Geoid and Gravity in Earth Sciences – An Overview

Precise global geoid and gravity anomaly information serves essentially three different kinds of applications in Earth sciences: gravity and geoid anomalies reflect density anomalies in oceanic and continental lithosphere and the mantle; dynamic ocean topography as derived from the combination of satellite altimetry and a global geoid model can be directly transformed into a global map of ocean surface circulation; any redistribution or exchange of mass in Earth system results in temporal gravity and geoid changes. After completion of the dedicated gravity satellite missions GRACE and GOCE a high standard of global gravity determination, both of the static and of the time varying field will be attained. Thus, it is the right time to investigate the future needs for improvements in the various fields of Earth sciences and to define the right strategy for future gravity field satellite missions.     

A combined theory for zonal harmonic and resonance perturbations of a near-circular orbit with applications to COSMOS 1603 (1984-106A)

Theory for the motion of a satellite in a near-circular orbit and perturbed by zonal and resonance terms in the Earth's gravity field is developed. Commensurability with respect to both primary and secondary terms is considered with the solution dependent on the depths of the resonances. The theory is applied to the motion of COSMOS 1603 (1984-106A) which approached 14 : 1 resonance in 1987. Values of lumped harmonics derived from least-squares analysis are in close agreement with previous studies of 1984-106A and global gravity field models. The theory is finally extended to incorporate the effects of air drag.     

A new method for computing the spectrum of the gravitational perturbations on satellite orbits

Some aspects for efficient computation of the tidal perturbation due to the ellipticity effects of the Earth, the luni-solar potential on an Earth-orbiting satellite and the perturbations of the satellite's radial, transverse and normal position components due to the effects of the Earth's gravitational and ocean tide fields are presented. A straightforward method for computing the spectrum of the geopotential and the tidal-induced perturbations of the orbit elements and the radial, transverse and normal components is described.     

A Non-Planar Circular Model for the 4/7 Resonance

An adiabatic approximation for the non-planar, circular, restricted 3BP is presented for the external resonance 4/7. It can be used as a model for resonant Kuiper belt objects. The Hamiltonian is truncated at the fourth order in eccentricities and inclinations. After averaging, we have a system of two degrees of freedom with two frequencies. Numerical calculations show that the ratio of these frequencies is ~10². Having introduced suitable canonical variables, we used the adiabatic approach introduced by Wisdom in a different context. We left slow variables frozen and after solving the pendulum problem for fast variables, we used the averaged effect of fast variables on slow variables. In this way we obtained the guiding trajectories for slow variables as contour lines of adiabatic invariant. We discuss the existence of a chaotic region which is formed by trajectories crossing a critical curve which corresponds to the separatrix of fast pendulum motion, where the assumption of sharp division between fast and slow frequencies is not correct and the adiabatic theory fails. The model works well for e ~ 0.1 and can be used for finding the chaotic regions, but for e~ 0.17 it becomes unsatisfactory due to truncation and bad convergence of the Laplace expansion. Qualitatively it can, however, help us to understand how the protective mechanism works as the interplay of mean motion and Kozai–Lidov resonance.     

TreePM: A code for cosmological N-body simulations

We describe the TreePM method for carrying out large N-Body simulations to study formation and evolution of the large scale structure in the Universe. This method is a combination of Barnes and Hut tree code and Particle-Mesh code. It combines the automatic inclusion of periodic boundary conditions of PM simulations with the high resolution of tree codes. This is done by splitting the gravitational force into a short range and a long range component. We describe the splitting of force between these two parts. We outline the key differences between TreePM and some other N-Body methods.     

Sunyaev–Zel'dovich predictions for the Planck Surveyor satellite using the Hubble Volume simulations

We use the billion-particle Hubble Volume simulations to make statistical predictions for the distribution of galaxy clusters that will be observed by the Planck Surveyor satellite through their effect on the cosmic microwave background – the Sunyaev–Zel'dovich (SZ) effect. We utilize the lightcone data sets for both critical density ( τ CDM) and flat low-density (ΛCDM) cosmologies: a 'full-sky' survey out to z ∼0.5 , two 'octant' data sets out to beyond z =1 , and a 100 square degree data set extending to z ∼4 . Making simple, but robust, assumptions regarding both the thermodynamic state of the gas and the detection of objects against an unresolved background, we present the expected number of SZ sources as a function of redshift and angular size, and also as a function of flux (for both the thermal and kinetic effects) for three of the relevant High Frequency Instrument frequency channels. We confirm the expectation that the Planck Surveyor will detect around 5×10⁴ clusters, though the exact number is sensitive to the choice of several parameters including the baryon fraction, and also to the cluster density profile, so that either cosmology may predict more clusters. We also find that the majority of detected sources should be at z <1.5 , and we estimate that around 1 per cent of clusters will be spatially resolved by the Planck Surveyor , though this has a large uncertainty.     

A fast method for finding bound systems in numerical simulations: Results from the formation of asteroid binaries

We present a new code (companion) that identifies bound systems of particles in O(NlogN) time. Simple binaries consisting of pairs of mutually bound particles and complex hierarchies consisting of collections of mutually bound particles are identifiable with this code. In comparison, brute force binary search methods scale as O(N²) while full hierarchy searches can be as expensive as O(N³), making analysis highly inefficient for multiple data sets with N?¹⁰³. A simple test case is provided to illustrate the method. Timing tests demonstrating O(NlogN) scaling with the new code on real data are presented. We apply our method to data from asteroid satellite simulations [Durda et al., 2004. Icarus 167, 382-396; Erratum: Icarus 170, 242; reprinted article: Icarus 170, 243-257] and note interesting multi-particle configurations. The code is available at http://www.astro.umd.edu/zoe/companion/ and is distributed under the terms and conditions of the GNU Public License.     

一种单站精确测量通信卫星本振频率的方法

星载振荡器频率的测量对利用通信卫星进行标准时间和频率传递有重要的意义,测量的难点是多普勒频移的处理。提出了一种只需要一个地面站而不需要定轨系统就可以精密测量卫星本振频率的方法。根据卫星两个下行信号的频差与多普勒频移的关系,可以计算得到卫星相对于主控站的径向速度。然后测量其中一个下行频率后,就能计算星载振荡器的频率值。实际测量结果表明,这种方法的测量精度优于2.4×10-10。     

A method to determine regional lunar gravity fields from earth-based satellite tracking data

A method to determine regional gravity fields of the Moon from Earth-based Doppler and range satellite tracking data residuals of a low Moon-orbiting satellite has been developed and thoroughly tested in a controlled simulation environment. A short-arc approach, where one arc consists of the time it takes the satellite to cross the grid of interest on the lunar surface, is used in order to filter out most long-wavelength signal that can still be present in the residuals. Simulation results where the data are contaminated with either typical systematic or stochastic noise show that recovery of the local gravity field down to the level of several mGal is possible. The inclusion of extremely low-altitude data also means that regularisation in the sense of including a priori information in the form of a regularisation matrix is not necessary in order to obtain a good solution at high resolution.     

A new dynamical model for the Uranian satellites

We have developed a new dynamical model of the main Uranian satellites, based on numerical integration and fitted to astrometric observations. Old observations, as well as modern and Voyager observations have been included. This model has provided ephemerides that have already been used for predicting the mutual events during the PHE-URA campaign. It is updated here to improve the prediction of these events. We also tried to assess the real accuracy of our ephemerides by checking the distance differences of the Uranian satellites, using simultaneously our former and new model. It appears that both solutions are very close to each other (within few tens of kilometers), and most probably accurate at the level of few hundred of kilometers. Using new available meridian observations of the Uranian satellites, we have checked the Uranian ephemeris accuracy using DE406. An error of more than 0.1 arcsec on the Uranian position is observed.     

Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests

We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular “atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to centrifuging as a function of rotation rate.     

A new parallel PM code for very large-scale cosmological simulations

We have developed a parallel Particle–Particle, Particle–Mesh (P³M) simulation code for the Cray T3E parallel supercomputer that is well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in cosmological contexts. The parallel code is based upon the public-domain serial Adaptive P³M-SPH (http://coho.astro.uwo.ca/pub/hydra/hydra.html) code of Couchman et al. (1995)[ApJ, 452, 797]. The algorithm resolves gravitational forces into a long-range component computed by discretizing the mass distribution and solving Poisson's equation on a grid using an FFT convolution method, and a short-range component computed by direct force summation for sufficiently close particle pairs. The code consists primarily of a particle–particle computation parallelized by domain decomposition over blocks of neighbour-cells, a more regular mesh calculation distributed in planes along one dimension, and several transformations between the two distributions. The load balancing of the P³M code is static, since this greatly aids the ongoing implementation of parallel adaptive refinements of the particle and mesh systems. Great care was taken throughout to make optimal use of the available memory, so that a version of the current implementation has been used to simulate systems of up to 10⁹ particles with a 1024³ mesh for the long-range force computation. These are the largest Cosmological N-body simulations of which we are aware. We discuss these memory optimizations as well as those motivated by computational performance. Performance results are very encouraging, and, even without refinements, the code has been used effectively for simulations in which the particle distribution becomes highly clustered as well as for other non-uniform systems of astrophysical interest.     

三星星座对地定位的最佳构形研究

用数值方法对三星星座几何构形与定位精度的关系进行了仿真计算，结果表明对满足较高定位精度的区域进行定位，三星的几何构形呈等边三角形时，定位精度最高。     

The Loci of Satellite Positions: A Constellation Design Approach

In special cases in which satellite constellations can be described by a limited set of parameters, a correlation between the latter and the constellation characteristics (i.e. shape and kinematics of the satellite configurations) has been investigated. Such cases may be a useful starting point for designing more complex constellations in order to achieve better the desired performances. Therefore, this proves to be one way to fix an initial set of parameters once the desired behaviour of the constellation has been established on the basis of the operational purposes required. This revised version was published online in August 2006 with corrections to the Cover Date.     

An averaging method to study the motion of lunar artificial satellites II: Averaging and Applications

On this, the second part of a two part study (Steichen, 1998) we further develop a semi-analytical theory for a lunar artificial satellite. This theory is obtained by averaging analytically the Hamiltonian function over period up to a month. The averaged equations are then numerically integrated. The solution is free from singularities at e = 0 and I = 0 and is not expanded in powers of these variables. In the last section, the analytic work is applied to characteristic examples to validate the method used. This revised version was published online in July 2006 with corrections to the Cover Date.     

PSDF: Particle Stream Data Format for N-body simulations

We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output.     

双通道终端进行卫星双向法时间比对的归算方法

用双通道终端进行卫星双向法时间比对,可同时实现多台站时间同步。但是,目前双通道终端卫星双向法时间比对仍采用经典二台站归算方法,同时性的优点并没有得到充分的利用,其结果不闭合,比对得到的结果不统一。为了避免了上述问题,给出了新的归算方法,在同一系统下给出时间比对结果。新的归算方法不但提高了时间比对精度,同时还给出卫星到地面站之间的精确伪距,籍此精确地测定卫星的实时位置。