Corrections to Newton's law of gravitation - application to hybrid Bloch brane

We present in this work, the calculations of corrections in the Newton's law of gravitation due to Kaluza-Klein gravitons in five-dimensional warped thick braneworld scenarios. We consider here a recently proposed model, namely, the hybrid Bloch brane. This model couples two scalar fields to gravity and is engendered from a domain wall-like defect. Also, two other models the so-called asymmetric hybrid brane and compact brane are considered. As a matter of fact, these models are obtained from deformations of the phi4 and sine-Gordon topological defects. Then, we constructed the branes upon such defects, and the corresponding corrections in Newton's law of gravitation are computed. In order to attain the mass spectrum and its corresponding eigenfunctions which are the essential quantities for computing the correction to the Newtonian potential, we develop a suitable numerical technique.Comment: 7 pages, 3 figures, Proceedings of The XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25

The formation of the solar system

The solar system started to form about 4.56 Gyr ago and despite the long intervening time span, there still exist several clues about its formation. The three major sources for this information are meteorites, the present solar system structure and the planet-forming systems around young stars. In this introduction we give an overview of the current understanding of the solar system formation from all these different research fields. This includes the question of the lifetime of the solar protoplanetary disc, the different stages of planet formation, their duration, and their relative importance. We consider whether meteorite evidence and observations of protoplanetary discs point in the same direction. This will tell us whether our solar system had a typical formation history or an exceptional one. There are also many indications that the solar system formed as part of a star cluster. Here we examine the types of cluster the Sun could have formed in, especially whether its stellar density was at any stage high enough to influence the properties of today's solar system. The likelihood of identifying siblings of the Sun is discussed. Finally, the possible dynamical evolution of the solar system since its formation and its future are considered.Comment: 36 pages, 7 figures, invited review in Physica Script

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

Transiting Disintegrating Planetary Debris around WD 1145+017

More than a decade after astronomers realized that disrupted planetary material likely pollutes the surfaces of many white dwarf stars, the discovery of transiting debris orbiting the white dwarf WD 1145+017 has opened the door to new explorations of this process. We describe the observational evidence for transiting planetary material and the current theoretical understanding (and in some cases lack thereof) of the phenomenon.Comment: Invited review chapter. Accepted March 23, 2017 and published October 7, 2017 in the Handbook of Exoplanets. 15 pages, 10 figure

Constraining planet formation around 6M⊙-8M⊙ stars

Identifying planets around O-type and B-type stars is inherently difficult; the most massive known planet host has a mass of only about 3M⊙. However, planetary systems which survive the transformation of their host stars into white dwarfs can be detected via photospheric trace metals, circumstellar dusty and gaseous discs, and transits of planetary debris crossing our line-of-sight. These signatures offer the potential to explore the efficiency of planet formation for host stars with masses up to the core-collapse boundary at ≈8M⊙, a mass regime rarely investigated in planet formation theory. Here, we establish limits on where both major and minor planets must reside around ≈6M⊙ − 8M⊙ stars in order to survive into the white dwarf phase. For this mass range, we find that intact terrestrial or giant planets need to leave the main sequence beyond approximate minimum star-planet separations of respectively about 3 and 6 au. In these systems, rubble pile minor planets of radii 10, 1.0, and 0.1 km would have been shorn apart by giant branch radiative YORP spin-up if they formed and remained within, respectively, tens, hundreds and thousands of au. These boundary values would help distinguish the nature of the progenitor of metal-pollution in white dwarf atmospheres. We find that planet formation around the highest mass white dwarf progenitors may be feasible, and hence encourage both dedicated planet formation investigations for these systems and spectroscopic analyses of the highest mass white dwarfs

Eight billion asteroids in the Oort cloud

The Oort cloud is usually thought of as a collection of icy comets inhabiting the outer reaches of the Solar system, but this picture is incomplete. We use simulations of the formation of the Oort cloud to show that ∼4 per cent of the small bodies in the Oort cloud should have formed within 2.5 au of the Sun, and hence be ice-free rock-iron bodies. If we assume that these Oort cloud asteroids have the same size distribution as their cometary counterparts, the Large Synoptic Survey Telescope should find roughly a dozen Oort cloud asteroids during 10 years of operations. Measurement of the asteroid fraction within the Oort cloud can serve as an excellent test of the Solar system's formation and dynamical history. Oort cloud asteroids could be of particular concern as impact hazards as their high mass density, high impact velocity, and low visibility make them both hard to detect and hard to divert or destroy. However, they should be a rare class of object, and we estimate globally catastrophic collisions should only occur about once per billion years.AS andMWare supported by the European Union through ERC grant number 279973. DV is supported by the European Union through ERC grant number 320964.This is the final published version. It first appeared at http://mnras.oxfordjournals.org/content/446/2/2059

Manejo correto da ordenha e qualidade do leite.

Muitas vezes o produtor se questiona quais as vantagens de adotar duas ou três ordenhas diárias. A resposta para esta pergunta tem que considerar uma série de fatores, tais como o custo da mão de obra, custos adicionais conseqüentes da realização de uma terceira ordenha (luz, material de limpeza, etc.), incremento na produção de leite obtido e o valor recebido pelo leite.bitstream/item/55815/1/CR27-02.pd

Strangelet dwarfs

If the surface tension of quark matter is low enough, quark matter is not self bound. At sufficiently low pressure and temperature, it will take the form of a crystal of positively charged strangelets in a neutralizing background of electrons. In this case there will exist, in addition to the usual family of strange stars, a family of low-mass large-radius objects analogous to white dwarfs, which we call "strangelet dwarfs". Using a generic parametrization of the equation of state of quark matter, we calculate the mass-radius relationship of these objects.Comment: 10 pages, LaTeX, added discussion of CFL phase and strangelet pollution, version to appear in journal. arXiv admin note: text overlap with arXiv:0808.067

Degeneracy in the characterization of non-transiting planets from transit timing variations

The transit timing variation (TTV) method allows the detection of non-transiting planets through their gravitational perturbations. Since TTVs are strongly enhanced in systems close to mean-motion resonances (MMR), even a low mass planet can produce an observable signal. This technique has thus been proposed to detect terrestrial planets. In this letter, we analyse TTV signals for systems in or close to MMR in order to illustrate the difficulties arising in the determination of planetary parameters. TTVs are computed numerically with an n-body integrator for a variety of systems close to MMR. The main features of these TTVs are also derived analytically. Systems deeply inside MMR do not produce particularly strong TTVs, while those close to MMR generate quasiperiodic TTVs characterised by a dominant long period term and a low amplitude remainder. If the remainder is too weak to be detected, then the signal is strongly degenerate and this prevents the determination of the planetary parameters. Even though an Earth mass planet can be detected by the TTV method if it is close to a MMR, it may not be possible to assert that this planet is actually an Earth mass planet. On the other hand, if the system is right in the center of a MMR, the high amplitude oscillation of the TTV signal vanishes and the detection of the perturber becomes as difficult as it is far from MMR.Comment: 5 pages, 3 figures, submitted to MNRA