Relative motion of satellites exploiting the super-integrability of Kepler’s problem

This paper builds upon the work of Palmer and Imre exploring the relative motion of satellites on neighbouring Keplerian orbits. We make use of a general geometrical setting from Hamiltonian systems theory to obtain analytical solutions of the variational Kepler equations in an Earth centred inertial coordinate frame in terms of the relevant conserved quantities: relative energy, relative angular momentum and the relative eccentricity vector. The paper extends the work on relative satellite motion by providing solutions about any elliptic, parabolic or hyperbolic reference trajectory, including the zero angular momentum case. The geometrical framework assists the design of complex formation flying trajectories. This is demonstrated by the construction of a tetrahedral formation, described through the relevant conserved quantities, for which the satellites are on highly eccentric orbits around the Sun to visit the Kuiper belt.     

An attempt to test Ambartsumian's idea of the origin of the galaxy . II. location of galaxies within clusters and galaxy position angles

The location of galaxies in 377 rich Abell galaxy clusters is discussed. We compared the distributions of galaxies in the sample containing all galaxies with the sample compiled from the 20 brightest objects. Counts in circular sectors with angle width equal to 30î show isotropy. Only in the case of BM I clusters and the coordinate system related to the cluster major axis did we find anisotropic distributions. We investigated also the distributions of galaxy position angles within clusters exhibiting isotropy. The structure position angles for both samples have been studied as well. They appeared to be different. The difference in location of galaxies in the case of cD clusters, as well as the more elliptical shape and different position angles of samples containing bright galaxies is observed.     

Post-Newtonian effect on the variation of time of periastron passage of binary stars in three gravitational theories

The equation for the variation of the time of a periastron passage of binary stars has been solved by using the perturbation approach. The post-Newtonian effect on the variation of the time of a periastron passage has been examined within three gravitational theories. The results clearly show that the periastron passage of a binary star occurs earlier (advances) at each revolution. This effect has been calculated and discussed for ten binary stars.     

AMR Simulations of Magnetohydrodynamic Problems by the CESE Method in Curvilinear Coordinates

The objective of this paper is to present new extensions of the space – time conservation element and solution element (CESE) method for simulations of magnetohydrodynamic (MHD) problems in general curvilinear coordinates by using an adaptive mesh refinement (AMR) grid system. By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation, the CESE method is established for MHD in the curvilinear coordinates. Utilizing the parallel AMR package PARAMESH, we present the first implementation of applying the AMR CESE method for MHD (AMR-CESE-MHD) in both Cartesian and curvilinear coordinates. To show the validity and capabilities of the AMR-CESE-MHD code, a suite of numerical tests in two and three dimensions including ideal MHD and resistive MHD are carried out, with two of them in both Cartesian and curvilinear coordinates. Numerical tests show that our results are highly consistent with those obtained previously by other authors, and the results under both coordinate systems confirm each other very well.     

Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four-body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. In both problems, the assumed symmetries reduce the determination of linear stability to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability with respect to collinear and symmetric perturbations.     

Extracting information from the gravitational redshift of compact rotating objects

Essential macroscopic internal properties of compact objects can be related to each other with the help of General Relativity. A somewhat familiar example is the relationship between the compactness M/R and the gravitational redshift for nonrotating bodies. Rotation poses new challenges when trying to relate observed or potentially observed quantities such as the graviational redshift, mass, radius, and angular velocity. Using a perturbative approach, we present an analytical approximation whose purpose is to relate these quantities. Two main results are highlighted: Derivation of a new maximal angular velocity depending only on the mass of the object and a possible estimate of the radius from a measurement of the gravitational redshift.     

Habitable zones and UV habitable zones around host stars

Ultraviolet radiation is a double-edged sword to life. If it is too strong, the terrestrial biological systems will be damaged. And if it is too weak, the synthesis of many biochemical compounds cannot go along. We try to obtain the continuous ultraviolet habitable zones, and compare the ultraviolet habitable zones with the habitable zones of host stars. Using the boundary ultraviolet radiation of ultraviolet habitable zone, we calculate the ultraviolet habitable zones of host stars with masses from 0.08 to 4.00 M _⊙. For the host stars with effective temperatures lower than 4,600 K, the ultraviolet habitable zones are closer than the habitable zones. For the host stars with effective temperatures higher than 7,137 K, the ultraviolet habitable zones are farther than the habitable zones. For a hot subdwarf as a host star, the distance of the ultraviolet habitable zone is about ten times more than that of the habitable zone, which is not suitable for the existence of life.     

Evaluation of the intermediate-term periodicities in solar and cosmic ray activities during cycle 23

In this paper we investigate the presence and temporal evolution of galactic cosmic rays (GCRs) time-series and three solar parameters, namely the daily sunspot number, the coronal green line and the 10.7 cm solar radio flux over the period 1996–2003 by the wavelet technique. A number of short- and intermediate-term quasi-periodicities were also detected in both GCR and solar parameters. For the short-term range, we have identified quasi-periods of 16–30 days, 40–55 days, 60–70 days, 80–90 days and 80–100 days. In the case of intermediate range, the significant periods were 120–140 days, 150–170 days, 190–210 days, 240–260 days, ≈1.09 yr. and ≈1.23 yr. The wavelet power spectra show that all the above-mentioned periods are intermittent in nature and occurred in different time-series in different intervals. The result exhibits that the well-known “Rieger period” of (150–160 days) was prominent in both GCR and solar data sets during the ascending phase of cycle 23. Possible reasons behind the observed periods were discussed with the help of previous results and existing numerical models.     

Effects of copper pollution on the activity of soil invertase and urease in loquat orchards

Dealt with in this paper is the relationship between Cu contents of soil and activity parameters for soil invertase and urease from the Changtai loquat orchards in Fujian Province. The soil invertase activity and maximum reaction velocity (enzyme kinetic parameters: Vmax and Vmax/Km) have no remarkable negative correlation with Cu concentrations, but Cu concentrations have an obvious positive effect on invertase Kin, indicating a reversible com-petitive restraint on the reaction between Cu and invertase. The soil urease activity and maximum reaction velocity (Vmax,Vmax/Km) have a remarkable negative correlation with Cu concentrations, and in this aspect, they can be used as ecological indices of the soil polluted by Cu. A slightly variable Km indicates the non-reversible competitive restraint level.     

Relationship between the variation of water quality in rivers and the characteristics of watershed at Miyun,Beijing, China

Based on the characteristics of land use and drainage network of the upper watershed of the Miyun Res-ervoir, Beijing, 26 monitoring and sampling sites were selected in different sub-catchments. Temporal and spatial variations in nutrient loss were dealt with in this paper in terms of the monitoring data on the water quality of the main tributaries flowing into the Miyun Reservoir. In combination with the monitoring data on water quality, the impacts of watershed characteristics including land-use type, landscape pattern, and drainage density were assessed, The concentrations of nutrients in the rainy season are higher than those in other seasons, and the concentrations of NO3--N are linearly related to those of total N which is the main form of nitrogen present in the fiver water. The concentrations of nitrogen become higher toward the reservoir along the main rivers. The seasonal variation of ni-trogen in the watershed affected by intensive human activities is very obvious; in the watershed with steady or low water flow, the seasonal variation of nitrogen is less obvious. Forest land and grassland can trap and filter nitrogen effectively. Land-use pattern also has important impacts on the loss of nitrogen. The concentrations of nitrogen and phosphorus in the water bodies show great temporal and spatial variations. On a temporal scale, the concentrations of TN and TP in the rainy reason are higher than those in other seasons. On a spatial scale, the concentrations of TN and NO3--N in the Qingshui River and Chaohe River are highest all the time. The spatial variation of TP is distinct, being obvious at sampling sites near villages. The form of nitrogen and phosphorus loss varies in different hydrological seasons. Dissolved nitrogen and phosphorus are the main forms in streams in non-rainy seasons, the dissolved nitro-gen and total nitrogen decrease in percentage in the rainy season. Particulate nitrogen and phosphorus are the main forms in some rivers. The concentrations of TN and NO3--N from orchards and villages are high whereas those from forest land are lowest. Land-use pattern has impacts on TN and NO3--N losses, at the sampling sites near the source landscape, the concentrations are higher than those at the sampling sites near the sink landscape. Water quality of the rivers which flow into the Miyuan Reservior is influenced by the composition of adjacent soils.