Extrasolar planetary dynamics with a generalized planar Laplace-Lagrange secular theory

The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration, and implies that the apsidal rate of a small body is a function of its initial eccentricity, dependencies which are absent from the traditional theory. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the planetary eccentricity variation. Comparison with numerical integrations indicates that the improvement afforded by the fourth-order theory over the second-order theory sometimes dwarfs the improvement needed to reproduce the actual dynamical evolution. We conclude that LL secular theory, to any order, generally represents a poor barometer for predicting secular dynamics in extrasolar planetary systems, but does embody a useful tool for extracting an accurate long-term dynamical description of systems with small bodies and/or near-circular orbits.Comment: 14 pages, 12 figures, 1 table, accepted for publication in Ap

A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876

Investigations of two resonant planets orbiting a star or two resonant satellites orbiting a planet often rely on a few resonant and secular terms in order to obtain a representative quantitative description of the system's dynamical evolution. We present a semianalytic model which traces the orbital evolution of any two resonant bodies in a first- through fourth-order eccentricity or inclination-based resonance dominated by the resonant and secular arguments of the user's choosing. By considering the variation of libration width with different orbital parameters, we identify regions of phase space which give rise to different resonant ''depths,'' and propose methods to model libration profiles. We apply the model to the GJ 876 extrasolar planetary system, quantify the relative importance of the relevant resonant and secular contributions, and thereby assess the goodness of the common approximation of representing the system by just the presumably dominant terms. We highlight the danger in using ''order'' as the metric for accuracy in the orbital solution by revealing the unnatural libration centers produced by the second-order, but not first-order, solution, and by demonstrating that the true orbital solution lies somewhere ''in-between'' the third- and fourth-order solutions. We also present formulas used to incorporate perturbations from central-body oblateness and precession, and a protoplanetary or protosatellite thin disk with gaps, into a resonant system. We quantify these contributions to the GJ 876 system, and thereby highlight the conditions which must exist for multi-planet exosystems to be significantly influenced by such factors. We find that massive enough disks may convert resonant libration into circulation; such disk-induced signatures may provide constraints for future studies of exoplanet systems.Comment: 39 pages of body text, 21 figures, 5 tables, 1 appendix, accepted for publication in Celestial Mechanics and Dynamical Astronom

THE EUROPEAN LOCATION FRAMEWORK – FROM NATIONAL TO EUROPEAN

The European Location Framework (ELF) means a technical infrastructure which will deliver authoritative, interoperable geospatial reference data from all over Europe for analysing and understanding information connected to places and features. The ELF has been developed and set up through the ELF Project, which has been realized by a consortium of partners (public, private and academic organisations) since March 2013. Their number increased from thirty to forty in the year 2016, together with a project extension from 36 to 44 months. The project is co-funded by the European Commission’s Competitiveness and Innovation Framework Programme (CIP) and will end in October 2016. In broad terms, the ELF Project will deliver a unique gateway to the authoritative reference geospatial information for Europe (harmonised pan-European maps, geographic and land information) sourced from the National Mapping and Cadastral Authorities (NMCAs) around Europe and including transparent licensing. This will be provided as an online ELF web service that will deliver an up-to-date topographic base map and also as view & download services for access to the ELF datasets. To develop and build up the ELF, NMCAs are accompanied and collaborate with several research & academia institutes, a standardisation body, system integrators, software developers and application providers. The harmonisation is in progress developing and triggering a number of geo-tools like edge-matching, generalisation, transformation and others. ELF will provide also some centralised tools like Geo Locator for searching location based on geographical names, addresses and administrative units, and GeoProduct Finder for discovering the available web-services and licensing them. ELF combines national reference geo-information through the ELF platform. ELF web services will be offered to users and application developers through open source (OSKARI) and proprietary (ArcGIS Online) cloud platforms. Recently, 29 NMCAs plus the EuroGeographics – their pan-European umbrella association, contribute to the ELF through an enrichment of data coverage. As a result, over 20 European countries will be covered with the ELF topo Base Map in 2016. Most countries will contribute also with other harmonized thematic data for viewing or down-loading. To overcome the heterogeneity of data resources and diversity of languages in tens of European countries, ELF builds on the existing INSPIRE rules and its own coordination and interoperability measures. ELF realisation empowers the implementation of INSPIRE in Europe and it complements related activities of European NMCAs, e.g. Czech Office for Surveying, Mapping and Cadastre (CUZK), which provides a large portfolio of spatial data/services and contributes significantly to the NSDI of Czech Republic. CUZK is also responsible for the Base Register of Territorial Identification, Addresses and Real Estates (RUIAN) – an important pillar of Czech e-Government. CUZK became an early-bird in implementing INSPIRE and it provides to the ELF a number of compliant datasets and web services. CUZK and the Polish NMCA (GUGiK) collaborate in the Central-European ELF Pilot (cluster) and test various cross-border prototypes. The presentation combines the national and crossborder view and experiences of CUZK and the European perspective of EuroGeographics