Publicações

Celestial Mechanics & Dynamical Astronomy

We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbital configurations of Jupiter and Saturn. We carried out simulations in the context of the classical model with disk surface densities proportional to r−0.5,r−1

“>r−0.5,r−1r−0.5,r−1 and r−1.5

“>r−1.5r−1.5, and also using partially depleted, non-uniform disks as in the recent model of Mars formation by Izidoro et al. (Astrophys J 782:31, 2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because as a result of the interactions of giant planets with the protoplanetary disk, secular resonances will also play important roles in the orbital assembly and properties of the final terrestrial planets, we will study the effect of these resonances as well. In that respect, we divide this study into two parts. When using a partially depleted disk (Part 1), we are particularly interested in examining the effect of secular resonances on the formation of Mars and orbital stability of terrestrial planets. When using the disk in the classical model (Part 2), our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results of our study show that in general, the ν5

“>ν5ν5 resonance does not have a significant effect on the dynamics of planetesimals and planetary embryos, and the final orbits of terrestrial planets. However, ν6

“>ν6ν6 and ν16

“>ν16ν16 resonances play important roles in clearing their affecting areas. While these resonances do not alter the orbits of Mars and other terrestrial planets, they strongly deplete the region of the asteroid belt ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In the context of the classical model, the effects of these resonances are stronger in disks with less steep surface density profiles. Our results indicate that when considering the classical model (Part 2), the final planetary systems do not seem to show a trend between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. Some small correlations were observed where, for instance, in disks with steeper surface density profiles, the final planets were drier, or their water contents decreased when Saturn was added to the simulations. However, in general, the final orbital and physical properties of terrestrial planets seem to vary from one system to another and depend on the mass of the disk, the spatial distribution of protoplanetary bodies (i.e., disk surface density profile), and the initial orbital configuration of giant planets. We present results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects such as their masses and water contents.

doi: http://dx.doi.org/10.1007/s10569-015-9663-y
arxiv: https://arxiv.org/abs/1512.02852

Monthly Notices of the Royal Astronomical Society

The rotational fission of asteroids has been studied previously with simplified models restricted to planar motion. However, the observed physical configuration of contact binaries leads one to conclude that most of them are not in a planar configuration and hence would not be restricted to planar motion once they undergo rotational fission. This motivated a study of the evolution of initially non-planar binaries created by fission. Using a two-ellipsoid model, we performed simulations taking only gravitational interactions between components into account. We simulate 91 different initial inclinations of the equator of the secondary body for 19 different mass ratios. After disruption, the binary system dynamics are chaotic, as predicted from theory. Starting the system in a non-planar configuration leads to a larger energy and enhanced coupling between the rotation state of the smaller fissioned body and the evolving orbital system, and enables re-impact to occur. This leads to differences with previous planar studies, with collisions and secondary spin fission occurring for all mass ratios with inclinations θ₀ ≥ 40^o, and mimics a Lidov–Kozai mechanism. Out of 1729 studied cases, we found that ∼14 per cent result in secondary fission, ∼25 per cent result in collisions and ∼6 per cent have lifetimes longer than 200 yr. In Jacobson & Scheeres stable binaries only formed in cases with mass ratios q < 0.20. Our results indicate that it should be possible to obtain a stable binary with the same mechanisms for cases with mass ratios larger than this limit, but that the system should start in a non-planar configuration. doi: http://dx.doi.org/10.1093/mnras/stw1607

Monthly Notices of the Royal Astronomical Society

Several space-based climate engineering methods, including shading the Earth with a particle ring for active cooling, or the use of orbital reflectors to increase the total insolation of Mars for climate warming have been considered to modify planetary climates in a controller manner. In this study, solar reflectors on polar orbits are proposed to intervene in the Earth’s climate system, involving near circular polar orbits normal to the ecliptic plane of the Earth. Similarly, a family of displaced polar orbits (non-Keplerian orbits) are also characterized to mitigate future natural climate variability, producing a modest global temperature increase, again to compensate for possible future cooling. These include deposition of aerosols in the stratosphere from large volcanic events. The two-body problem is considered, taking into account the effects of solar radiation pressure and the Earth’s J2

“>J2 oblateness perturbation.

doi: http://dx.doi.org/10.1016/j.asr.2016.04.007

Astrophysical Journal

The Centaur population is composed of minor bodies wandering between the giant planets that frequently perform close gravitational encounters with these planets, leading to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence of a well-defined system of rings around a body in such a perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of 100 Myr. We found, on average, that each clone experiences during its lifetime more than 150 close encounters with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters that were able to significantly disrupt or disturb the rings of Chariklo. About 3% of the clones lose their rings and about 4% of the clones have their rings significantly disturbed. Therefore, our results show that in most cases (more than 90%), the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common among these kinds of Centaurs.

doi: http://dx.doi.org/10.3847/0004-637X/824/2/80
arxiv: https://arxiv.org/abs/1604.07323

Astrophysical Journal

The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ~10⁻³ Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.

doi: http://dx.doi.org/10.3847/1538-4357/833/1/40
arxiv: https://arxiv.org/abs/1609.04970

Computational & Applied Mathematics

Escape trajectories from the Earth–Moon system can be obtained through a single gravity assist maneuver of a spacecraft with the Moon. This paper presents a semi-analytical study of variations in the semi-major axis and the eccentricity of a spacecraft for a geocentric frame—before and after a close encounter of the spacecraft with the Moon. Studies on the swing-by dynamics between a spacecraft and the Moon were performed in order to establish a set of initial conditions in terms of eccentricities and semi-major axes of geocentric initial orbits. This way, it was possible identify which orbits, launched from Earth parking orbits, accomplish swing-bys with the Moon and generate escape trajectories.

doi: http://dx.doi.org/10.1007/s40314-015-0287-3

Monthly Notices of the Royal Astronomical Society

Since 2004, the images obtained by the Cassini spacecraft’s on-board cameras have revealed the existence of several small satellites in the Saturn system. Some of these small satellites are embedded in arcs of particles. While these satellites and their arcs are known to be in corotation resonances with Mimas, their origin remains unknown. This work investigates one possible process for capturing bodies into a corotation resonance, which involves increasing the eccentricity of a perturbing body. Therefore, through numerical simulations and analytical studies, we show a scenario in which the excitation of Mimas’s eccentricity could capture particles in a corotation resonance. This is a possible explanation for the origin of the arcs.

doi: http://dx.doi.org/10.1093/mnras/stw1055
arxiv: https://arxiv.org/abs/1606.05190

Monthly Notices of the Royal Astronomical Society

Asteroid families form as a result of large-scale collisions among main belt asteroids. The orbital distribution of fragments after a family-forming impact could inform us about their ejection velocities. Unfortunately, however, orbits dynamically evolve by a number of effects, including the Yarkovsky drift, chaotic diffusion, and gravitational encounters with massive asteroids, such that it is difficult to infer the ejection velocities eons after each family’s formation. Here, we analyse the inclination distribution of asteroid families, because proper inclination can remain constant over long time intervals, and could help us to understand the distribution of the component of the ejection velocity that is perpendicular to the orbital plane (v_W). From modelling the initial break up, we find that the distribution of v_Wof the fragments, which manage to escape the parent body’s gravity, should be more peaked than a Gaussian distribution (i.e. be leptokurtic) even if the initial distribution was Gaussian. We surveyed known asteroid families for signs of a peaked distribution of v_W using a statistical measure of the distribution peakedness or flatness known as kurtosis. We identified eight families whose v_W distribution is significantly leptokurtic. These cases (e.g. the Koronis family) are located in dynamically quiet regions of the main belt, where, presumably, the initial distribution of v_W was not modified by subsequent orbital evolution. We suggest that, in these cases, the inclination distribution can be used to obtain interesting information about the original ejection velocity field.

doi: http://dx.doi.org/10.1093/mnras/stw043
arxiv: https://arxiv.org/abs/1602.04486

Icarus

An asteroid family forms as a result of a collision between an impactor and a parent body. The fragments with ejection speeds higher than the escape velocity from the parent body can escape its gravitational pull. The cloud of escaping debris can be identified by the proximity of orbits in proper element, or frequency, domains. Obtaining estimates of the original ejection speed can provide valuable constraints on the physical processes occurring during collision, and used to calibrate impact simulations. Unfortunately, proper elements of asteroids families are modified by gravitational and non-gravitational effects, such as resonant dynamics, encounters with massive bodies, and the Yarkovsky effect, such that information on the original ejection speeds is often lost, especially for older, more evolved families.

It has been recently suggested that the distribution in proper inclination of the Koronis family may have not been significantly perturbed by local dynamics, and that information on the component of the ejection velocity that is perpendicular to the orbital plane (v_W), may still be available, at least in part. In this work we estimate the magnitude of the original ejection velocity speeds of Koronis members using the observed distribution in proper eccentricity and inclination, and accounting for the spread caused by dynamical effects. Our results show that (i) the spread in the original ejection speeds is, to within a 15% error, inversely proportional to the fragment size, and (ii) the minimum ejection velocity is of the order of 50 m/s, with larger values possible depending on the orbital configuration at the break-up.

doi: http://dx.doi.org/10.1016/j.icarus.2016.01.006
arxiv: https://arxiv.org/abs/1602.04491

Monthly Notices of the Royal Astronomical Society

Ceres is the largest and most massive body in the asteroid main belt. Observational data from the Dawn spacecraft reveal the presence of at least two impact craters about 280 km in diameter on the Ceres surface, that could have expelled a significant number of fragments. Yet, standard techniques for identifying dynamical asteroid families have not detected any Ceres family. In this work, we argue that linear secular resonances with Ceres deplete the population of objects near Ceres. Also, because of the high escape velocity from Ceres, family members are expected to be very dispersed, with a considerable fraction of km-sized fragments that should be able to reach the pristine region of the main belt, the area between the 5J:-2A and 7J:-3A mean-motion resonances, where the observed number of asteroids is low. Rather than looking for possible Ceres family members near Ceres, here we propose to search in the pristine region. We identified 156 asteroids whose taxonomy, colours, albedo could be compatible with being fragments from Ceres. Remarkably, most of these objects have inclinations near that of Ceres itself.

doi: http://dx.doi.org/10.1093/mnras/stw380
arxiv: https://arxiv.org/abs/1602.04736

Monthly Notices of the Royal Astronomical Society

Asteroid families are groups of minor bodies produced by high-velocity collisions. After the initial dispersions of the parent bodies fragments, their orbits evolve because of several gravitational and non-gravitational effects, such as diffusion in mean-motion resonances, Yarkovsky and Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effects, close encounters of collisions, etc. The subsequent dynamical evolution of asteroid family members may cause some of the original fragments to travel beyond the conventional limits of the asteroid family. Eventually, the whole family will dynamically disperse and no longer be recognizable. A natural question that may arise concerns the time-scales for dispersion of large families. In particular, what is the oldest still recognizable family in the main belt? Are there any families that may date from the late stages of the late heavy bombardment and that could provide clues on our understanding of the primitive Solar system? In this work, we investigate the dynamical stability of seven of the allegedly oldest families in the asteroid main belt. Our results show that none of the seven studied families has a nominally mean estimated age older than 2.7 Gyr, assuming standard values for the parameters describing the strength of the Yarkovsky force. Most ‘paleo-families’ that formed between 2.7 and 3.8 Gyr would be characterized by a very shallow size–frequency distribution, and could be recognizable only if located in a dynamically less active region (such as that of the Koronis family). V-type asteroids in the central main belt could be compatible with a formation from a paleo-Eunomia family.

doi: http://dx.doi.org/10.1093/mnras/stw533
arxiv: https://arxiv.org/abs/1603.00818

The Astronomical Journal

The Karin cluster is a young asteroid family thought to have formed only  Myr ago. The young age can be demonstrated by numerically integrating the orbits of Karin cluster members backward in time and showing the convergence of the perihelion and nodal longitudes (as well as other orbital elements). Previous work has pointed out that the convergence is not ideal if the backward integration only accounts for the gravitational perturbations from the solar system planets. It improves when the thermal radiation force known as the Yarkovsky effect is accounted for. This argument can be used to estimate the spin obliquities of the Karin cluster members. Here we take advantage of the fast growing membership of the Karin cluster and show that the obliquity distribution of diameter  km Karin asteroids is bimodal, as expected if the YORP effect acted to move obliquities toward extreme values (0° or 180°). The measured magnitude of the effect is consistent with the standard YORP model. The surface thermal conductivity is inferred to be 0.07–0.2 W m⁻¹ K⁻¹ (thermal inertia  J m⁻² K⁻¹ s). We find that the strength of the YORP effect is roughly  of the nominal strength obtained for a collection of random Gaussian spheroids. These results are consistent with a surface composed of rough, rocky regolith. The obliquity values predicted here for 480 members of the Karin cluster can be validated by the light-curve inversion method.

doi: http://dx.doi.org/10.3847/0004-6256/151/6/164
arxiv: https://arxiv.org/abs/1603.09612

Monthly Notices of the Royal Astronomical Society

Among asteroid families, the Astrid family is peculiar because of its unusual inclination distribution. Objects at a ≃ 2.764 au are quite dispersed in this orbital element, giving the family a ‘crab-like’ appearance. Recent works showed that this feature is caused by the interaction of the family with the s − s_C nodal secular resonance with Ceres, that spreads the inclination of asteroids near its separatrix. As a consequence, the currently observed distribution of the v_W component of terminal ejection velocities obtained from inverting Gauss equation is quite leptokurtic, since this parameter mostly depends on the asteroids inclination. The peculiar orbital configuration of the Astrid family can be used to set constraints on key parameters describing the strength of the Yarkovsky force, such as the bulk and surface density and the thermal conductivity of surface material. By simulating various fictitious families with different values of these parameters, and by demanding that the current value of the kurtosis of the distribution in v_W be reached over the estimated lifetime of the family, we obtained that the thermal conductivity of Astrid family members should be ≃0.001 W m⁻¹ K⁻¹, and that the surface and bulk density should be higher than 1000 kg m⁻³. Monte Carlo methods simulating Yarkovsky and stochastic Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) evolution of the Astrid family show its age to be T = 140 ± 30 Myr old, in good agreement with estimates from other groups. Its terminal ejection velocity parameter is in the range

 m s⁻¹. Values of V_EJ larger than 25 m s⁻¹ are excluded from constraints from the current inclination distribution.

doi: http://dx.doi.org/10.1093/mnras/stw1445
arxiv: https://arxiv.org/abs/1606.05189

Monthly Notices of the Royal Astronomical Society

v_W leptokurtic asteroid families are families for which the distribution of the normal component of the terminal ejection velocity field v_W is characterized by a positive value of the γ₂ Pearson kurtosis, i.e. they have a distribution with a more concentrated peak and larger tails than the Gaussian one. Currently, eight families are known to have γ₂(v_W) > 0.25. Among these, three are highly inclined asteroid families, the Hansa, Barcelona, and Gallia families. As observed for the case of the Astrid family, the leptokurtic inclination distribution seems to be caused by the interaction of these families with node secular resonances. In particular, the Hansa and Gallia family are crossed by the s − s_V resonance with Vesta, that significantly alters the inclination of some of their members. In this work we use the time evolution of γ₂(v_W) for simulated families under the gravitational influence of all planets and the three most massive bodies in the main belt to assess the dynamical importance (or lack of) node secular resonances with Ceres, Vesta, and Pallas for the considered families, and to obtain independent constraints on the family ages. While secular resonances with massive bodies in the main belt do not significantly affect the dynamical evolution of the Barcelona family, they significantly increase the γ₂(v_W) values of the simulated Hansa and Gallia families. Current values of the γ₂(v_W) for the Gallia family are reached over the estimated family age only if secular resonances with Vesta are accounted for.

doi: http://dx.doi.org/10.1093/mnras/stw2047
arxiv: https://arxiv.org/abs/1606.05189

Monthly Notices of the Royal Astronomical Society

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 this paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layered) 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 this 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-layered structure and the smallest one occurs in the position of the E3 point for the three-layered 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.

doi: http://dx.doi.org/10.1093/mnras/stw2619
arxiv: https://arxiv.org/abs/1610.02338

Monthly Notices of the Royal Astronomical Society

The Hoffmeister family is a C-type group located in the central main belt. Dynamically, it is important because of its interaction with the ν_1C nodal secular resonance with Ceres, which significantly increases the dispersion in inclination of family members at a lower semimajor axis. As an effect, the distribution of inclination values of the Hoffmeister family at a semimajor axis lower than its centre is significantly leptokurtic, and this can be used to set constraints on the terminal ejection velocity field of the family at the time it was produced. By performing an analysis of the time behaviour of the kurtosis of the v_W component of the ejection velocity field [γ₂(v_W)], as obtained from Gauss’ equations, for different fictitious Hoffmeister families with different values of the ejection velocity field, we were able to exclude that the Hoffmeister family should be older than 335 Myr. Constraints from the currently observed inclination distribution of the Hoffmeister family suggest that its terminal ejection velocity parameter V_EJ should be lower than 25 m s⁻¹. Results of a Yarko-YORP Monte Carlo method to family dating, combined with other constraints from inclinations and γ₂(v_W), indicate that the Hoffmeister family should be

Myr old, with an ejection parameter V_EJ = 20 ± 5 m s⁻¹.

doi: http://dx.doi.org/10.1093/mnras/stw3022
arxiv: https://arxiv.org/abs/1611.06176

Advances in Space Research

Space missions to visit small bodies of the Solar System are important steps to improve our knowledge of the Solar System. Usually those bodies do not have well known characteristics, as their gravity field, which make the mission planning a difficult task. The present paper has the goal of studying orbits around the triple asteroid 2001SN₂₆₃, a Near-Earth Asteroid (NEA). A mission to this system allows the exploration of three bodies in the same trip. The distances reached by the spacecraft from those three bodies have fundamental importance in the quality of their observations. Therefore, the present research has two main goals: (i) to develop a semi-analytical mathematical model, which is simple, but able to represent the main characteristics of that system; (ii) to use this model to find orbits for a spacecraft with the goal of remaining the maximum possible time near the three bodies of the system, without the need of space maneuvers. This model is called “Precessing Inclined Bi-Elliptical Problem with Radiation Pressure” (PIBEPRP). The use of this model allow us to find important natural orbits for the exploration of one, two or even the three bodies of the system. These trajectories can be used individually or combined in two or more parts using orbital maneuvers.

doi: http://dx.doi.org/10.1016/j.asr.2015.12.007

Computational & Applied Mathematics

The main goal of the present paper is to study the lifetime of orbits around moons that are in elliptic motion around their parent planet. The lifetime of the orbits is defined as the time the orbit stays in orbit around the moon without colliding with its surface. The mathematical model used to solve this problem is the second order expansion of the potential of the disturbing planet, assumed to be in an elliptical orbit. The results are presented in maps showing the lifetime of the orbit as a function of its initial inclination and eccentricity. The only perturbation acting on the orbit of the spacecraft is assumed to be the gravity of the planet, so the problem is solved by studying the orbital evolution of the spacecraft perturbed by a third body in an elliptical orbit. The region of inclination above the critical value of the third-body perturbation (around 63∘“>∘∘) is studied, since below that value the orbits survive for a long time. The influence of the eccentricity of the primaries is also investigated, assuming a hypothetical system that has the same mass parameter and sizes of the Earth–Moon system, but the eccentricity can be in the range 0.0–0.2.

doi: http://dx.doi.org/10.1016/j.asr.2015.12.007

Computational & Applied Mathematics

The goal of the present paper is to study close approaches of a cloud of particles with an oblate planet, which means that there is a J2“>J2J2 term in the gravitational potential of the planet. This cloud of particles is assumed to be created during the passage of a spacecraft by the periapsis of its orbit, by an explosion or any other disruptive event. The system is formed by two large bodies (Sun and planet), assumed to be in circular orbits around the center of mass of the system, and the cloud of particles. The particles that belong to the cloud make a close approach to the flat planet and then they are dispersed by the gravitational force of the planet. The motion is governed by the equations of motion given by the planar restricted circular three-body problem plus the effects of the oblateness of the planet. Jupiter is used for numerical simulations. The results show the differences between the behavior of the cloud after the passage, considering or not the effects of the oblateness of the planet. The results show that the oblateness of the planet is equivalent to an increase in the mass of the planet.

doi: http://dx.doi.org/10.1007/s40314-015-0264-x

Computational & Applied Mathematics

A maneuver called “Aero-Gravity Assisted” is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. In a sequence of studies related to this problem, the present paper studies close approaches between a spacecraft and the Earth, in situations where the passage is close enough to the surface of the Earth such that the spacecraft crosses its atmosphere. The dynamical model considers the atmosphere of the Earth, in terms of drag and lift, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag and lift. The primary objective is to map the variations of energy of the orbits of the spacecraft due to this close approach. The results show how the atmosphere affects the trajectory of the spacecraft, generating situations where the variation of energy changes sign with respect to the gravity part of the maneuver or where they have a zero net result, based in the equilibrium between atmospheric and gravity forces. This result opens the possibility of changing only the eccentricity of the orbit, keeping fixed its semi-major axis.

doi: http://dx.doi.org/10.1007/s40314-015-0256-x

Advances in the Astronautical Sciences

Advances in Space Research

Previous studies for small formation flying dynamics about triangular libration points have determined the existence of regions of zero and Minimum Relative Radial Acceleration with respect to the nominal trajectory, that prevent from the expansion or contraction of the constellation. However, these studies only considered the gravitational force of the Earth and the Moon using the Circular Restricted Three Body Problem (CRTBP) scenario. Although the CRTBP model is a good approximation for the dynamics of spacecraft in the Earth–Moon system, the nominal trajectories around equilateral libration points are strongly affected when the primary orbit eccentricity and solar gravitational force are considered. In this manner, the goal of this work is the analysis of the best regions to place a formation that is flying close a bounded solution around L4

“>L4, taking into account the Moon’s eccentricity and Sun’s gravity. This model is not only more realistic for practical engineering applications but permits to determine more accurately the fuel consumption to maintain the geometry of the formation.

doi: http://dx.doi.org/10.1016/j.asr.2015.03.028

Internacional Journal of Bifurcation and Chaos in Applied Sciences and Engineering

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth–Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth–Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth–Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon’s gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

doi: http://dx.doi.org/10.1142/s0218127415500777

Monthly Notices of the Royal Astronomical Society

The near-Earth Asteroid 2001 SN263 is a triple system of asteroids and it is the target of the ASTER mission – First Brazilian Deep Space Mission. The announcement of this mission has motivated a study aimed to characterize regions of stability of the system. Araujo et al., characterized the stable regions around the components of the triple system for the planar and prograde cases. Through numerical integrations they found that the stable regions are in two tiny internal zones, one of them placed very close to Alpha and another close to Beta, and in the external region. For a space mission aimed to place the probe in the internal region of the system those results do not seem to be very interesting. Therefore, 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° < I ≤ 180°, 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°, 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.

doi: http://dx.doi.org/10.1093/mnras/stv592
arxiv: https://arxiv.org/abs/1503.07546

Astronomy & Astrophysics

Context. Co-orbital systems are bodies that share the same mean orbit. They can be divided into different families according to the relative mass of the co-orbital partners and the particularities of their movement. Janus and Epimetheus are unique in that they are the only known co-orbital pair of comparable masses and thus the only known system in mutual horseshoe orbit.

Aims. We aim to establish whether the Janus-Epimetheus system might have formed by disruption of an object in the current orbit of Epimetheus.

Methods. We assumed that four large main fragments were formed and neglected smaller fragments. We used numerical integration of the full N-body problem to study the evolution of different fragment arrangements. Collisions were assumed to result in perfectly inelastic merging of bodies. We statistically analysed the outcome of these simulations to infer whether co-orbital systems might have formed from the chosen initial conditions.

Results. Depending on the range of initial conditions, up to 9% of the simulations evolve into co-orbital systems. Initial velocities around the escape velocity of Janus yield the highest formation probability. Analysis of the evolution shows that all co-orbital systems are produced via secondary collisions. The velocity of these collisions needs to be low enough that the fragments can merge and not be destroyed. Generally, collisions are found to be faster than an approximate cut-off velocity threshold. However, given a sufficiently low initial velocity, up to 15% of collisions is expected to result in merging. Hence, the results of this study show that the considered formation scenario is viable.

doi: http://dx.doi.org/10.1051/0004-6361/201425543
arxiv: https://arxiv.org/abs/1509.06933

Monthly Notices of the Royal Astronomical Society

The Erigone family is a C-type group in the inner main belt. Its age has been estimated by several researchers to be less then 300 Myr, so it is a relatively young cluster. Yarko-YORP Monte Carlo methods to study the chronology of the Erigone family confirm results obtained by other groups. The Erigone family, however, is also characterized by its interaction with the z₂ secular resonance. While less than 15 per cent of its members are currently in librating states of this resonance, the number of objects, members of the dynamical group, in resonant states is high enough to allow us to use the study of dynamics inside the z₂resonance to set constraints on the family age. Like the ν₆ and z₁ secular resonances, the z₂ resonance is characterized by one stable equilibrium point at σ = 180° in the z₂ resonance plane

, where σ is the resonant angle of the z₂ resonance. Diffusion in this plane occurs on time-scales of ≃ 12 Myr, which sets a lower limit on the Erigone family age. Finally, the minimum time needed to reach a steady-state population of z₂ librators is about 90 Myr, which allows us to impose another, independent constraint on the group age.

doi: http://dx.doi.org/10.1093/mnras/stv2430

Monthly Notices of the Royal Astronomical Society

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^−5.5reproduces 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.

doi: http://dx.doi.org/10.1093/mnras/stv1835
arxiv: https://arxiv.org/abs/1508.01365

Advances in Space Research

The present research studies Swing-By maneuvers combined with the application of an impulse at the spacecraft periapsis passage. The studies were made for different values of rp“>rp (periapsis distance), δV“>δV (magnitude of the impulse), Ψ“>Ψ (angle of approach) and α“>α (angle that defines the direction of the impulse). The results show the best direction to apply the impulse for each specific geometry of the passage, maximizing the gains or energy losses. The results show, as an example, that an angle α“>α near 20° gives the best solution to maximize the energy gains for the situation where the periapsis distance is 1.1 Moon’s radius and Ψ=90°“>Ψ=90°. This value goes to near –20°“>-20° when Ψ=270°“>Ψ=270°. In the case of maximizing the energy losses, two families with impulses against the direction of the spacecraft motion are found to be the best solutions. Conditions where the impulse generates a capture around the Moon or a collision are also mapped. For values larger than 1.1 Moon’s radius for the periapsis distance, the angle that maximizes the energy variation increases. Empirical analytical equations are obtained that express the energy variation as a function of the angle of approach, which replaces well-known equations obtained from the two-body approximation

doi: http://dx.doi.org/10.1016/j.asr.2015.04.016

Journal of Aerospace Technology and Management

doi: http://dx.doi.org/10.5028/jatm.v7i3.530

Icarus

doi: http://dx.doi.org/10.1016/j.icarus.2014.04.003

International Journal of Astrobiology

doi: http://dx.doi.org/10.1017/S1473550414000330

Advances in Space Research

doi: http://dx.doi.org/10.1016/j.asr.2015.07.001

Matemática Aplicada e Computacional 

doi: http://dx.doi.org/10.1007/s40314-014-0181-4

Celestial Mechanics & Dynamical Astronomy

doi: http://dx.doi.org/10.1007/s10569-015-9650-3

Computational & Applied Mathematics

doi: http://dx.doi.org/10.1007/s40314-015-0270-z

Matemática Aplicada e Computacional

doi: http://dx.doi.org/10.1007/s40314-015-0270-z

Icarus

doi: http://dx.doi.org/10.1016/j.icarus.2014.04.029

Mathematical Problems in Engineering

doi: http://dx.doi.org/10.1155/2015/940427

Journal of Physics

Today, computational simulatios are the best method to describe the formation of our Solar System, however this kind of simulations contain numerical errors caused by boundary conditions and choises of the grid, for instance. In this paper we will present results from several hidrodynamical simulations of the formation of a planet like Jupiter able to migrate using different computational parameters. We will compare the density profile, the semimajor axis and the eccentricity of the planet for those different parameters and measure the effect of them. We will not extend our results for planets with initial eccentric orbits in this paper.

doi: http://dx.doi.org/10.1088/1742-6596/641/1/012012

Journal of Physics

Collisions between operational vehicles and space debris can completely derail the continuity of space missions, especially if there is chain collisions between debris, which generate even smaller fragments. In this paper, we investigate the dynamics on between an operational vehicle and space debris that form a cloud, considering the possibility of collisions between debris during an evasive maneuver the vehicle. For a radius of 3 km celestial sphere, we find possibilities of collision between debris up to 10 m, while the vehicle performs an evasive maneuver in time 3,000 s range. These results depend on the time collision, the angular positions of the collisional objects and the amount of debris that form the cloud.

doi: http://dx.doi.org/10.1088/1742-6596/641/1/012021

Monthly Notices of the Royal Astronomical Society 

In the last two decades, new computational tools have been developed in order to aid space missions to orbit around irregular small bodies. One of the techniques consists in rebuilding their shape in tetrahedral polyhedron. This method is well suited to determine the shape and estimate certain physical features of asteroids. However, a large computational effort is necessary depending on the quantity of triangular faces chosen. Another method is based on a representation of the central body in terms of mascons (discrete spherical masses). The main advantage of the method is its simplicity which makes the calculation faster. Nevertheless, the errors are non-negligible when the attraction expressions are calculated near the surface of the body. In this work, we carry out a study to develop a new code that determines the centre of mass of each tetrahedron of a shaped polyhedral source and evaluates the gravitational potential function and its first- and second-order derivatives. We performed a series of tests and compared the results with the classical polyhedron method. We found good agreement between our determination of the attraction expressions close to the surface, and the same determination by the classical polyhedron method. However, this agreement does not occur inside the body. Our model appears to be more accurate in representing the potential very close to the body’s surface when we divide the tetrahedron in three parts. Finally, we have found that in terms of CPU time requirements, the execution of our code is much faster compared with the polyhedron method.

doi: http://dx.doi.org/10.1093/mnras/stv845

Monthly Notices of the Royal Astronomical Society 

The Cybele region, located between the 2J:-1A and 5J:-3A mean-motion resonances, is adjacent and exterior to the asteroid main belt. An increasing density of three-body resonances makes the region between the Cybele and Hilda populations dynamically unstable, so that the Cybele zone could be considered the last outpost of an extended main belt. The presence of binary asteroids with large primaries and small secondaries suggested that asteroid families should be found in this region, but only relatively recently the first dynamical groups were identified in this area. Among these, the Sylvia group has been proposed to be one of the oldest families in the extended main belt. In this work we identify families in the Cybele region in the context of the local dynamics and non-gravitational forces such as the Yarkovsky and stochastic Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effects. We confirm the detection of the new Helga group at ≃3.65 au, which could extend the outer boundary of the Cybele region up to the 5J:-3A mean-motion resonance. We obtain age estimates for the four families, Sylvia, Huberta, Ulla, and Helga, currently detectable in the Cybele region, using Monte Carlo methods that include the effects of stochastic YORP and variability of the solar luminosity. The Sylvia family should be T = 1220 ± 40 Myr old, with a possible older secondary solution. Any collisional Cybele group formed prior to the Late Heavy Bombardment would have been most likely completely dispersed in the jumping Jupiter scenario of planetary migration.

doi: http://dx.doi.org/10.1093/mnras/stv845
arxiv: https://arxiv.org/abs/1505.03745

Astrophysical Journal

The Euphrosyne asteroid family is uniquely situated at high inclination in the outer Main Belt, bisected by the  secular resonance. This large, low albedo family may thus be an important contributor to specific subpopulations of the near-Earth objects. We present simulations of the orbital evolution of Euphrosyne family members from the time of breakup to the present day, focusing on those members that move into near-Earth orbits. We find that family members typically evolve into a specific region of orbital element-space, with semimajor axes near  AU, high inclinations, very large eccentricities, and Tisserand parameters similar to Jupiter family comets. Filtering all known Near-Earth objects (NEOs) with our derived orbital element limits, we find that the population of candidate objects is significantly lower in albedo than the overall NEO population, although many of our candidates are also darker than the Euphrosyne family, and may have properties more similar to comet nuclei. Followup characterization of these candidates will enable us to compare them to known family properties, and confirm which ones originated with the breakup of (31) Euphrosyne.

doi: http://dx.doi.org/10.1088/0004-637X/809/2/179
arxiv: https://arxiv.org/abs/1507.07887

Icarus

Many asteroid families are identified and well characterized all over the main asteroid belt. Interestingly, however, none of them are older than 4 Gyr. Many mechanisms have been proposed to disperse such old primordial asteroid families that presumably have existed, but only very few have really worked. Here we present a plausible mechanism for dispersing primordial asteroid families that is based on the 5-planet instability model known as jumping Jupiter. Using two different evolutions for the jumping-Jupiter model, we have numerically integrated orbits of eight putative primordial families. Our results show that the most important effect on the asteroid families’ eccentricity and inclination dispersal is that of the secular resonances, in some cases associated with the mean motion resonances. As for the semimajor axes spreading we find that the principal effect is that of close encounters with the fifth giant planet whose orbit briefly overlaps with (part of) the main belt. Therefore, the existence of a fifth giant planet with the mass comparable with that of Uranus’ or Neptune’s could contribute in important ways to dispersal of the primordial asteroid families. To have that effect, the interloper planet should go into and considerably interact with the asteroids during the instability phase.

doi: http://dx.doi.org/10.1016/j.icarus.2015.11.015

Advances in the Astronautical Sciences

We study the secular dynamics of hierarchical (if there is a clearly defined binary and a third body which stays separate from the binary) triple systems composed by a Sun-like central star and a Jupiter-like planet, which are under the gravitational influence of a further perturbing star (brown dwarf). The main goal is to study the orbital evolution of the planet. In special, we investigate the orientation (inclination) and the shape (eccentricity) of its orbit. One key feature explored is the time needed for the first flip in its orientation (prograde to retrograde). The gravitational potential is developed in closed form up to the third order. We have compared the secular evolution of systems with and without the third order term of the disturbing potential. The R2 (quadrupole) and R3 (octupole) terms of the disturbing potential are developed without using the elimination of nodes. Numerical simulations were also performed to compare with the analytical model using the N-body simulations with the Mercury code. The results show that the analytical model are in agreement with the numeric simulations.

Computational & Applied Mathematics

This paper has the goal of searching for natural trajectories that can be used for a particle or a spacecraft coming from a region of the space far from Jupiter system to be captured into this system by making close approaches with the Galilean satellites of the planet. The opposite situation is also possible and escape trajectories can also be found. This type of maneuver is called “Swing-By” and it is usual in astrodynamics. It was used in many space missions to reduce the fuel consumption by gaining or loosing energy from the gravity of a celestial body. Several famous examples are the Voyager, Cassini, Galileo and other missions. The idea of the present research is to study this type of maneuver using the Galilean satellites of Jupiter, to search for trajectories that change the two-body energy (particle or spacecraft)–(Jupiter) from positive to negative (a capture trajectory) or from negative to positive (an escape trajectory). Those trajectories can be used for a spacecraft going or leaving the planet Jupiter or to explain how particles can be captured or escape from Jupiter system by close approaches with the Galilean satellites. Initial conditions are varied to cover the whole possible alternatives and then small regions of captures and escapes are identified. After that, a study is made to see the accuracy of the Tisserand’s method when applied to those close approach trajectories.

doi: http://dx.doi.org/10.1007/s40314-014-0152-9

The Astrophysical Journal

Models of terrestrial planet formation for our solar system have been successful in producing planets with masses and orbits similar to those of Venus and Earth. However, these models have generally failed to produce Mars-sized objects around 1.5 AU. The body that is usually formed around Mars’ semimajor axis is, in general, much more massive than Mars. Only when Jupiter and Saturn are assumed to have initially very eccentric orbits (e ~ 0.1), which seems fairly unlikely for the solar system, or alternately, if the protoplanetary disk is truncated at 1.0 AU, simulations have been able to produce Mars-like bodies in the correct location. In this paper, we examine an alternative scenario for the formation of Mars in which a local depletion in the density of the protosolar nebula results in a non-uniform formation of planetary embryos and ultimately the formation of Mars-sized planets around 1.5 AU. We have carried out extensive numerical simulations of the formation of terrestrial planets in such a disk for different scales of the local density depletion, and for different orbital configurations of the giant planets. Our simulations point to the possibility of the formation of Mars-sized bodies around 1.5 AU, specifically when the scale of the disk local mass-depletion is moderately high (50%-75%) and Jupiter and Saturn are initially in their current orbits. In these systems, Mars-analogs are formed from the protoplanetary materials that originate in the regions of disk interior or exterior to the local mass-depletion. Results also indicate that Earth-sized planets can form around 1 AU with a substantial amount of water accreted via primitive water-rich planetesimals and planetary embryos. We present the results of our study and discuss their implications for the formation of terrestrial planets in our solar system.

doi: http://dx.doi.org/10.1088/0004-637x/782/1/31
arxiv: https://arxiv.org/abs/1312.3959

Monthly Notices of the Royal Astronomical Society

One of the techniques used in the past decade to determine the shape with a good accuracy and estimate certain physical features (volume, mass, moments of inertia) of asteroids is the polyhedral model method. We rebuild the shape of the asteroid 433 Eros using data from 1998 December observations of the probe Near-Earth-Asteroid-Rendezvous-Shoemaker. In our computations, we use a code that avoids singularities from the line integrals of a homogeneous arbitrary shaped polyhedral source. This code evaluates the gravitational potential function and its first- and second-order derivatives. Taking the rotation of asteroid 433 Eros into consideration, the aim of this work is to analyse the dynamics of numerical simulations of 3D initially equatorial orbits near the body. We find that the minimum radius for direct, equatorial circular orbits that cannot impact with the Eros surface is 36 km and the minimum radius for stable orbits is 31 km despite significant perturbations of its orbit. Moreover, as the orbits suffer less perturbations due to the irregular gravitational potential of Eros in the elliptic case, the most significant result of the analysis is that stable orbits exist at a periapsis radius of 29 km for initial eccentricities e_i ≤ 0.2.

doi: http://dx.doi.org/10.1093/mnras/stt2383

Advances in Space Research

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth–Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon’s sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon’s gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.

doi: http://dx.doi.org/10.1016/j.asr.2013.11.055

Astronomy & Astrophysics

The asteroids that may cross, or approach, the orbit of the terrestrial planets compose the NEAs population. In the present work we studied the effects of close encounters between hypothetical NEAs’ binaries and the Earth to determine the limiting stability of their satellites as a function of the encounter conditions. We were able to estimate the frequency of such encounters, thus, the expected lifetime of the NEAs binaries. Through numerical simulations, all the encounters between asteroids and the Earth that were closer than 100 Earth radii were recorded. The next step consisted of simulating a representative sample of those encounters considering the Earth, and the asteroid with a cloud of non-interacting satellites around it. The largest radial distance for which all the satellites survive (no collision or disruption) was defined as the critical radius R_C. We present a statistical analysis of the recorded encounters, and the critical radius given as a function of the impact parameter and of the relative velocity, defining the stable and unstable encounter conditions for the NEAs satellites. In all these simulations and analyses three distinct satellite masses were considered: massless satellites, satellites with ten percent of the asteroid mass, and satellites with the same mass of the asteroid. We found that the close encounters that are able to remove the most internal satellites are quite frequent. For the NEAs of the sample initially belonging to the Atens group, we found that ≈93% of them suffer an encounter with such characteristics within 10 Myr and that 50% of these encounters happen within approximately 330 thousand years. Our results confirm that, in fact, the close encounter of binaries with the Earth is a powerful mechanism for disrupting these systems and that their lifetimes are strongly influenced by the planetary close encounters.

doi: http://dx.doi.org/10.1051/0004-6361/201322979

Astronomy & Astrophysics

Context. The Brazilian Aster project plans a space mission to rendezvous and characterize (153591) 2001 SN263, one of the only two known triple near-Earth asteroids (NEAs). Improving the knowledge of its physical properties is necessary to optimize the mission planning and science return.

Aims. We study the surface composition and physical nature of 2001 SN263 by analyzing and comparing its reflectance spectra with laboratory spectra of minerals and meteorites.

Methods. We performed spectroscopic observations of 2001 SN263 using the UV-to-NIR X-Shooter spectrograph at the ESO Very Large Telescope (VLT). Complementary photometric observations of the target were acquired with the FORS2 instrument.

Results. We find B-type, featureless convex spectra (Themis- or Polana-like). 2001 SN263 presents the bluest visible spectrum ever observed for small bodies in the solar system, even bluer than NEAs Phaethon and Bennu. The spectra suggest that the surface composition is organic- and magnetite-rich, similar to that of heated CI carbonaceous chondrites. Phyllosilicates may be abundant as well. We find hints of a coarse-grained surface and composition variety within the triple system.

Conclusions. Both the large grain size and surface variability might be connected to the formation of the triple system. The Aster mission will have the intriguing possibility of checking current models of asteroid binary formation.

doi: http://dx.doi.org/10.1051/0004-6361/201424447

Monthly Notices of the Royal Astronomical Society

Giuliatti Winter et al. found several stable regions for a sample of test particles located between the orbits of Pluto and Charon. One peculiar stable region in the space of the initial orbital elements is located at a = (0.5d, 0.7d) and e = (0.2, 0.9), where a and e are the initial semimajor axis and eccentricity of the particles, respectively, and d is the Pluto–Charon distance. This peculiar region (hereafter called the sailboat region) is associated with a family of periodic orbits derived from the planar, circular, restricted three-body problem (Pluto–Charon–particle). In this work, we study the origin of this stable region by analysing the evolution of such family of periodic orbits. We show that they are not in resonances with Charon. The period of the periodic orbit varies along the family, decreasing with the increase of the Jacobi constant. We also explore the extent of the sailboat region by adopting different initial values of the orbital inclination (I) and argument of the pericentre (ω) of the particles. The sailboat region is present for I = [0°, 90°] and for two intervals of ω, ω = [−10°, 10°] and (160°, 200°). A crude estimative of the size of the hypothetical bodies located at the sailboat region can be derived by computing the tidal damping in their eccentricities. If we neglect the orbital evolution of Pluto and Charon, the time-scale for circularization of their orbits is longer than the age of the Solar system for bodies smaller than 500 m in radius.

doi: http://dx.doi.org/10.1093/mnras/stu147

Advances in Space Research

Assume a constellation of satellites is flying near a given nominal trajectory around L4“>L4 or L5“>L5 in the Earth–Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around L4“>L4 or L5“>L5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth–Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit.

doi: http://dx.doi.org/10.1016/j.asr.2014.07.018

Nature

Hitherto, rings have been found exclusively around the four giant planets in the Solar System¹. Rings are natural laboratories in which to study dynamical processes analogous to those that take place during the formation of planetary systems and galaxies. Their presence also tells us about the origin and evolution of the body they encircle. Here we report observations of a multichord stellar occultation that revealed the presence of a ring system around (10199) Chariklo, which is a Centaur—that is, one of a class of small objects orbiting primarily between Jupiter and Neptune—with an equivalent radius of 124  9 kilometres (ref. 2). There are two dense rings, with respective widths of about 7 and 3 kilometres, optical depths of 0.4 and 0.06, and orbital radii of 391 and 405 kilometres. The present orientation of the ring is consistent with an edge-on geometry in 2008, which provides a simple explanation for the dimming³ of the Chariklo system between 1997 and 2008, and for the gradual disappearance of ice and other absorption features in its spectrum over the same period^4,5. This implies that the rings are partly composed of water ice. They may be the remnants of a debris disk, possibly confined by embedded, kilometre-sized satellites.

doi: http://dx.doi.org/10.1038/nature13155

New Journal of Physics

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process—a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small- and intermediate-size fragments obeys a power law, F(m)∝m^−3/2, in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.

doi: http://dx.doi.org/10.1088/1367-2630/16/1/013031
arxiv: https://arxiv.org/pdf/1106.2721.pdf

New Journal of Physics

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process—a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small- and intermediate-size fragments obeys a power law, F(m)∝m^−3/2, in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.

doi: http://dx.doi.org/10.1088/1367-2630/16/1/013031
arxiv: https://arxiv.org/pdf/1106.2721.pdf

Monthly Notices of the Royal Astronomical Society

V-type asteroids are associated with basaltic composition, and are supposed to be fragments of crust of differentiated objects. Most V-type asteroids in the main belt are found in the inner main belt, and are either current members of the Vesta dynamical family (Vestoids), or past members that drifted away. However, several V-type photometric candidates have been recently identified in the central and outer main belt.

The origin of this large population of V-type objects is not well understood. Since it seems unlikely that Vestoids crossing the 3J:-1A mean-motion resonance with Jupiter could account for the whole population of V-type asteroids in the central and outer main belt, origin from local sources, such as the parent bodies of the Eunomia, and of the Merxia and Agnia asteroid families, has been proposed as an alternative mechanism.

In this work, we investigated the dynamical evolution of the V-type photometric candidates in the central main belt, under the effect of gravitational and non-gravitational forces. Our results show that dynamical evolution from the parent bodies of the Eunomia and Merxia/Agnia families on time-scales of 2 Byr or more could be responsible for the current orbital location of most of the low-inclined V-type asteroids.

doi: http://dx.doi.org/10.1093/mnras/stu192
arxiv: https://arxiv.org/abs/1401.6332

The Astrophysical Journal

The asteroid (31) Euphrosyne is the largest body of its namesake family, and it contains more than 99% of the family mass. Among large asteroid families, the Euphrosyne group is peculiar because of its quite steep size-frequency distribution (SFD), significantly depleted in large- and medium-sized asteroids (8 < D < 12 km). The current steep SFD of the Euphrosyne family has been suggested to be the result of a grazing impact in which only the farthest, smallest members failed to accrete. The Euphrosyne family is, however, also very peculiar because of its dynamics: near its center it is crossed by the ν₆ = g – g ₆ linear secular resonance, and it hosts the largest population (140 bodies) of asteroids in ν₆ antialigned librating states (or Tina-like asteroids) in the main belt. In this work we investigated the orbital evolution of newly obtained members of the dynamical family, with an emphasis on its interaction with the ν₆ resonance. Because of its unique resonant configuration, large- and medium-sized asteroids tend to migrate away from the family orbital region faster than small-sized objects, which were ejected farther away from the family center. As a consequence, the SFD of the Euphrosyne family becomes steeper in time with a growing depletion in the number of the largest family members. We estimate that the current SFD could be attained from a typical, initial SFD on timescales of 500 Myr, consistent with estimates of the family age obtained with other independent methods.

doi: http://dx.doi.org/10.1088/0004-637X/792/1/46

Monthly Notices of the Royal Astronomical Society

V-type asteroids, characterized by two absorption bands at 1.0 and 2.0 μm, are usually thought to be portions of the crust of differentiated or partially differentiated bodies. Most V-type asteroids are found in the inner main belt and are thought to be current or past members of the Vesta dynamical family. Recently, several V-type photometric candidates have been identified in the central and outer main belt. While the dynamical evolution of V-type photometric candidates in the central main belt has been recently investigated, less attention has been given to the orbital evolution of basaltic material in the outer main belt as a whole. Here, we identify known and new V-type photometric candidates in this region, and study their orbital evolution under the effect of gravitational and non-gravitational forces. A scenario in which a minimum of three local sources, possibly associated with the parent bodies of (349) Dembowska, (221) Eos, and (1459) Magnya, could in principle explain the current orbital distribution of V-type photometric candidates in the region.

doi: http://dx.doi.org/10.1093/mnras/stu1655
arxiv: https://arxiv.org/abs/1408.7080

Journal of Physics

Future Moon missions devoted to Lunar surface remote sensing, for example, will require very fine and accurate orbit control. It is well known that Lunar satellites in polar orbits will suffer a high increase on the eccentricity due to the gravitational perturbation of the Earth. Without proper orbit correction the satellite lifetime will decrease and end up in a collision with the Moon surface. It is pointed out by many authors that this effect is a natural consequence of the Lidov-Kozai resonance. We studied different arcs of active lunar satellite propulsion, centered on the orbit apoapsis or periapsis, in order to be able to introduce a correction of the eccentricity at each cycle. The proposed method is based on an approach intended to keep the orbital eccentricity of the satellite at low values.

doi: http://dx.doi.org/10.1088/1742-6596/511/1/012074

Mathematical Problems in Engineering

The fuel consumption required by the orbital maneuvers when correcting perturbations on the orbit of a spacecraft due to a perturbing body was estimated. The main goals are the measurement of the influence of the eccentricity of the perturbing body on the fuel consumption required by the station keeping maneuvers and the validation of the averaged methods when applied to the problem of predicting orbital maneuvers. To study the evolution of the orbits, the restricted elliptic three-body problem and the single- and double-averaged models are used. Maneuvers are made by using impulsive and low thrust maneuvers. The results indicated that the averaged models are good to make predictions for the orbital maneuvers when the spacecraft is in a high inclined orbit. The eccentricity of the perturbing body plays an important role in increasing the effects of the perturbation and the fuel consumption required for the station keeping maneuvers. It is shown that the use of more frequent maneuvers decreases the annual cost of the station keeping to correct the orbit of a spacecraft. An example of an eccentric planetary system of importance to apply the present study is the dwarf planet Haumea and its moons, one of them in an eccentric orbit.

doi: http://dx.doi.org/10.1155/2014/359845

Applied Mechanics and Materials

This work is concerned with short arcs orbit determination using GPS signals. A special case of truncated arcs assuming that GPS data is only available when the satellite carrying the GPS receiver passes over a ground tracking station is presented. The behaviour of an Extended Kalman filter (EKF) in real time satellite orbit determination using short arcs of data is analysed. The algorithm is a simplified and compact model with low computational cost, and uses the EKF to estimate the state vector, composed of position and velocity components, and GPS receiver clock parameters. The algorithm may use different step-sizes between the GPS signal measurements. Its force model in the motion equations considered the perturbations as being due to the geopotential up to the 10^th order and degree of the spherical harmonics. The algorithm has been formerly qualified using raw single frequency pseudorange GPS measurements of the Topex/Poseidon (T/P) satellite, and used as reference in this work. However, the GPS data are truncated as if they had been collected by a single ground tracking station. In other words, the data are obtained only when the satellite T/P is within the viewing area of the station. The research results are presented showing the degradation of performance when compared to a full arc orbit determination.

doi: http://dx.doi.org/10.4028/www.scientific.net/amm.706.206