Orbit Determination with the two-body Integrals

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.Comment: 23 pages, 1 figur

Multiwavelength Studies of Young OB Associations

We discuss how contemporary multiwavelength observations of young OB-dominated clusters address long-standing astrophysical questions: Do clusters form rapidly or slowly with an age spread? When do clusters expand and disperse to constitute the field star population? Do rich clusters form by amalgamation of smaller subclusters? What is the pattern and duration of cluster formation in massive star forming regions (MSFRs)? Past observational difficulties in obtaining good stellar censuses of MSFRs have been alleviated in recent studies that combine X-ray and infrared surveys to obtain rich, though still incomplete, censuses of young stars in MSFRs. We describe here one of these efforts, the MYStIX project, that produced a catalog of 31,784 probable members of 20 MSFRs. We find that age spread within clusters are real in the sense that the stars in the core formed after the cluster halo. Cluster expansion is seen in the ensemble of (sub)clusters, and older dispersing populations are found across MSFRs. Direct evidence for subcluster merging is still unconvincing. Long-lived, asynchronous star formation is pervasive across MSFRs.Comment: 22 pages, 9 figures. To appear in "The Origin of Stellar Clusters", edited by Steven Stahler, Springer, 2017, in pres

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

Multiple Solutions in Preliminary Orbit Determination from Three Observations

SUMMARY Charlier's theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace's method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace's and Gauss' methods. We also provide a geometric definition of a curve that generalizes Charlier's limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier's: they may change according to the value of a parameter that depends on the observations

La tributación del agua en el Impuesto sobre el Valor Añadido

El Impuesto sobre el Valor Añadido (IVA) es, sin duda, uno de los tributos fundamentales del sistema fiscal español. Grava el consumo general de bienes y servicios bajo la estructura de un impuesto plurifásico sobre el valor añadido y se encuentra regulado en la Ley 37/1992, de 28 de diciembre, del Impuesto sobre el Valor Añadido (LIVA o Ley del IVA, en adelante). En el plano jurídico, el IVA sobresale, en primera instancia, por tratarse de un impuesto armonizado a nivel comunitario. Prueba de ello es la existencia de una Directiva que todos los Estados miembros de la Unión Europea, entre ellos el español, han traspuesto a su ordenamiento jurídico interno. Se trata, concretamente, de la Directiva 2006/112/CE del Consejo, de 28 de noviembre de 2006, relativa al sistema común del Impuesto sobre el Valor Añadido (en adelante, Directiva IVA), desarrollada a través del Reglamento de Ejecución (UE) nº 282/2011 del Consejo, de 15 de marzo de 2011, por el que se establecen disposiciones de aplicación de la Directiva 2006/112/CE relativa al sistema común del Impuesto sobre el Valor Añadido