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We consider the curved $4$-body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configurations on the equator of the sphere, we study two restricted $4$-body problems, one in which two masses are negligible and another in which only one mass is negligible. In the former, we prove the evidence square-like relative equilibria, whereas in the latter we discuss the existence of kite-shaped relative equilibria.
Obliquity (axial tilt) and its variability could play an important role in the climate and habitability of a planet. We explore the spin-axis dynamics of two specific habitable zone exoplanets, Kepler-62f and Kepler-186f, using numerical and analytical techniques. Based on our current understanding of their orbital architecture, we find that, in contrast with the typical conditions in the Solar System, Kepler-62f and 186f should have low obliquity variations except in fine-tuned conditions. Extra undetected planetary companions and/or the existence of a satellite could either stabilize or destabilize obliquities at a variety of values.
During the early stages of planet formation accretion of small bodies add mass to the planet and deposit their energy kinetic energy. Caused by frictional heating and/or large stagnation pressures within the dense and extended atmospheres most of the in-falling bodies get destroyed by melting or break-up before they impact on the planet’s surface. The energy is added to the atmospheric layers rather than heating the planet directly. These processes can significantly alter the physical properties of protoplanets before they are exposed with their primordial atmospheres to the early stellar source when the protoplanetary disk becomes evaporated.
The second (after Pluto) plausible target object for the New Horizons mission is 2014 MU69. It is a classical TNO, a primordial contact binary. Identifying any material in the vicinities of a target object is of an especial concern for planning cosmic fly-byes, as it is hazardous for a space probe. Luckily, no such material has been reported for MU69 up to now. The point of our report is that this lucky absence is just a dynamical consequence of the physical nature of MU69. Spinning gravitating dumbbells create zones of dynamical chaos around them, and this has a clearing effect: any material put in orbits around a rotating dumbbell (e.g., any material ejected from its surface) cannot be long-lived in such zones; it either escapes into space, or returns to the parent body’s surface. As the orbiting matter is removed in this way, a spinning gravitating dumbbell clears its vicinities. We show that MU69 is able to create such a clearing, making itself a safe and hospitable target for a space mission. Therefore, the guest probe is expected to be safe on arrival.
We continue to investigate the binary system Kepler-16, consisting of a K-type main-sequence star, a red dwarf and a circumbinary Saturnian planet. As part of our study, we describe the system's habitable zone based on different climate models. We also report on stability investigations for possible Earth-mass Trojans while expanding a previous study by B. L. Quarles and collaborators given in 2012. For the climate models, we carefully consider the relevance of the system's parameters. Furthermore, we pursue new stability simulations for the Earth-mass objects starting along the orbit of Kepler-16b. The eccentricity distribution as obtained prefers values close to circular, whereas the inclination distribution remains flat. The stable solutions are distributed near the co-orbital Lagrangian points, thus enhancing the plausibility that Earth-mass Trojans might be able to exist in the Kepler-16(AB) system.
Fomalhaut b was long thought to shape the eccentric debris belt in the Fomalhaut system, but its orbit was found to be too eccentric for it to be the dominant belt-shaping perturber. This indicates that Fomalhaut b is Earth-sized at most and that the belt-shaping perturber, hereafter named Fomalhaut c, remains to be discovered. In addition, since its orbit more or less crosses that of Fomalhaut b, it also indicates that the current configuration of the system is transient and was reached recently. In this talk, we show that this current configuration can be explained if Fomalhaut c is Saturn- to Neptune-sized, and Fomalhaut b originates from a mean-motion resonance with Fomalhaut c.
Deflection missions to near-Earth asteroids will encounter non-negligible uncertainties in the physical and orbital parameters of the target object. In order to reliably assess future impact threat mitigation operations such uncertainties have to be quantified and incorporated into the mission design. The implementation of deflection demonstration missions offers the great opportunity to test our current understanding of deflection relevant uncertainties and their consequences, e.g., regarding kinetic impacts on asteroid surfaces. In this contribution, we discuss the role of uncertainties in the NEOTωIST asteroid deflection demonstration concept, a low-cost kinetic impactor design elaborated in the framework of the NEOShield project. The aim of NEOTωIST is to change the spin state of a known and well characterized near-Earth object, in this case the asteroid (25143) Itokawa. Fast events such as the production of the impact crater and ejecta are studied via cube-sat chasers and a flyby vehicle. Long term changes, for instance, in the asteroid's spin and orbit, can be assessed using ground based observations. We find that such a mission can indeed provide valuable constraints on mitigation relevant parameters. Furthermore, the here proposed kinetic impact scenarios can be implemented within the next two decades without threatening Earth's safety.
While regular astronomical image archive searches can find images at a fixed location, they cannot find images of moving targets such as asteroids or comets. The Solar System Object Image Search (SSOIS) at the Canadian Astronomy Data Centre allows users to search for images of moving objects, allowing precoveries. SSOIS accepts as input either an object designation, a list of observations, a set of orbital elements, or a user-generated ephemeris for an object. It then searches for observations of that object over a range of dates. The user is then presented with a list of images containing that object from a variety of archives. Initially created to search the CFHT MegaCam archive, SSOIS has been extended to other telescopes including Gemini, Subaru/SuprimeCam, WISE, HST, the SDSS, AAT, the ING telescopes, the ESO telescopes, and the NOAO telescopes (KPNO/CTIO/WIYN), for a total of 24.5 million images. As the Pan-STARRS and Hyper Suprime-Cam archives become available, they will be incorporated as well. The SSOIS tool is located on the web at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/ssois/.
The problem of binary asteroids orbit determination is of particular interest, given knowledge of the orbit is the best way to derive the mass of the system. Orbit determination from observed points is a classic problem of celestial mechanics. However, in the case of binary asteroids, particularly with a small number of observations, the solution is not evident to derive. In the case of resolved binaries the problem consists in the determination of the relative orbit from observed relative positions of a secondary asteroid with respect to the primary. In this work, the problem is investigated as a statistical inverse problem. Within this context, we propose a method based on Bayesian modelling together with a global optimisation procedure that is based on the simulated annealing algorithm.
With the improvements of the observational technology for the new surveys the number of asteroid detections is rapidly increasing. For this reason we must use very efficient methods to compute orbits with these data. We have to identify observations taken in different nights as belonging to the same asteroid. If we do not have an efficient algorithm for that, the unidentified observation database can increase without control, and we risk to detect the same objects multiple times.
Recent investigations on small asteroids, initiated by the Chelyabinsk event, are reviewed. New estimates of the terrestrial impact rate, importance of Sun-grazing conditions in the evolution of near-Earth objects, and problems associated with dangerous objects approaching the Earth from the Sun direction are discussed.
We consider the role of the dwarf planet Ceres on the secular dynamics of the asteroid main belt. Specifically, we examine the post impact evolution of asteroid families due to the interaction of their members with the linear nodal secular resonance with Ceres. First, we find the location of this resonance and identify which asteroid families are crossed by its path. Next, we summarize our results for three asteroid families, namely (1726) Hoffmeister, (1128) Astrid and (1521) Seinajoki which have irregular distributions of their members in the proper elements space, indicative of the effect of the resonance. We confirm this by performing a set of numerical simulations, showcasing that the perturbing action of Ceres through its linear nodal secular resonance is essential to reproduce the actual shape of the families.
We review the most standard impact monitoring techniques. Linear methods are the fastest approach but their applicability regime is limited because of the chaotic dynamics of near-Earth asteroids. Among nonlinear methods, Monte Carlo algorithms are the most reliable ones but also most computationally intensive and so unpractical for routine impact monitoring. In the last 15 years, the Line of Variations method has been the most successful technique thanks to its computational efficiency and capability of detecting low probability events deep in the nonlinear regime. We also present some more recent techniques developed to deal with the new challenges arising in the impact hazard assessment problem. In particular, we describe keyhole maps as a tool to go beyond strongly scattering encounters and how to account for nongravitational perturbations, especially the Yarkovsky effect, when their contribution is the main source of prediction uncertainty. Finally, we discuss systematic ranging to deal with the short-term hazard assessment problem for newly discovered asteroids, when only a short observed arc is available thus leading to severe degeneracies in the orbit estimation process.
Planets have been revealed both in binary and triple stellar systems. Although there have been several studies of the late stages of planet formation in binary stars this process does not appear to have been studied in triple stellar systems. To understand how the late stage of planetary accretion is affected by a third companion, in this work we have numerically investigated the formation of planets in a hypothetical triple stellar system. The system is composed by an inner binary formed by two half-solar-mass components orbited by a solar-mass star. In our experiments, lunar and Mars-sized planetary embryos are distributed around the centre of mass of the inner binary system. Our main goal is to analyse how the formation of planets evolves depending on the orbital configuration of the massive distant companion. We have performed an extensive number of numerical simulations considering different orbital configurations for the third star. All simulations were numerically integrated for at least 107 years. The results show that when the protoplanetary disc and the stars are initially on coplanar orbits, one or two planets are quickly formed between 6 and 8 AU. In general such planets have also small eccentricities with values about 10−2. On the other hand, when the third star is considered initially on inclined orbits (even tiny values), there tends to occur a significant increase in the inclination of bodies of protoplanetary disc, which prevents the collisions between these objects and their growth. As a result, in this latter case we do not evidence the formation of planets during the timescale of our integrations but note the existence of several leftover objects that can survive for longer than 10 Myr, moving in orbits with semi-major axes ranging between ~6 and 8 AU. Thus, our results do not rule out the planet formation in this kind of stellar arrangements at all, but they indicate that, if planetary bodies keep stable orbits, the late stage of planet formation in systems with a highly inclined third star can be a very long process and many of these triple hierarchical systems might not have had time to form planets and planetary systems. They could be harbouring only debris discs, fragments or planetesimals.
By now, observations of exoplanets have found more than 50 binary star systems hosting 71 planets. We expect these numbers to increase as more than 70% of the main sequence stars in the solar neighborhood are members of binary or multiple systems. The planetary motion in such systems depends strongly on both the parameters of the stellar system (stellar separation and eccentricity) and the architecture of the planetary system (number of planets and their orbital behaviour). In case a terrestrial planet moves in the so-called habitable zone (HZ) of its host star, the habitability of this planet depends on many parameters. A crucial factor is certainly the amount of water. We investigate in this work the transport of water from beyond the snow-line to the HZ in a binary star system and compare it to a single star system.
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. For example, 55 Cancri is a system composed of 5 planets orbiting a member of a stellar binary for which a projected obliquity of 72±12 ° relative to the orbit of the innermost planet has been reported (Bourrier & Hébrard 2014). This large obliquity has been attributed to the perturbation induced by the binary. Here we describe the secular evolution of similar systems and we discuss the case of the 55 Cancri system more deeply. We provide two different orbital configurations compatible with the currently available observations.
The stability diagrams in the “pericentric distance — eccentricity” plane of initial data are built and analyzed for Kepler-38, Kepler-47, and Kepler-64 (PH1). This completes a survey of stability of the known up to now circumbinary planetary systems, initiated by Popova & Shevchenko (2013), where the analysis was performed for Kepler-16, 34, and 35. In the diagrams, the planets appear to be “embedded” in the fractal chaos border; however, I make an attempt to measure the “distance” to the chaos border in a physically consistent way. The obtained distances are compared to those given by the widely used numerical-experimental criterion by Holman & Wiegert (1999), who employed smooth polynomial approximations to describe the border. I identify the resonance cells, hosting the planets.
We study the secular dynamics of extrasolar planetary systems by extending the Lagrange-Laplace theory to high order and by including the relativistic effects. We investigate the long-term evolution of the planetary eccentricities via normal form and we find an excellent agreement with direct numerical integrations. Finally we set up a simple analytic criterion that allows to evaluate the impact of the relativistic effects in the long-time evolution.
In this paper we consider the special case of the planar circular restricted three-body problem by the example of the problem of the Earth, the Moon and a point mass, where the gravitational potentials of the Earth and the Moon are given as the Kislik potential. The Kislik potential takes into account the flattening of a celestial body on the poles. We find the relative equilibria solutions for a point mass and analyze their stability. We describe the difference between the obtained points and the classical solution of the three-body problem.