Abstract
In general, small bodies of the Solar system, e.g. asteroids and comets, have a very irregular shape. This feature affects significantly the gravitational potential around these irregular ...bodies, which hinders dynamical studies. The Poincaré surface of section technique is often used to look for stable and chaotic regions in two-dimensional dynamic cases. In this work, we show that this tool can be useful for exploring the surroundings of irregular bodies such as the asteroid 4179 Toutatis. Considering a rotating system with a particle, under the effect of the gravitational field computed three dimensionally, we define a plane in the phase space to build the Poincaré surface of section. Despite the extra dimension, the sections created allow us to find trajectories and classify their stabilities. Thus, we have also been able to map stable and chaotic regions, as well as to find correlations between those regions and the contribution of the third dimension of the system to the trajectory dynamics as well. As examples, we show details of periodic (resonant or not) and quasi-periodic trajectories.
Abstract
The recently discovered ring around the dwarf planet (136108) Haumea is located near the 1:3 resonance between the orbital motion of the ring particles and the spin of Haumea. In the current ...work, we study the dynamics of individual particles in the region where the ring is located. Using the Poincaré surface of section technique, the islands of stability associated with the 1:3 resonance are identified and studied. Throughout its existence, this resonance is shown to be doubled, producing pairs of periodic and quasi-periodic orbits. The fact of being doubled introduces a separatrix, which generates a chaotic layer that reduces the size of the stable regions of the 1:3 resonance significantly. The results also show that there is a minimum equivalent eccentricity (e1$\colon$3) required for the existence of such a resonance. This value seems to be too high to keep a particle within the borders of the ring. On the other hand, the Poincaré surface of sections shows the existence of much larger stable regions, but associated with a family of first-kind periodic orbits. They exist with equivalent eccentricity values lower than e1$\colon$3, covering a large radial distance, which encompasses the region of Haumea’s ring. Therefore, this analysis suggests that Haumea’s ring is in a stable region associated with a first-kind periodic orbit instead of the 1:3 resonance.
ABSTRACT
The potentially hazardous asteroid 99942 Apophis will have a very close approach to the Earth in 2029. The encounter on its own may provide measurements of Earth’s effects on Apophis’ ...surface and also contribute to the improvement of some physical characteristics of the asteroid. In a previous work, we assumed the existence of a hypothetical disc of particles around Apophis before the 2029 encounter, and identified the particles that would escape from the gravity domain of Apophis due to the Earth's gravitational perturbation during the close encounter. In the current work, we investigate the possibility of a meteor activity originating from this event. We study the orbital evolution of these particles computing the MOIDs of the particles with respect to the Earth for the following 200 yr. Our results are not favourable for a meteor activity on Earth. However, a meteoroid activity on the Moon might happen during the encircling period after 88 yr of the 2029 encounter.
ABSTRACT
The aim of this work is to verify the stability of the proposed orbital solutions for the third moonlet (Delta) taking into account a realistic gravitational potential for the central body ...of the quadruple system (Alpha). We also aim to estimate the location and size of a stability region inside the orbit of Gamma. First, we created a set of test particles with intervals of semimajor axis, eccentricities, and inclinations that covers the region interior to the orbit of Gamma, including the proposed orbit of Delta and a wide region around it. We considered three different models for the gravitational potential of Alpha: irregular polyhedron, ellipsoidal body, and oblate body. For a second scenario, Delta was considered a massive spherical body and Alpha an irregular polyhedron. Beta and Gamma were assumed as spherical massive bodies in both scenarios. The simulations showed that a large region of space is almost fully stable only when Alpha was modelled simply as an oblate body. For the scenario with Delta as a massive body, the results did not change from those as mass-less particles. Beta and Gamma do not play any relevant role in the dynamics of particles interior to the orbit of Gamma. Delta’s predicted orbital elements are fully unstable and far from the nearest stable region. The primary instability source is Alpha’s elongated shape. Therefore, in the determination of the orbital elements of Delta, it must be taken into account the gravitational potential of Alpha assuming, at least, an ellipsoidal shape.
ABSTRACT
Exomoons are a missing piece of exoplanetary science. Recently, two promising candidates were proposed, Kepler-1625 b-I and Kepler-1708 b-I. While the latter still lacks a dynamical analysis ...of its stability, Kepler-1625 b-I has already been the subject of several studies regarding its stability and origin. Moreover, previous works have shown that this satellite system could harbour at least two stable massive moons. Motivated by these results, we explored the stability of co-orbital exomoons using the candidates Kepler-1625 b-I and Kepler-1708 b-I as case studies. To do so, we performed numerical simulations of systems composed of the star, planet, and the co-orbital pair formed by the proposed candidates and another massive body. For the additional satellite, we varied its mass and size from a Mars-like to the case where both satellites have the same physical characteristics. We investigated the co-orbital region around the Lagrangian equilibrium point L4 of the system, setting the orbital separation between the satellites from θmin = 30° to θmax = 90°. Our results show that stability islands are possible in the co-orbital region of Kepler-1708 b-I as a function of the co-orbital companion’s mass and angular separation. Also, we identified that resonances of librational frequencies, especially the 2:1 resonance, can constrain the mass of the co-orbital companion. On the other hand, we found that the proximity between the host planet and the star makes the co-orbital region around Kepler-1625 b-I unstable for a massive companion. Finally, we provide TTV profiles for a planet orbited by co-orbital exomoons.
Context.
Chariklo has two narrow and dense rings, C1R and C2R, located at 391 km and 405 km, respectively.
Aims.
In the light of new stellar occultation data, we study the stability around Chariklo. ...We also analyse three confinement mechanisms that prevent the spreading of the rings, based on shepherd satellites in resonance with the edges of the rings.
Methods.
This study was performed through a set of numerical simulations and the Poincaré surface of section technique.
Results.
From the numerical simulation results, and from the current parameters referring to the shape of Chariklo, we verify that the inner edge of the stable region is much closer to Chariklo than the rings. The Poincaré surface of sections allows us to identify periodic and quasi-periodic orbits of the first kind, and also the resonant islands corresponding to the 1:2, 2:5, and 1:3 resonances. We construct a map of
a
eq
versus
e
eq
space that gives the location and width of the stable region and the 1:2, 2:5, and 1:3 resonances.
Conclusions.
We find that the first kind periodic orbit family can be responsible for a stable region whose location and size meet that of C1R, for specific values of the ring particle eccentricities. However, C2R is located in an unstable region if the width of the ring is assumed to be about 120 m. After analysing different systems, we propose that the best confinement mechanism is composed of three satellites: two satellites shepherding the inner edge of C1R and the outer edge of C2R, and the third satellite trapped in the 1:3 resonance.
ABSTRACT
The first proposed Brazilian mission to deep space, the ASTER mission, has the triple asteroid system (153591) 2001 SN263 as a target. One of the mission’s main goals is to analyse the ...physical and dynamical structures of the system to understand its origin and evolution. This work aims to analyse how the asteroid’s irregular shape interferes with the stability around the system. The results show that the irregular shape of the bodies plays an important role in the dynamics nearby the system. For instance, the perturbation due to the (153591) 2001 SN263 Alpha’s shape affects the stability in the (153591) 2001 SN263 Gamma’s vicinity. Similarly, the (153591) 2001 SN263 Beta’s irregularity causes a significant instability in its nearby environment. As expected, the prograde case is the most unstable, while the retrograde scenario presents more stability. Additionally, we investigate how the solar radiation pressure perturbs particles of different sizes orbiting the triple system. We found that particles with a 10–50 cm radius could survive the radiation pressure for the retrograde case. Meanwhile, to resist solar radiation, the particles in prograde orbit must be larger than the particles in retrograde orbits, at least one order of magnitude.
ABSTRACT
Since it was proposed, the exomoon candidate Kepler-1625 b-I has changed the way we see satellite systems. Because of its unusual physical characteristics, many questions about the stability ...and origin of this candidate have been raised. Currently, we have enough theoretical studies to show that if Kepler-1625 b-I is indeed confirmed, it will be stable. Regarding its origin, previous works indicated that the most likely scenario is capture, although conditions for in situ formation have also been investigated. In this work, we assume that Kepler-1625 b-I is an exomoon and study the possibility of an additional, massive exomoon being stable in the same system. To model this scenario, we perform N-body simulations of a system including the planet, Kepler-1625 b-I, and one extra Earth-like satellite. Based on previous results, the satellites in our system will be exposed to tidal interactions with the planet and to gravitational effects owing to the rotation of the planet. We find that the satellite system around Kepler-1625 b is capable of harbouring two massive satellites. The extra Earth-like satellite can be stable in various locations between the planet and Kepler-1625 b-I, with a preference for regions inside $25\, R_{\rm p}$. Our results suggest that the strong tidal interaction between the planet and the satellites is an important mechanism to ensure the stability of satellites in circular orbits closer to the planet, while the 2:1 mean motion resonance between the Earth-like satellite and Kepler-1625 b-I would provide stability for satellites in wider orbits.
ABSTRACT
The 99942 Apophis close encounter with Earth in 2029 may provide information about asteroid’s physical characteristics and measurements of Earth’s effects on the asteroid surface. In this ...work, we analysed the surface and the nearby dynamics of Apophis. The possible effects of its 2029 encounter on the surface and environment vicinity are also analysed. We consider a 340 m polyhedron with a uniform density (1.29, 2.2, and 3.5 g cm−3). The slope angles are computed, as well their variation that arises during the close approach. Such variation reaches 4° when low densities are used in our simulations and reaches 2° when the density is high. The zero-velocity curves, the equilibrium points, and their topological classification are obtained. We found four external equilibrium points and two of them are linearly stable. We also perform numerical simulations of bodies orbiting the asteroid, taking into account the irregular gravitational field of Apophis and two extra scenarios of perturbations: the solar radiation pressure and the Earth’s perturbation during the close approach. The radiation pressure plays an important role in the vicinity of the asteroid, only cm-sized particles survived for the time of integration. For densities of 2.2 and 3.5 g cm−3, a region of 5 cm radius particles survived for 30 yr of the simulation, and for 1.29 g cm−3, only particles with 15 cm of radius survived. The ejections and collisions are about 30–50 times larger when the close encounter effect is added but around 56–59 per cent of particles still survive the encounter.
ABSTRACT
The (153591) 2001 SN263 asteroid system, a target of the first Brazilian interplanetary space mission, is one of the known three triple systems within the population of near-Earth asteroids. ...One of the mission objectives is to collect data about the formation of this system. The analysis of these data will help in the investigation of the physical and dynamical structures of the components (Alpha, Beta, and Gamma) of this system, in order to find vestiges related to its origin. In this work, we assume the irregular shape of the 2001 SN263 system components as uniform-density polyhedra and computationally investigate the gravitational field generated by these bodies. The goal is to explore the dynamical characteristics of the surface and environment around each component. Then, taking into account the rotational speed, we analyse their topographic features through the quantities geometric altitude, tilt, geopotential, slope, and surface accelerations among others. Additionally, the investigation of the environment around the bodies made it possible to construct zero-velocity curves, which delimit the location of equilibrium points. The Alpha component has a peculiar number of 12 equilibrium points, all of them located very close to its surface. In the cases of Beta and Gamma, we found four equilibrium points not so close to their surfaces. Then, performing numerical experiments around their equilibrium points, we identified the location and size of just one stable region, which is associated with an equilibrium point around Beta. Finally, we integrated a spherical cloud of particles around Alpha and identified the location on the surface of Alpha where the particles have fallen.
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