Earth–Moon Weak Stability Boundaries in the restricted three and four body problem

This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally, the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach stable capture, which allows orbit circularization using low-thrust propulsion systems.     

Correlations between environment and other properties of galaxies from the Sloan Digital Sky Survey at fixed color

From the volume-limited Main galaxy sample of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we construct three samples with g–r color bins , labeled S1–S3, to investigate how other properties of galaxies depend on environment at fixed color. For each sample, we measure the local three-dimensional galaxy density in a comoving sphere with radius equal to the distance to the 5th nearest galaxy for each galaxy, select about 5% galaxies and construct the two subsamples at both extremes of density. Our study suggests that the environmental dependence of luminosity is mainly due to the environmental dependence of galaxy color and the correlation between color and luminosity. In addition, we preferentially conclude that concentration index and morphologies are not strongly correlated with local density at fixed color, and that galaxy color is a galaxy property very predictive of the local environment. Because SDSS spectroscopy is incomplete for bright galaxies at very low redshifts, we also use a volume-limited Main galaxy sample with a lower redshift limit z = 0.05, which contains 94,954 galaxies at 0.05 < z < 0.089 with −22.40 < M_r < −20.16, and reach the same conclusions.Due to the bimodality of the u–r color distribution, we classify galaxies as ‘red’ and ‘blue’, respectively, and further subdivide the samples into star-forming galaxies and passive ones using Hα equivalent width, W₀(Hα). Results show that color and star formation activity of galaxies are galaxy properties very predictive of the local environment.     

Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L ₁ and beyond L ₂ where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s².     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

A Mercury orientation model including non-zero obliquity and librations

Planetary orientation models describe the orientation of the spin axis and prime meridian of planets in inertial space as a function of time. The models are required for the planning and execution of Earth-based or space-based observational work, e.g. to compute viewing geometries and to tie observations to planetary coordinate systems. The current orientation model for Mercury is inadequate because it uses an obsolete spin orientation, neglects oscillations in the spin rate called longitude librations, and relies on a prime meridian that no longer reflects its intended dynamical significance. These effects result in positional errors on the surface of ~1.5 km in latitude and up to several km in longitude, about two orders of magnitude larger than the finest image resolution currently attainable. Here we present an updated orientation model which incorporates modern values of the spin orientation, includes a formulation for longitude librations, and restores the dynamical significance to the prime meridian. We also use modern values of the orbit normal, spin axis orientation, and precession rates to quantify an important relationship between the obliquity and moment of inertia differences.     

Abundance analysis of Barium stars

We obtain the chemical abundances of six barium stars and two CH subgiant stars based on the high signal-to-noise ratio and high resolution Echelle spectra. The neu- tron capture process elements Y, Zr, Ba, La and Eu show obvious overabundances relative to the Sun, for example, their [Ba/Fe] values are from 0.45 to 1.27. Other elements, in- cluding Na, Mg, A1, Si, Ca, Sc, Ti, V, Cr, Mn and Ni, show comparable abundances to the Solar ones, and their [Fe/H] covers a range from -0.40 to 0.21, which means they belong to the Galactic disk. The predictions of the theoretical model of wind accretion for bi- nary systems can explain the observed abundance patterns of the neutron capture process elements in these stars, which means that their overabundant heavy-elements could be caused by accreting the ejecta of AGB stars, the progenitors of present-day white dwarf companions in binary systems.     

Sub-micron scale distributions of trace elements in zircon

Sub-micron scale zoning of Ti concentrations and correlations between concentrations of Ti and other trace elements (P, Ce, and Y) and cathodoluminescent (CL) banding is observed in natural zircons. Ion images were made using the Caltech Microanalysis Center’s CAMECA NanoSIMS 50L with an O⁻ primary beam focused to ~300 nm on the sample surface. The high spatial resolution of this technique allows for interrogation of chemical variations at or below the scale of CL banding in natural zircons. Images produced in this manner display two types of correlations among Ti, P, Ce, and Y (which appears to be a proxy for CL intensity): strong (correlation coefficients >0.8) and subtle (correlation coefficients ~0.15–0.4). Strongly correlated images, which display Ti variations of ca. a factor of 3 between adjacent CL bands and overall elevated trace element concentrations in CL-dark bands, were found within an oscillatory-zoned, trace element enriched sector of a CL sector-zoned zircon. Three possible causes for such correlations include: temperature-dependent equilibrium partitioning, trace element partitioning limited by diffusion in the host melt and surface-controlled, non-equilibrium growth. Comparison of our data with the expected results of these processes suggests that: (1) Ti partitioning in zircon is dependent upon non-equilibrium effects in addition to temperature and/or (2) the incorporation of elements that co-vary with Ti in zircon (e.g., Y, P and Ce) is also temperature-dependent. Sub-micron scale, high-Ti regions are also found within Proterozoic Adirondack and >4 Ga Jack Hills zircons as well as trace element enrichments (including Ti) along cracks within Jack Hills zircons.     

A restudy of the Ostracoda <Emphasis Type="Italic">Cypris cylindrica</Emphasis> Sowerby (in Malcolmson, 1840) from the Deccan Intertrappean beds (late cretaceous) of Lakshmipur,Kachchh, Gujarat

Cypris cylindrica was originally described by Sowerby (in Malcolmson, 1840) from the Deccan Intertrappean sedimentary beds of the Sichel Hills, Andhra Pradesh. Whatley and Bajpai (2000) recorded the species during recent years from the Intertrappean of Lakshmipur, Kachchh district, Gujarat and stated that Kachchh specimens are identical with the types of the species housed in the Natural History Museum (NHM), London. They recorded the species as Mongolianella cylindrica. The species, however, lacks distinctive shape and hinge structure of Mongolianella and on the contrary closely resembles Stenocypris cylindrica major (Baird, 1859) in shape and internal characters including having adont hinge, large anterior vestibulum, arcuate lists or striae on free part of inner lamella, numerous short marginal pore canals and 6 large adductor scars, the topmost being much elongated. On these bases the species is herein transferred to the genus Stenocypris Sars, 1889.