special attention given to the motion of some "irregular" stars, which showed later to be planets. Considering the advances in the technology, those earlier studies generated the space activities that are well known nowadays. Different topics, like orbital and attitude maneuvers and determination of spacecrafts, mission design, etc. are covered. The present Focus Issue publishes several papers related to aerospace engineering in general and can be useful for further studies and planning of space missions. [ABSTRACT FROM AUTHOR]

Studies related to Celestial Mechanics started long ago, and it is one of the oldest fields in Astronomy. It started to try to explain the motions of the stars in the sky, in particular the irregular motion of some of those of then, which were really the planets of the Solar System. In the 20th century, with the arrival of the 'Space Age', many applications related to the motion of artificial spacecrafts appeared. This new field was called 'Astrodynamics', to designate the use of Celestial Mechanics in man-made objects. Several aspects, like orbit determination, maneuvers to change the orbit of the spacecraft, etc., are covered by this topic. The present Focus Issue in Celestial Mechanics publishes a list of papers in topics related to applications in Celestial Mechanics to both situations: natural and artificial satellites. [ABSTRACT FROM AUTHOR]

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disc between 1 and 3 au. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 au and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas drag, as has been proposed to explain the formation of close-in super-Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar system. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from discs of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Discs with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogues significantly more massive than the real planet. In contrast, a disc with a surface density gradient proportional to r-5.5 reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disc profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The “patched-conics” approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here. [ABSTRACT FROM AUTHOR]

The article discusses the association between astronautics and astronomy, and launch of various artificial satellites.