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"Celestial mechanics"
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Finding our place in the universe : how we discovered Laniakea-- the Milky Way's home
\"The book tells the story of how Courtois and her cosmography colleagues discovered and mapped the Laniakea galactic supercluster, the first and most accurate description to date of our home galaxy's location in the universe. Courtois reveals the joys and challenges of international astronomy research and collaborations, humanizing the scientists along the way and making the science accessible. She also makes an effort to shed light on the life and work of herself and other women astronomers. It's a story that would appeal to a wide audience.\"-- Provided by publisher.
Book
Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem
We prove the existence of an almost full measure set of
The
proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of
degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection
invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, common
tool of previous literature.
eBook
Machine learning applied to asteroid dynamics
Machine learning (ML) is the branch of computer science that studies computer algorithms that can learn from data. It is mainly divided into supervised learning, where the computer is presented with examples of entries, and the goal is to learn a general rule that maps inputs to outputs, and unsupervised learning, where no label is provided to the learning algorithm, leaving it alone to find structures. Deep learning is a branch of machine learning based on numerous layers of artificial neural networks, which are computing systems inspired by the biological neural networks that constitute animal brains. In asteroid dynamics, machine learning methods have been recently used to identify members of asteroid families, small bodies images in astronomical fields, and to identify resonant arguments images of asteroids in three-body resonances, among other applications. Here, we will conduct a full review of available literature in the field and classify it in terms of metrics recently used by other authors to assess the state of the art of applications of machine learning in other astronomical subfields. For comparison, applications of machine learning to Solar System bodies, a larger area that includes imaging and spectrophotometry of small bodies, have already reached a state classified as progressing. Research communities and methodologies are more established, and the use of ML led to the discovery of new celestial objects or features, or new insights in the area. ML applied to asteroid dynamics, however, is still in the emerging phase, with smaller groups, methodologies still not well-established, and fewer papers producing discoveries or insights. Large observational surveys, like those conducted at the Zwicky Transient Facility or at the Vera C. Rubin Observatory, will produce in the next years very substantial datasets of orbital and physical properties for asteroids. Applications of ML for clustering, image identification, and anomaly detection, among others, are currently being developed and are expected of being of great help in the next few years.
Journal Article
Retrograde resonances at high mass ratio in the circular restricted 3-body problem
Studies involving retrograde orbits have been an emerging field in recent years, particularly in the case where there are resonances between objects orbiting in opposite directions. The high amount of data from space exploration missions increases the possibility of observing binary stellar systems which may have additional bodies with retrograde orbits. Furthermore, such orbits are relevant to understanding the dynamics of spacecrafts around binary asteroids, being essential to planning exploratory missions. In this work, we survey retrograde orbits around binary systems with mass ratio between 0.01 (hierarchical) and 0.5 (equal masses) in the framework of the planar circular restricted three-body problem (PCR3BP). We build surfaces of section and identify retrograde resonances up to fifth order, namely the 2/−1, 3/−2, 1/−1, 2/−3, 1/−2, 1/−3 and 1/−4 resonances. We conclude that retrograde resonances occur in binary systems at high mass ratio, including the co-orbital (1/−1) resonance. Period doubling bifurcations occur for the 1/−1 resonance, and period doubling and period tripling bifurcations are observed for the 1/−2 resonance. Asymmetric retrograde resonances of the type 1/−n occur for almost equal masses of the binary system. This study may be used for identifying retrograde planets in extrasolar systems and may possibly have applications to astrodynamics mission planning.
Journal Article
The p : q resonance for dissipative spin–orbit problem in celestial mechanics
In this paper, we investigate the existence of p : q resonant orbit for the dissipative spin–orbit problem of the celestial mechanics. Our result is the generalization of the work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) from C∞ topology to analytic and finitely differentiable topology. Moreover, our result gives the existence condition of p : q resonance solutions for concrete dissipative spin–orbit model under arbitrary potential frequency μ, which can reduce to result in work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) when μ=2. It is also a generalization from low-order resonance to arbitrary-order resonance. Our proof is based on Lyapunov–Schmidt decomposition, the contraction mapping principle on Sobolev space Hs and Hρ,s and perturbation theory.
Journal Article
Use of Transit Timing to Detect Terrestrial-Mass Extrasolar Planets
Future surveys for transiting extrasolar planets are expected to detect hundreds of jovian-mass planets and tens of terrestrial-mass planets. For many of these newly discovered planets, the intervals between successive transits will be measured with an accuracy of 0.1 to 100 minutes. We show that these timing measurements will allow for the detection of additional planets in the system (not necessarily transiting) by their gravitational interaction with the transiting planet. The transit-time variations depend on the mass of the additional planet, and in some cases terrestrial-mass planets will produce a measurable effect. In systems where two planets are seen to transit, the density of both planets can be determined without radial-velocity observations.
Journal Article
Dynamical stability of the Laplace resonance
We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all resonant arguments are librating. The sequence of equilibria exists all along the possible states balancing resonance offsets and forced eccentricities. Possible additional new de Sitter equilibria may exist when at least one of the forced eccentricities is large (the paradigmatic case is Gliese 876). In the present work, these families of equilibria are traced up to crossing exact commensurability, where approximate first-order solutions diverge. Explicit exact location of the equilibria is determined allowing us to verify the Lyapunov stability of the standard de Sitter equilibrium and of the stable branches of the additional ones.
Journal Article
The orbit of Aegaeon and the 7:6 Mimas-Aegaeon resonance
Aegaeon (S/2008 S 1) is the last satellite discovered by the Cassini spacecraft at the end of the 2000 s. Like the satellites Methone and Anthe, it is involved in mean motion resonance with the mid-sized Mimas. In this work, we give a detailed analysis of the current orbit of Aegaeon identifying the resonant, secular and long-term perturbations due to Mimas and the oblateness of Saturn, and the effects of Tethys. For this task, we perform thousands of numerical simulations of full equations of motion of ensembles of small bodies representing clones of Aegaeon. We have mapped the domain of the 7:6 Mimas-Aegaeon resonance in the phase space of the semi-major axis and eccentricity. It displays a large area dominated by regular motions associated with the 7:6 corotation resonance surrounded by chaotic layers. Aegaeon is currently located very close to the periodic orbit of the resonance, which extends up to eccentricities ∼0.025 centered at semi-major axis ∼168,028 km. We show that the current orbit of Aegaeon has an important forced component in eccentricity due to the 7:6 resonance. The orbital inclination of Aegaeon has a non-negligible forced value due to long-term perturbations of Mimas. These two forced modes explain the complex perturbed orbit of Aegaeon without requiring the co-existence of multiple resonances.
Journal Article