Possible Future Use of Laser Gravity Gradiometers

With the GRACE mission under way and the GOCE mission well along in the design process, detailed questions concerning the type of future mission that may follow them have arisen. It is generally agreed that determining the time variations in the Earth's gravity field with as high spatial and temporal resolution as is feasible will be the main driver for such a mission. The possible use of laser heterodyne measurements between separate satellites in such a mission has been discussed by a number of people. The first suggestion of emphasizing time variation measurements in a laser mission was the TIDES concept presented in 1992 by Colombo and Chao. Then, in 2000, a GRACE Follow-On mission using laser measurements between two drag-free satellites was discussed by Watkins el al. (2000). More recently, the possibility of utilizing laser measurements between more than two satellites in order to determine two or more components of the gravity gradient tensor simultaneously has been proposed by Balmino. This approach may be desirable in order to reduce the aliasing of time variations between geopotential terms of different degree and order, as well as to improve the resolution in longitude, despite the cost of the additional satellites. In this paper, we discuss specific possible mission geometries for measuring the two diagonal in-plane components of the gravity gradient tensor simultaneously. This could be done, for example, by laser heterodyne measurements between two pairs of satellites in coplanar and nearly polar orbits. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microscope Instrument Development,Lessons for GOCE

Two space missions are presently under development with payload based on ultra-sensitive electrostatic accelerometers. The GOCE mission takes advantage of a three axis gradiometer accommodated in a very stable thermal case on board a drag-free satellite orbiting at a very low altitude of 250 km. This ESA mission will perform the very highly accurate mapping of the Earth gravity field with a geographical resolution of 100 km. The MICROSCOPE mission is devoted to the test of the “Universality of free fall” in view of the verification of the Einstein Equivalence Principle (EP) and of the search of a new interaction. The MICROSCOPE instrument is composed of two pairs of differential electrostatic accelerometers and the accelerometer proof-masses are the bodies of the EP test. The satellite is also a drag-free satellite exhibiting a fine attitude control and in a certain way, each differential accelerometer is a one axis gradiometer with an arm of quite null length. The development of this instrument much interests the definition and the evaluation of the sensor cores of the gradiometer. The in flight calibration process of both instruments is also very similar. Lessons form these parallel developments are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamic Modelling of the Hipparcos Attitude

We present a new method for a high-accuracy reconstruction of the attitude for a slowly spinning satellite. This method, referred to as the fully-dynamic approach, explores the possibility to describe the satellite's attitude as that of a rigid body subject to continuous external torques. The method is tried out on the Hipparcos data and is shown to reduce the noise for the along-scan attitude reconstruction for that mission by about a factor two to three. The dynamic modelling is expected to give a more accurate representation of the satellite's attitude than was obtained with a pure mathematical modelling. As such, it decreases the degrees of freedom in the a posteriori reconstruction. Some of the decrease is obtained through accumulating and subsequently implementing information on high frequency components in the solar radiation torques, which show to be systematic and predictable. This could be expected, as they are primarily linked to the external geometry and optical properties of the satellite. In the context of an astrometric mission, the methods presented here can only be applied as a final iteration step: the star positions that are used to reconstruct the attitude are also part of the scientific objectives of the mission. An estimate for the potential of a re-reduction of the Hipparcos data using the fully-dynamic model for the attitude reconstruction was obtained from test reductions of the first 24 months of mission data. Improvement of the accuracies of the astrometric parameters for all stars brighter than Hp=9.0 appears possible. The noise on the astrometric parameters for these stars was affected significantly by the along-scan attitude noise, which dominated for stars brighter than Hp=4.5. The possible improvement for stars brighter than about Hp=4.5 may, after iterations, be as much as a factor three. The reduced noise levels also allow a more accurate calibration and monitoring of instrument parameters, leading potentially to a better understanding of the instrument and the scientific data obtained with it. This revised version was published online in August 2006 with corrections to the Cover Date.     

Aiming at a 1-cm Orbit for Low Earth Orbiters: Reduced-Dynamic and Kinematic Precise Orbit Determination

The computation of high-accuracy orbits is a prerequisite for the success of Low Earth Orbiter (LEO) missions such as CHAMP, GRACE and GOCE. The mission objectives of these satellites cannot be reached without computing orbits with an accuracy at the few cm level. Such a level of accuracy might be achieved with the techniques of reduced-dynamic and kinematic precise orbit determination (POD) assuming continuous Satellite-to-Satellite Tracking (SST) by the Global Positioning System (GPS). Both techniques have reached a high level of maturity and have been successfully applied to missions in the past, for example to TOPEX/POSEIDON (T/P), leading to (sub-)decimeter orbit accuracy. New LEO gravity missions are (to be) equipped with advanced GPS receivers promising to provide very high quality SST observations thereby opening the possibility for computing cm-level accuracy orbits. The computation of orbits at this accuracy level does not only require high-quality GPS receivers, but also advanced and demanding observation preprocessing and correction algorithms. Moreover, sophisticated parameter estimation schemes need to be adapted and extended to allow the computation of such orbits. Finally, reliable methods need to be employed for assessing the orbit quality and providing feedback to the different processing steps in the orbit computation process. This revised version was published online in August 2006 with corrections to the Cover Date.     

VII: CLOSING SESSION: GOCE: ESA's First Earth Explorer Core Mission

This paper introduces the first ESA Core Earth Explorer mission, GOCE, in the context of ESA's Living Planet programme. GOCE will measure highly accurate, high spatial resolution differential accelerations in three dimensions along a well characterised orbit: the mission is planned for launch in early 2006. The mission objectives are to obtain gravity gradient data such that new global and regional models of the static Earth's gravity field and of the geoid can be deduced at length scales down to 100 km. These products will have broad application in the fields of geodesy, oceanography, solid-earth physics and glaciology. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ground Compatibility Tests for Gravity Measurement of SELENE: Accuracies of Two- and Four-Way Doppler and Range Measurements

The Japanese lunar mission Selenological and Engineering Explorer (SELENE) was launched in September 2007 and continued its mission until June 2009, when the main orbiter impacted with the surface of the Moon. SELENE consisted of three satellites: Main, Rstar, and Vstar. Rstar’s tasks were to forward up-link signals from the Usuada Deep Space Center (UDSC) to Main, and to down-link returning signals from Main to UDSC. We refer to this tracking sub-system as a four-way Doppler measurement. In contrast, conventional tracking systems between Rstar and UDSC as well as between Main and ground stations are referred to as two-way Doppler and range measurements. Using Main and Rstar, we successfully observed the gravity field over the farside of the Moon. Because four-way Doppler measurements via a relay sub-satellite were a fundamental experiment in space for Japanese space agencies, compatibility of radiometric instruments onboard Main and Rstar to UDSC were carefully examined at the UDSC using components manufactured for flight models. These tests not only proved the feasibility of the four-way Doppler measurements but also provided biases and variations of the four-way Doppler and two-way Doppler and range measurements that were later taken into account during the processing of tracking data and the analysis of the lunar global gravity field.     

Gravity modeling in aerospace applications

The science of inertial navigation has evolved to the point that the traditional gravity model is a principal error source in advanced, precise systems. Specifically, the unmodeled vertical deflections of the earth's gravitational field are a major contributor to CEP (circular error probable) divergence in precise terrestrial inertial navigation systems (INS). Over the years, several studies have been undertaken to the development of advanced techniques for accurate, real-time compensation of gravity disturbance vectors. More complex on-board gravity models which compute vertical deflection components will reduce the CEP divergence rate, but imperfect modeling due to on-board processing limitations will still cause residual vertical deflection errors. In order to eliminate or reduce gravity-induced errors in the INS requires measurement of gravity disturbance values and in-flight compensation to the inertial navigator. It is assumed in this paper that gravity disturbance values have been measured prior to the airborne mission and various techniques for compensation are to be considered. As part of a screening process in this study, several gravity compensation techniques (both deterministic and stochastic models) were investigated. The screening process involved identification of gravity models and algorithms, and developments of selection criteria for subsequent screening of the candidates.     

Radiative damping of gravity waves in the solar atmosphere

The nonlocal character of the radiation field sianificantly modifies the radiative damping of perturbations in the solar photosphere. Gravity waves are not usually considered to exist in the solar photosphere because the radiative damping time, when based on the Newtonian approximation, is too short. However, this restriction does not apply to low order gravity waves. In fact, with the inclusion of nonlocal effects, the radiative damping for low order gravity waves becomes negative for some region in the photosphere and thus acts as a driving mechanism for gravity waves there.     

What Might GRACE Contribute to Studies of Post Glacial Rebound?

The NASA/DLR satellite gravity mission GRACE, launched in March, 2002, will map the Earth's gravity field at scales of a few hundred km and greater, every 30 days for five years. These data can be used to solve for time-variations in the gravity field with unprecedented accuracy and resolution. One of the many scientific problems that can be addressed with these time-variable gravity estimates, is post glacial rebound (PGR): the viscous adjustment of the solid Earth in response to the deglaciation of the Earth's surface following the last ice age. In this paper we examine the expected sensitivity of the GRACE measurements to the PGR signal, and explore the accuracy with which the PGR signal can be separated from other secular gravity signals. We do this by constructing synthetic GRACE data that include contributions from a PGR model as well as from a number of other geophysical processes, and then looking to see how well the PGR model can be recovered from those synthetic data. We conclude that the availability of GRACE data should result in improved estimates of the Earth's viscosity profile. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modelling of the MICROSCOPE Mission

The French space mission MICROSCOPE aims at testing the Equivalence Principle (EP) up to an accuracy of 10^?15. The experiment will be carried out on a satellite which is developed and produced within the CNES Myriade series. The measuring accuracy will be achieved by means of two high-precision capacitive differential accelerometers that are built by the French institute ONERA, see Touboul and Rodrigues (Class. Quantum Gravity 18:2487–2498, 2001). At ZARM, which is a member of the science team, the data evaluation process is prepared. Therefore, a comprehensive simulation of the real system including the science signal and all error sources is built for the development and testing of data reduction and data analysis algorithms to extract the EP violation signal. Currently, the ZARM Drag-Free simulator, a tool to support mission modelling, is adapted for the MICROSCOPE mission in order to simulate test mass and satellite dynamics. Models of environmental disturbances like solar radiation pressure are considered, also. Additionally, detailed modelling of the on-board capacitive sensors is done. The actual status of the mission modelling will be presented. Particularly, the modelling of disturbances forces will be discussed in detail.     

Gravity Recovery and Interior Laboratory (GRAIL): Mapping the Lunar Interior from Crust to Core

The Gravity Recovery and Interior Laboratory (GRAIL) is a spacecraft-to-spacecraft tracking mission that was developed to map the structure of the lunar interior by producing a detailed map of the gravity field. The resulting model of the interior will be used to address outstanding questions regarding the Moon’s thermal evolution, and will be applicable more generally to the evolution of all terrestrial planets. Each GRAIL orbiter contains a Lunar Gravity Ranging System instrument that conducts dual-one-way ranging measurements to measure precisely the relative motion between them, which in turn are used to develop the lunar gravity field map. Each orbiter also carries an Education/Public Outreach payload, Moon Knowledge Acquired by Middle-School Students (MoonKAM), in which middle school students target images of the Moon for subsequent classroom analysis. Subsequent to a successful launch on September 10, 2011, the twin GRAIL orbiters embarked on independent trajectories on a 3.5-month-long cruise to the Moon via the EL-1 Lagrange point. The spacecraft were inserted into polar orbits on December 31, 2011 and January 1, 2012. After a succession of 19 maneuvers the two orbiters settled into precision formation to begin science operations in March 1, 2012 with an average altitude of 55 km. The Primary Mission, which consisted of three 27.3-day mapping cycles, was successfully completed in June 2012. The extended mission will permit a second three-month mapping phase at an average altitude of 23 km. This paper provides an overview of the mission: science objectives and measurements, spacecraft and instruments, mission development and design, and data flow and data products.     

Interrelation between KOSI experiments and comet nucleus sampling

In situ observations of comet Halley yielded information on the nucleus and its environment. These measurements are related to properties of and processes at the nucleus by theoretical modelling and by simulation experiments in the laboratory. The objective of the KOSI (Kometensimulation) experiments is to study in detail processes which occur near the surface of ice-dust mixtures under irradiation by light, like heat transport into the sample, chemical fractionation of sample material, emission of gases, and others. The KOSI experiments are carried out at the large space simulation chamber in Köln. By providing an in-depth understanding of potential cometary processes the results from the KOSI experiments are relevant to any comet nucleus sample return mission.     

An Overview of the Fast Auroral SnapshoT (FAST) Satellite

The FAST satellite is a highly sophisticated scientific satellite designed to carry out in situ measurements of acceleration physics and related plasma processes associated with the Earth's aurora. Initiated and conceptualized by scientists at the University of California at Berkeley, this satellite is the second of NASA's Small Explorer Satellite program designed to carry out small, highly focused, scientific investigations. FAST was launched on August 21, 1996 into a high inclination (83°) elliptical orbit with apogee and perigee altitudes of 4175 km and 350 km, respectively. The spacecraft design was tailored to take high-resolution data samples (or `snapshots') only while it crosses the auroral zones, which are latitudinally narrow sectors that encircle the polar regions of the Earth. The scientific instruments include energetic electron and ion electrostatic analyzers, an energetic ion instrument that distinguishes ion mass, and vector DC and wave electric and magnetic field instruments. A state-of-the-art flight computer (or instrument data processing unit) includes programmable processors that trigger the burst data collection when interesting physical phenomena are encountered and stores these data in a 1 Gbit solid-state memory for telemetry to the Earth at later times. The spacecraft incorporates a light, efficient, and highly innovative design, which blends proven sub-system concepts with the overall scientific instrument and mission requirements. The result is a new breed of space physics mission that gathers unprecedented fields and particles observations that are continuous and uninterrupted by spin effects. In this and other ways, the FAST mission represents a dramatic advance over previous auroral satellites. This paper describes the overall FAST mission, including a discussion of the spacecraft design parameters and philosophy, the FAST orbit, instrument and data acquisition systems, and mission operations.     

复杂任务场景无人机集群自组织侦察建模与仿真

基于agent的作战建模与仿真是无人机集群侦察效能评估的重要方法,但以往方法中agent行为机制 和模型结构难以描述复杂任务场景下的自组织侦察行为。以反海盗侦察任务为例,提出一种面向集群自组织 侦察的作战建模与仿真方法。设计多agent分层复合行为机制和可组合模块化agent模型结构,通过简单行为 的组合描述复杂行为;通过信息素图模块与航路管理模块的交互,实现自组织航路规划与飞行控制;并通过仿 真算例,来验证方法的可行性,对比分析不同航路规划方法的侦察效能。结果表明:自组织航路规划对中断航 路侦察的动态事件的适应性更强;对于大区域、长时间、低目标密度的区域覆盖侦察任务,仅通过改进航路规划 方法来降低访问间隔难以显著提高目标发现概率。     

发动机飞行任务剖面的主成份聚类法

本文提出了利用主成份分析对航空发动机飞行任务剖面进行分类的方法 ,并对某战斗机发动机 1 8个飞行任务剖面进行了聚类分析。选取了飞行高度、飞行马赫数、发动机转速以及发动机重心法向过载等 4个参数作为分类的原始依据参数。对上述 4个参数进行主成份分析 ,得到 4个独立的主成份 ,其中第一、二主成份的累积贡献率可达 81 .1 %。因此 ,可以根据主平面内各飞行任务剖面的第一、二主成分的分布情况直观地进行定性地分类。最后 ,本文利用重心法进行了定量的聚类 ,得到了分类的树状图。研究结果表明本文提出的方法是合理可行的     

Gravity Field Recovery from GRACE: Unique Aspects of the High Precision Inter-Satellite Data and Analysis Methods

The very high accuracy of the Doppler and range measurements between the two low-flying and co-orbiting spacecraft of the GRACE mission, which will be at the μm/sec and ≈10 μm levels respectively, requires that special procedures be applied in the processing of these data. Parts of the existing orbit determination and gravity field parameters retrieval methods and software must be modified in order to fully benefit from the capabilities of this mission. This is being done in the following areas: (i) numerical integration of the equations of motion (summed form, accuracy of the predictor-corrector loop, Encke's formulation): (ii) special inter-satellite dynamical parameterization for very short arcs; (iii) accurate solution of large least-squares problems (normal equations vs. orthogonal decomposition of observation equations); (iv) handling the observation equations with high accuracy. Theoretical concepts and first tests of some of the newly implemented algorithms are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Impact of gravitation on gaseous pollutant source identification

 It is necessary to identify a gaseous pollutant source rapidly so that prompt actions can be taken, but this is one of the difficulties in the inverse problem areas. In this paper, an approach to identifying a sudden continuous emission pollutant source based on single sensor information is developed to locate a source in an enclosed space with a steady velocity field. Because the gravity has a very important influence on the gaseous pollutant transport and the source identification, its influence is analyzed theoretically and a conclusion is drawn that the velocity of fluid is a key factor to effectively help weaken the gravitational influence. Further studies for a given 2-D case by using the computational fluid dynamics (CFD) method show that when the velocity of inlet is less than one certain value, the influence of gravity on the pollutant transport is very significant, which will change the velocity field obviously. In order to quantitatively judge the practical applicability of identification approach, a synergy degree of the velocity fields before and after a source appearing is proposed as a condition for considering the influence of gravity. An experimental device simulating pollutant transmission was set up and some experiments were conducted to verify the practical application of the above studies in the actual gravitational environment. The results show that the proposed approach can successfully locate the sudden constant source when the experimental situations meet the identified conditions.     

The Scientific Measurement System of the Gravity Recovery and Interior Laboratory (GRAIL) Mission

The Gravity Recovery and Interior Laboratory (GRAIL) mission to the Moon utilized an integrated scientific measurement system comprised of flight, ground, mission, and data system elements in order to meet the end-to-end performance required to achieve its scientific objectives. Modeling and simulation efforts were carried out early in the mission that influenced and optimized the design, implementation, and testing of these elements. Because the two prime scientific observables, range between the two spacecraft and range rates between each spacecraft and ground stations, can be affected by the performance of any element of the mission, we treated every element as part of an extended science instrument, a science system. All simulations and modeling took into account the design and configuration of each element to compute the expected performance and error budgets. In the process, scientific requirements were converted to engineering specifications that became the primary drivers for development and testing. Extensive simulations demonstrated that the scientific objectives could in most cases be met with significant margin. Errors are grouped into dynamic or kinematic sources and the largest source of non-gravitational error comes from spacecraft thermal radiation. With all error models included, the baseline solution shows that estimation of the lunar gravity field is robust against both dynamic and kinematic errors and a nominal field of degree 300 or better could be achieved according to the scaled Kaula rule for the Moon. The core signature is more sensitive to modeling errors and can be recovered with a small margin.     

Impact Cratering Theory and Modeling for the Deep Impact Mission: From Mission Planning to Data Analysis

The cratering event produced by the Deep Impact mission is a unique experimental opportunity, beyond the capability of Earth-based laboratories with regard to the impacting energy, target material, space environment, and extremely low-gravity field. Consequently, impact cratering theory and modeling play an important role in this mission, from initial inception to final data analysis. Experimentally derived impact cratering scaling laws provide us with our best estimates for the crater diameter, depth, and formation time: critical in the mission planning stage for producing the flight plan and instrument specifications. Cratering theory has strongly influenced the impactor design, producing a probe that should produce the largest possible crater on the surface of Tempel 1 under a wide range of scenarios. Numerical hydrocode modeling allows us to estimate the volume and thermodynamic characteristics of the material vaporized in the early stages of the impact. Hydrocode modeling will also aid us in understanding the observed crater excavation process, especially in the area of impacts into porous materials. Finally, experimentally derived ejecta scaling laws and modeling provide us with a means to predict and analyze the observed behavior of the material launched from the comet during crater excavation, and may provide us with a unique means of estimating the magnitude of the comet’s gravity field and by extension the mass and density of comet Tempel 1.     

Ocean Tides in GRACE Monthly Averaged Gravity Fields

The GRACE mission will map the Earth's gravity fields and its variations with unprecedented accuracy during its 5-year lifetime. Unless ocean tide signals and their load upon the solid earth are removed from the GRACE data, their long period aliases obscure more subtle climate signals which GRACE aims at. In this analysis the results of Knudsen and Andersen (2002) have been verified using actual post-launch orbit parameter of the GRACE mission. The current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower than 47. The accumulated tidal errors may affect the GRACE data up to harmonic degree 60. A study of the revised alias frequencies confirm that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields. The S₂ and the K₂ terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages. Those results have been verified using a simulated 30 days GRACE orbit. The results show that the magnitudes of the monthly averaged values are slightly higher than the previous values. This may be caused by insufficient sampling to fully resolve and reduce the tidal signals at short wavelengths and close to the poles. This revised version was published online in August 2006 with corrections to the Cover Date.