Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.Comment: 19 pages, 5 figures, 7 tables, accepted by the Astronomical Journa

Impact flux of asteroids and water transport to the habitable zone in binary star systems

By now, observations of exoplanets have found more than 50 binary star systems hosting 71 planets. We expect these numbers to increase as more than 70% of the main sequence stars in the solar neighborhood are members of binary or multiple systems. The planetary motion in such systems depends strongly on both the parameters of the stellar system (stellar separation and eccentricity) and the architecture of the planetary system (number of planets and their orbital behaviour). In case a terrestrial planet moves in the so-called habitable zone (HZ) of its host star, the habitability of this planet depends on many parameters. A crucial factor is certainly the amount of water. We investigate in this work the transport of water from beyond the snow-line to the HZ in a binary star system and compare it to a single star system

Multi-shock assembly for protecting a spacecraft surface from hypervelocity impactors

A hypervelocity impact shield assembly for protecting a spacecraft surface from hypervelocity impactors. The shield assembly includes at least one sacrificial impactor disrupting/shocking layer of hypervelocity impactor disrupting/shocking material. A primary spacing element, including space-rated open cell foam material, is positioned between the at least one sacrificial impactor disrupting/shocking layer and a spacecraft surface. A cover member is arranged and disposed relative to the sacrificial impactor disrupting/shocking layer and the primary spacing element to maintain the integrity of the hypervelocity impact shield assembly. In the event of exposure to a hypervelocity impactor, the sacrificial impactor disrupting/shocking layer is perforated while shocking the impactor breaking it into fragments, and/or melting it, and/or vaporizing it, thus providing a dispersion in the form of an expanding debris cloud/plume which spreads the impact energy of the impactor over a volume formed by the primary spacing element between the sacrificial impactor disrupting/shocking layer and the spacecraft surface. This significantly reduces impact lethality at the spacecraft surface. The space-rated open cell foam material provides an extremely lightweight, low-cost, efficient means of spacing and supporting the at least one sacrificial impactor disrupting/shocking layer before, during, and after launch. In a preferred embodiment, the invention is in the form of a multi-shock assembly including a plurality of sacrificial impactor disrupting/shocking layers. In such instance, the hypervelocity impact shield assembly includes a plurality of secondary spacing elements. Each secondary spacing element is positioned adjacent an associated sacrificial impactor disrupting/shocking layer to form a multi-shock subassembly. Thus, a plurality of multi-shock subassemblies are provided which include alternating layers of sacrificial impactor disrupting/shocking layers and secondary spacing elements

Investigation to advance prediction techniques of the low-speed aerodynamics of V/STOL aircraft

A computer program, VSAERO, has been applied to a number of V/STOL configurations with a view to advancing prediction techniques for the low-speed aerodynamic characteristics. The program couples a low-order panel method with surface streamline calculation and integral boundary layer procedures. The panel method--which uses piecewise constant source and doublet panels-includes an iterative procedure for wake shape and models boundary layer displacement effect using the source transpiration technique. Certain improvements to a basic vortex tube jet model were installed in the code prior to evaluation. Very promising results were obtained for surface pressures near a jet issuing at 90 deg from a flat plate. A solid core model was used in the initial part of the jet with a simple entrainment model. Preliminary representation of the downstream separation zone significantly improve the correlation. The program accurately predicted the pressure distribution inside the inlet on the Grumman 698-411 design at a range of flight conditions. Furthermore, coupled viscous/potential flow calculations gave very close correlation with experimentally determined operational boundaries dictated by the onset of separation inside the inlet. Experimentally observed degradation of these operational boundaries between nacelle-alone tests and tests on the full configuration were also indicated by the calculation. Application of the program to the General Dynamics STOL fighter design were equally encouraging. Very close agreement was observed between experiment and calculation for the effects of power on pressure distribution, lift and lift curve slope

Dynamical Stability and Habitability of Gamma Cephei Binary-Planetary System

It has been suggested that the long-lived residual radial velocity variations observed in the precision radial velocity measurements of the primary of Gamma Cephei (HR8974, HD222404, HIP116727) are likely due to a Jupiter-like planet around this star (Hatzes et al, 2003). In this paper, the orbital dynamics of this plant is studied and also the possibility of the existence of a hypothetical Earth-like planet in the habitable zone of its central star is discussed. Simulations, which have been carried out for different values of the eccentricity and semimajor axis of the binary, as well as the orbital inclination of its Jupiter-like planet, expand on previous studies of this system and indicate that, for the values of the binary eccentricity smaller than 0.5, and for all values of the orbital inclination of the Jupiter-like planet ranging from 0 to 40 degrees, the orbit of this planet is stable. For larger values of the binary eccentricity, the system becomes gradually unstable. Integrations also indicate that, within this range of orbital parameters, a hypothetical Earth-like planet can have a long-term stable orbit only at distances of 0.3 to 0.8 AU from the primary star. The habitable zone of the primary, at a range of approximately 3.1 to 3.8 AU, is, however, unstable.Comment: 25 pages, 7 figures, 3 tables, submitted for publicatio

Asteroid flux towards circumprimary habitable zones in binary star systems: I. Statistical Overview

So far, multiple stellar systems harbor more than 130 extra solar planets. Dynamical simulations show that the outcome of planetary formation process can lead to various planetary architecture (i.e. location, size, mass and water content) when the star system is single or double. In the late phase of planetary formation, when embryo-sized objects dominate the inner region of the system, asteroids are also present and can provide additional material for objects inside the habitable zone (hereafter HZ). In this study, we make a comparison of several binary star systems and their efficiency to move icy asteroids from beyond the snow-line into orbits crossing the HZ. We modeled a belt of 10000 asteroids (remnants from the late phase of planetary formation process) beyond the snow-line. The planetesimals are placed randomly around the primary star and move under the gravitational influence of the two stars and a gas giant. As the planetesimals do not interact with each other, we divided the belt into 100 subrings which were separately integrated. In this statistical study, several double star configurations with a G-type star as primary are investigated. Our results show that small bodies also participate in bearing a non-negligible amount of water to the HZ. The proximity of a companion moving on an eccentric orbit increases the flux of asteroids to the HZ, which could result into a more efficient water transport on a short timescale, causing a heavy bombardment. In contrast to asteroids moving under the gravitational perturbations of one G-type star and a gas giant, we show that the presence of a companion star can not only favor a faster depletion of our disk of planetesimals but can also bring 4 -- 5 times more water into the whole HZ.Comment: Accepted for publication in A&

Urban Agriculture Case Studies in Central Texas: From the Ground to the Rooftop

Urban agriculture is practiced in various forms and scales. Practices range from the production of edibles in small to large lots or plazas to vertical production on walls and rooftops. Produce is grown in rural locations and sold at farmers markets in urban locations or grown onsite. Efforts to produce, maintain and sell products of urban agriculture involve many participants and leaders from multiple disciplines. This chapter highlights an introduction to several urban agriculture concepts and case study examples representing activities in Central Texas, home of the Texas A&M University. These case studies highlight a modular pavilion type farmers market and urban garden in downtown Bryan, Texas, designed and built by students and faculty collaborations. The farmers market is designed to be a flexible structure to accommodate current and future needs. A rooftop crop pilot study at Texas A&M on walls and roof deck highlights the varieties grown on top of a four-storey building. The diversity of activities taking place in Central Texas exhibits concepts transferable to many locations across the world. The challenges for these projects include adaptability of crops to the Central Texas climate, structural and community support and the presence of a viable market for locally grown produce

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 billion years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 < a < 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids' orbit was varied in the range 0 < i < 60 and the semimajor axes were fixed. It turned out that only four 'windows' of stable orbits survive: these are the orbits for the initial inclinations 0 < i < 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.Comment: 15 pages, 12 figures, submitted to CMD

Multiple Components in Narrow Planetary Rings

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.Comment: 4 pages, 7 figures (some in colors

Latitude and Longing: Cartography of Desire

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