Unveiling the Physical Address of the JWST Telescope

<p></p><p>The spatial location of the future James Webb Satellite Telescope (JWST), in a position known as the L2 in relation to the Sun-Earth system, direct us to the most celebrated problem in dynamics, which is the three-body problem. In this work we demonstrate the calculation of the JWST position in space, whose launch is expected to occur in 2019. For this purpose, we consider the body restricted problem, studying the movement of large masses moving over mutual gravitational attraction, considering in this case that the third body (JWST) has negligible mass when compared to the others. In addition to making a brief historical interlude, we show the forces involved in calculating the position of the JWST telescope in space and we provide some simplified mathematical expressions for such a Lagrange point. This study involves the problem of central force explored in mechanics, the problem of lagrange points and their locations, explored in astronomy and dynamics of the solar system and Newton's classical gravitation.</p><p></p

Modeling Habitat Split: Landscape and Life History Traits Determine Amphibian Extinction Thresholds

<div><p>Habitat split is a major force behind the worldwide decline of amphibian populations, causing community change in richness and species composition. In fragmented landscapes, natural remnants, the terrestrial habitat of the adults, are frequently separated from streams, the aquatic habitat of the larvae. An important question is how this landscape configuration affects population levels and if it can drive species to extinction locally. Here, we put forward the first theoretical model on habitat split which is particularly concerned on how split distance – the distance between the two required habitats – affects population size and persistence in isolated fragments. Our diffusive model shows that habitat split alone is able to generate extinction thresholds. Fragments occurring between the aquatic habitat and a given critical split distance are expected to hold viable populations, while fragments located farther away are expected to be unoccupied. Species with higher reproductive success and higher diffusion rate of post-metamorphic youngs are expected to have farther critical split distances. Furthermore, the model indicates that negative effects of habitat split are poorly compensated by positive effects of fragment size. The habitat split model improves our understanding about spatially structured populations and has relevant implications for landscape design for conservation. It puts on a firm theoretical basis the relation between habitat split and the decline of amphibian populations.</p></div

Population size of adults in the fragment as a function of the split distance,

<p> This picture points a critical split distance above which the population gets extinct. The three curves indicated in the figure represent different values of the juvenile mortality that can be caused by differences in matrix quality. The parameters used were , and .</p

Curve of adult population size versus split distance.

<p>In this figure we point the effect of the size of the fragment on the critical split distance. This figures show that large forest fragments have only a limited effect to reduce the habitat split local extinction prevision. The parameters used and .</p

The spatial configuration for the habitat split model.

<p>The model has three main landscape elements: the river (or any aquatic breeding habitat), at , the inhospitable matrix and the forest fragment. Split distance is defined by while fragment size () is defined by .</p