Space-Wise,Time-Wise,Torus and Rosborough Representations in Gravity Field Modelling

The decade of the geopotentials started July 2000 with the launch of the German high-low SST mission CHAMP. Together with the joint NASA-DLR low-low SST mission GRACE and the ESA gradiometry mission GOCE an unprecedented wealth of geopotential data becomes available over the next few years. Due to the sheer number of unknown gravity field parameters (up to 100 000) and of observations (millions), especially the latter two missions are highly demanding in terms of computational requirements. In this paper several modelling strategies are presented that are based on a semi-analytical approach. In this approach the set of normal equations becomes block-diagonal with maximum block-sizes smaller than the spherical harmonic degree of resolution. The block-diagonality leads to a rapid and powerful gravity field analysis tool. Beyond the more-or-less conventional space-wise and time-wise formulations, the torus approach and Rosborough's representation are discussed. A trade-off between pros and cons of each of the modelling strategies will be given. This revised version was published online in August 2006 with corrections to the Cover Date.     

可重复使用运载器磁悬浮助推发射参数研究

针对磁悬浮助推水平起飞运载器这种新型发射概念,采用概念性分析方法,研究地面发射参数对可重复使用运载器性能的影响规律。结果表明,助推发射水平起飞运载器在降低初始推重比、推进剂和结构质量等方面具有优势,最后得出地面发射参数的一组优化值。     

惯导平台式重力测量技术实现及应用

详细阐述了解析方位双轴惯导平台式重力测量的工作原理,并通过基于方位余弦积的惯导力学编排解决了极区工作问题。在常规平台式重力测量数据处理方法的基础上,针对高动态环境提出了基于Kalman滤波的运动扰动修正方法。在此基础上研制了ZL11-1A型国产惯导平台式海洋重力仪。通过与国外主流重力仪产品海上同船作业比对,结果表明,该型重力仪在高海况下测量精度依然优于1mGal,满足重力测量作业要求。     

Semi-stochastic modification of second-order radial derivative of Abel–Poisson’s formula for validating satellite gravity gradiometry data

The geoid can be used to validate the satellite gravity gradiometry data. Validation of such data is important prior to their downward continuation because of amplification of the data errors through this process. In this paper, the second-order radial derivative of Abel–Poisson’s formula is modified stochastically to reduce the effect of the far-zone geoid and generate the second-order radial derivative of geopotential at 250 km level. The numerical studies over Fennoscandia show that this method yields the gradients with an error of 10 mE and when the long wavelength of geoid is removed from the estimator and restored after the computations (remove–compute–restore) the error will be in 1 mE level. We name this method semi-stochastic modification. The best case scenario is found when the degree of modification of the integral formula is 200 and the long wavelength geoid to degree 100 is removed and restored. In this case the geoid should have a resolution of 15′ × 15′ and the integration should be performed over a cap size of 3°.     

Gravity wave momentum flux generation close to mid-latitude Andes in mesoscale simulations of late 20th and 21st centuries

Adequate representations of diverse dynamical processes in general circulation models (GCM) are necessary to obtain reliable simulations of the present and the future. The parameterization of orographic gravity wave drag (GWD) is one of the critical components of GCM. It is therefore convenient to evaluate whether standard orographic GWD parameterizations are appropriate. One alternative is to study the generation of gravity waves (GW) with horizontal resolutions that are higher than those used in current GCM simulations. Here we assess the seasonal pattern of topographic GW momentum flux (GWMF) generation for the late 20th and 21st centuries in a downscaling using the Rossby Centre regional atmospheric model under the Intergovernmental Panel on Climate Change A1B emission conditions. We focus on one of the world’s strongest extra-tropical GW zones, the Andes Mountains at mid-latitudes in the Southern Hemisphere. The presence of two GCM sub-grid scale structures locally contributing to GWMF (one positive and one negative) is found to the East of the mountains. For the late 21st century the strength of these structures during the GW high season increases around 23% with respect to the late 20th century, but the GWMF average over GCM grid cell scales remains negative and nearly constant around −0.015 Pa. This constitutes a steady significant contribution during GW high season, which is not related to the GWMF released by individual sporadic strong GW events. This characteristic agrees with the fact that no statistically significant variation in GWMF at source level has been observed in recent GCM simulations of atmospheric change induced by increases in greenhouse gases.     

Optimization and verification of free flight separation similarity law in high-speed wind tunnel

Based on the similarity of separation time, a similarity law optimization method for high-speed weapon delivery test is derived. The typical separation state under wind load is simulated by the numerical method. The real separation data of aircraft, separation data of previous test methods, separation data of ideal wind tunnel test of previous methods, and simulation data of the proposed optimization method are obtained. A comparison of the data shows that the method proposed can improve the performance of tracking. Similarity law optimization starts with the development of motion equations and dynamic equations in the windless state to address the problems of mismatching between vertical and horizontal displacement, and to address the problems of separation trajectory distortion caused by insufficient gravity acceleration of the scaling model of existing light model. The ejection velocity of the model is taken as a factor/vector, and is adjusted reasonably to compensate the linear displacement insufficiency caused by the insufficient vertical acceleration of the light model method, so as to ensure the matching of the vertical and horizontal displacement of the projectile, and to improve the consistency between the test results of high-speed projection and the actual separation trajectory. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels. The optimized similarity law is not affected by the ejection velocity and hanging mode of the projectile. The optimized similarity law is suitable not only for the launching of the buried ammunition compartment and external stores, but also for the test design of projectile launching and gravity separation.     

Method of virtual trajectories for the design of gravity assisted missions

A method of virtual trajectories is proposed for the design of multiple gravity assist trajectories. The method comprises two principal stages. First, for a chosen planetary sequence, a database of virtual trajectories is tabulated. Then the database screening and refinement are performed. The design of trajectory to Jupiter is presented.     

A comparative and numerical study of effects of gravity waves in small miss-distance and miss-time GPS radio occultation temperature profiles

The Global Positioning System (GPS) Radio Occultation (RO) technique has global coverage and is capable of generating high vertical resolution temperature profiles of the upper troposphere and lower stratosphere with sub-Kelvin accuracy and long-term stability, regardless of weather conditions. In this work, we take advantage of the anomalously high density of occultation events at the eastern side of the highest Andes Mountains during the initial mission months of COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate). This region is well-known for its high wave activity. We choose to study two pairs of GPS RO, both containing two occultations that occurred close in time and space. One pair shows significant differences between both temperature profiles. Numerical simulations with a mesoscale model were performed, in order to understand this discrepancy. It is attributed to the presence of a horizontal inhomogeneous structure caused by gravity waves.     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery

The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities.