Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.Comment: 19 pages, 5 figures, 7 tables, accepted by the Astronomical Journa

Impact flux of asteroids and water transport to the habitable zone in binary star systems

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

Dynamical Stability and Habitability of Gamma Cephei Binary-Planetary System

It has been suggested that the long-lived residual radial velocity variations observed in the precision radial velocity measurements of the primary of Gamma Cephei (HR8974, HD222404, HIP116727) are likely due to a Jupiter-like planet around this star (Hatzes et al, 2003). In this paper, the orbital dynamics of this plant is studied and also the possibility of the existence of a hypothetical Earth-like planet in the habitable zone of its central star is discussed. Simulations, which have been carried out for different values of the eccentricity and semimajor axis of the binary, as well as the orbital inclination of its Jupiter-like planet, expand on previous studies of this system and indicate that, for the values of the binary eccentricity smaller than 0.5, and for all values of the orbital inclination of the Jupiter-like planet ranging from 0 to 40 degrees, the orbit of this planet is stable. For larger values of the binary eccentricity, the system becomes gradually unstable. Integrations also indicate that, within this range of orbital parameters, a hypothetical Earth-like planet can have a long-term stable orbit only at distances of 0.3 to 0.8 AU from the primary star. The habitable zone of the primary, at a range of approximately 3.1 to 3.8 AU, is, however, unstable.Comment: 25 pages, 7 figures, 3 tables, submitted for publicatio

Asteroid flux towards circumprimary habitable zones in binary star systems: I. Statistical Overview

So far, multiple stellar systems harbor more than 130 extra solar planets. Dynamical simulations show that the outcome of planetary formation process can lead to various planetary architecture (i.e. location, size, mass and water content) when the star system is single or double. In the late phase of planetary formation, when embryo-sized objects dominate the inner region of the system, asteroids are also present and can provide additional material for objects inside the habitable zone (hereafter HZ). In this study, we make a comparison of several binary star systems and their efficiency to move icy asteroids from beyond the snow-line into orbits crossing the HZ. We modeled a belt of 10000 asteroids (remnants from the late phase of planetary formation process) beyond the snow-line. The planetesimals are placed randomly around the primary star and move under the gravitational influence of the two stars and a gas giant. As the planetesimals do not interact with each other, we divided the belt into 100 subrings which were separately integrated. In this statistical study, several double star configurations with a G-type star as primary are investigated. Our results show that small bodies also participate in bearing a non-negligible amount of water to the HZ. The proximity of a companion moving on an eccentric orbit increases the flux of asteroids to the HZ, which could result into a more efficient water transport on a short timescale, causing a heavy bombardment. In contrast to asteroids moving under the gravitational perturbations of one G-type star and a gas giant, we show that the presence of a companion star can not only favor a faster depletion of our disk of planetesimals but can also bring 4 -- 5 times more water into the whole HZ.Comment: Accepted for publication in A&

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 billion years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 < a < 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids' orbit was varied in the range 0 < i < 60 and the semimajor axes were fixed. It turned out that only four 'windows' of stable orbits survive: these are the orbits for the initial inclinations 0 < i < 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.Comment: 15 pages, 12 figures, submitted to CMD

Multiple Components in Narrow Planetary Rings

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.Comment: 4 pages, 7 figures (some in colors

Physical mapping of chromosomes 3HS and 3DS

Relatório de estágio do mestrado em Ensino da Educação Física nos Ensinos Básico e Secundário, apresentado à Faculdade de Ciências do Desporto e Educação Física da Universidade de CoimbraO presente documento divide-se em duas partes: a reflexão dos aspetos relacionados com o estágio pedagógico e o desenvolvimento do tema-problema. Numa primeira fase será dado enfoque à prática da docência, desenvolvida na escola E.B.2,3 Dr. Daniel de Matos. Serão apresentadas as expectativas iniciais em relação à prática, serão apresentadas e justificadas as opções metodológicas tomadas ao longo do estágio, serão relatadas as atividades desenvolvidas durante o estágio e será realçada a componente ética e profissional da profissão. De seguida será realizada uma justificação das opções tomadas. Para finalizar a primeira parte do presente trabalho será feita uma análise reflexiva sobre a prática pedagógica. Na segunda parte temos o tema-problema e seu desenvolvimento, num documento que se pretende orientador da prática docente e auxiliar de como resolver comportamentos de desvio da tarefa por parte dos alunos. Servirá também para analisar e mostrar conclusões sobre o problema que a escola atual, enquanto organização enfrenta, a indisciplina. Será efetuada uma pequena investigação, em que o objetivo é analisar a perceção dos docentes de uma escola pública sobre a gravidade dos comportamentos de indisciplina praticados. O objetivo é chegar a alguma conclusão que possa ajudar/beneficiar os professores da escola na procura de estratégias e metodologias que possam minimizar o impacto deste tipo de comportamentos no normal funcionamento da aula. This document is divided into two parts: a reflection of aspects related to teaching practice and development of the “theme-issue”. Initially focus will be given to the practice of teaching, developed in E.B.2, 3 Dr. Daniel de Matos school. Initial expectations will be presented, as well as the methodological choices made along the stage and its reasons. The activities made during the internship will be reported and I will emphasize ethics and professional component of the teacher’s profession. Then I will do a justification of the choices made. To finish the first part of this work I will make a reflective analysis of teaching practice. In the second part we have the “theme-issue” and its development, a document intended to be the guiding teaching practice and assist in solving the task behaviors of misuse by students. Will also serve to analyze and display conclusions about the problem that the current school, as an organization, faces, the indiscipline. Will be performed a little investigation, in which the objective is to analyze the perceptions of teachers in a public school on the severity of disruptive behaviors committed. The goal is to achieve some conclusion that can help / benefit school teachers in finding strategies and methodologies that can minimize the impact of such behaviors on normal class

Does the Spine Surgeon’s Experience Affect Fracture Classification, Assessment of Stability, and Treatment Plan in Thoracolumbar Injuries?

Study Design: Prospective survey-based study. Objectives: The AO Spine thoracolumbar injury classification has been shown to have good reproducibility among clinicians. However, the influence of spine surgeons’ clinical experience on fracture classification, stability assessment, and decision on management based on this classification has not been studied. Furthermore, the usefulness of varying imaging modalities including radiographs, computed tomography (CT) and magnetic resonance imaging (MRI) in the decision process was also studied. Methods: Forty-one spine surgeons from different regions, acquainted with the AOSpine classification system, were provided with 30 thoracolumbar fractures in a 3-step assessment: first radiographs, followed by CT and MRI. Surgeons classified the fracture, evaluated stability, chose management, and identified reasons for any changes. The surgeons were divided into 2 groups based on years of clinical experience as \u3c10 years (n = 12) and \u3e10 years (n = 29). Results: There were no significant differences between the 2 groups in correctly classifying A1, B2, and C type fractures. Surgeons with less experience hadmore correct diagnosis in classifyingA3 (47.2% vs 38.5%in step 1, 73.6% vs 60.3% in step 2 and 77.8% vs 65.5% in step 3), A4 (16.7% vs 24.1% in step 1, 72.9% vs 57.8% in step 2 and 70.8% vs 56.0%in step3) and B1 injuries (31.9% vs 20.7% in step 1, 41.7% vs 36.8% in step 2 and 38.9% vs 33.9% in step 3). In the assessment of fracture stability and decision on treatment, the less and more experienced surgeons performed equally. The selection of a particular treatment plan varied in all subtypes except in A1 and C type injuries. Conclusion: Surgeons’ experience did not significantly affect overall fracture classification, evaluating stability and planning the treatment. Surgeons with less experience had a higher percentage of correct classification in A3 and A4 injuries. Despite variations between them in classification, the assessment of overall stability and management decisions were similar between the 2 groups. © The Author(s) 2017