883 research outputs found

    The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

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    We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.Comment: 10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysic

    The relevance of prior inclination determination for direct imaging of Earth-like planets

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    Direct imaging and characterization of extrasolar Earth-like planets is strongly impacted by the orbital inclination of the planet to be studied, as a combination of pure geometrical effects and the impact of exozodiacal dust. Here, we perform simulations to quantify the impact of a priori knowledge of inclination for the efficiency of a typical coronagraphic or occulter-based mission. The relative impact and complementarity with prior knowledge of exozodiacal brightness down to achievable levels is examined and discussed. It is found that inclination has an even greater impact than the exozodiacal brightness, though the two have excellent complementarity. We also discuss different methods for inclination determination, and their respective applicability to the context of precursor science to an imaging mission. It is found that if technologically achievable, a combined effort to determine inclinations and exozodiacal brightnesses with ground-based facilities would substantially increase the efficiency of a space-based dedicated mission to image and characterize Earth-like planets.Comment: 9 pages, 5 figures, accepted for publication in MNRA

    Astrobiological Complexity with Probabilistic Cellular Automata

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    Search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata (PCA) represent the best quantitative framework for modeling astrobiological history of the Milky Way and its Galactic Habitable Zone. The relevant astrobiological parameters are to be modeled as the elements of the input probability matrix for the PCA kernel. With the underlying simplicity of the cellular automata constructs, this approach enables a quick analysis of large and ambiguous input parameters' space. We perform a simple clustering analysis of typical astrobiological histories and discuss the relevant boundary conditions of practical importance for planning and guiding actual empirical astrobiological and SETI projects. In addition to showing how the present framework is adaptable to more complex situations and updated observational databases from current and near-future space missions, we demonstrate how numerical results could offer a cautious rationale for continuation of practical SETI searches.Comment: 37 pages, 11 figures, 2 tables; added journal reference belo
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