重力卫星中的“法拉利”太空中的“牛顿”

欧洲航天局于2009年3月17日用俄罗斯火箭轰鸣号发射了“地球重力场和静态洋流探测”（Gravity field and steady-state Ocean Explorer——简称GOCE）卫星。GOCE——也译为重力场和稳恒态海洋环流探索者,属于“地球探索者”系列卫星的首颗,可对地球的大气圈,生物圈,水圈,冰冻圈和地球内部进行最前沿研究。     

GRACE重力计划在揭示地球系统质量重新分布中的应用

2002年3月成功发射的美德合作卫星重力计划GRACE(Gravity Recovery And ClimateExperiment),即将提供空间分辨率约为200 km而时间分辨率为1个月的时变地球重力场模型序列。GRACE计划的星座由两颗相距约220 km,高度保持为300-500 km、倾角保持约90°的近极轨卫星组成。由于采用星载GPS和非保守力加速度计等高精度定轨技术,以及高精度的星一星跟踪数据反演地球重力场,在几百公里和更大空间尺度上, GRACE重力场的精度大大超过此前的卫星重力计划。根据GRACE时变重力场反演的地球系统质量重新分布,将对固体地球物理、海洋物理、气候学以及大地测量等应用有重要的意义。虽然其设计寿命只有5 yr,但研究表明GRACE的结果可用于研究北极冰长期时间尺度的变化,并进而研究极冰融化对全球气候变化,特别是对海平面长期变化的影响。在季节性时间尺度上,利用GRACE重力场反演的质量重新分布足以揭示平均小于1 cm的地表水变化,或小于1 mbar。的海底压强变化。除了巨大的社会效益和经济效益外,这些变化对了解地球系统的物质循环(主要是水循环)和能量循环有非常重要的意义。介绍GRACE重力场揭示的地球系统质量重新分布,为理解其地球物理应用提供必需的准备;同时针对我国大陆和沿海地区的地球物理应用提出初步的设想。     

卫星跟踪卫星模式中轨道参数需求分析

首次基于半解析法利用GRACE(Gravity Recovery and Climate Experiment)双星K波段星间速度误差、GPS接收机轨道误差和加速度计非保守力误差影响累计大地水准面精度的联合模型开展了卫星跟踪卫星模式中轨道参数的需求分析.建议我国将来首颗重力卫星的平均轨道高度设计为400 km和平均星间距离设计为220 km较优.此研究不仅为我国将来卫星重力测量计划中轨道参数的优化选取以及全球重力场精度的有效和快速估计提供了理论基础和计算保证,同时对将来国际GRACE Follow-On地球重力测量计划和GRAIL(Gravity Recovery and Interior Laboratory)月球重力探测计划的发展方向具有一定的指导意义.     

伽利略卫星的等势面和正常重力场

给出了轨道面接近赤道面的轨旋同步卫星的正常重力场在等势面上分布的展开式，并讨论了潮汐对其正常重力场的影响，利用这一方法，讨论了伽利略卫星正常重力场及其在等势面上的分布，以及木星的潮汐对伽利略卫星的正常重力场的影响，计算表明，潮汐对伽利略卫星的正常重力场影响不大，其径向的影响grt大约是10^-3-10^-5m/s^2的量级，与重力场在经度和纬度方向的分量接近，通过估算，月球的重力场所受到的潮汐影响要比绝大多数伽利略卫星受到的潮汐影响小。     

利用低轨卫星激光资料检验地球引力场模型的精度

地球引力场模型是人造卫星轨道计算中最重要的动力学模型之一.近年来国际上空间重力卫星计划取得了极大成功,相继推出了一系列新的引力场模型.从近地卫星轨道计算的角度检验了2种传统引力场模型(JGM3,EGM96)和4种新引力场模型(EIGENCHAMP05S,GGM03S,GOCE02S,EGM2008)的精度,利用4颗近地卫星的激光测距资料进行精密定轨预报,统计比较了不同模型的定轨残差和预报误差.结果表明:(1)4种新引力场模型精度基本在同一水平,对于近地卫星定轨精度普遍优于9 cm,最高达到5cm,相对于JGM3和EGM96模型有明显改善;(2)以JGM3模型为基准,EGM96模型的精度有所提高,2000年以后的4种新模型的精度则普遍提高了12%～47%(定轨)和63%(预报).70阶之前定轨精度随着模型阶次增大而提高,70阶以后定轨精度基本保持稳定,这表明对于近地卫星轨道计算而言,70阶的引力场已经能够满足厘米级的精度需求.     

模拟研究卫-卫跟踪中星间隔的选择问题

从两要从两个方面讨论了低轨卫星在做卫-卫跟踪(SST)观测时,星间隔的选择问题．1)用地球重力位系数作为扰动量,比较该扰动引起的不同间隔的SST星间距离和速度变化大小．2)用随机误差为1μm／s的星间速度变化作为模拟观测量,恢复不同间隔的地球重力位系数,并做精度评估．两种结果表明,适当增大SST间隔对求解重力场有利,但无限制增大无实际意义,对于选定高度为420km卫星,在作SST观测时,星间隔不宜超过690km,此模拟方法及结果对我国确定重力卫星指标有着重要意义．     

天体物理中的重力波和磁重力波

本文简要综述重力波和磁重力波在各种天体物理场合中的应用 ,我们描述在具有开放径向磁场的恒星大气各种磁流体波之间的相互转换过程 ,强调磁重力波被束缚在恒星冕内的可能性 ,并探讨恒星内部高频的声波模 (p -模 )被低频的重力波模 (g -模 )所调制的过程 ,一旦有了足够长时间未间断高质量的日震数据 ,太阳内部的重力波模对声波模的调制效应—即每一个分立声波模的频率精细结构—则可被用来寻找深陷于太阳内部的重力波模或进一步独立地约束重力波模的振幅上限     

利用GRACE 数据监测中亚地区陆地水储量动态变化的研究?

利用2003年1月至2013年1月10 yr 间的GRACE (Gravity Recovery And Climate Experiment)重力场恢复与气候实验重力卫星数据,辅以 TRMM (Tropical Rainfall Measuring Mission)/CMAP (Climate Prediction Center’s Merged Analysis of Precipitation)降水量数、NDVI (Normalized Difference Vegetation Index)数据、DEM (Digital Elevation Model)数据等多种数据源及诸多GIS (Geographic Information System)手段,分析了121个月内研究区陆地水储量的动态变化情况。研究结果表明：⑴自东向西研究区陆地水储量变化程度由微弱逐步变化为非常剧烈;⑵巴尔喀什湖域外流区、鄂毕河流域以及部分叶尼塞河中下游地区的陆地水储量持续增长趋势显著;⑶锡尔河流域、阿姆河流域的交界处、幼发拉底-底格里斯河流域和里海西南海岸交界范围内,陆地水储量呈现了急剧降低的趋势;⑷降水量、蒸散发、地表植被的覆盖变化、地形因素等自然因素均对陆地水储量产生影响作用;⑸陆地水储量最大值出现的时间滞后于降水量最大值出现的时间。     

火星指向模型与重力场模型的发展回顾与使用

首先回顾了火星重力场模型的发展历程;然后介绍了火星重力场模型使用中涉及的坐标系统,并给出了各坐标系之间的相互转换关系,再比较了基于不同火星指向参数模型进行坐标转换的差异;最后从重力异常与星历积分两个方面对最新的火星重力场模型GMM-3与JGMRO 120d进行了比较,结果表明两个重力场模型在精度上较为一致,对于10 m量级精度的定轨要求,模型的选取无特殊要求。     

现代天王星卫星运动定量理论的研究和发展

1986年“旅行者2号”飞越天于星期间，由空间无线电和光学观测获得的卫星资料首次给出天王星5颗主要卫星质量的可靠估计，从而推动了现代天王星卫星运动定量理论的建立。Laskar于1986年建立了第一个相对完整的天王星主要卫星的(半）分析理论——GUST86，其高精度已被许多学者的实算证实。之后，对理论的改进作出贡献的学者有：Malhotra等人(1989）、Lazzaro等人(1987，1991)分析研究了天王星卫星系统中近共振项对长期摄动解的影响；Taylor(1998)采用数值积分拟合观测资料，以更精确地测定卫星质量；Christou和Murray(1997)则将一个2阶Laplace—Lagrange理论应用于天王星卫星系统。对这些学者的工作作一概述。     

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.     

Efficient Determination of Global Gravity Field from Satellite-to-satellite Tracking Mission

The gravity field dedicated satellite missions like CHAMP, GRACE, and GOCE are supposed to map the Earth's global gravity field with unprecedented accuracy and resolution. New models of the Earth's static and time-variable gravity fields will be available every month as one of the science products from GRACE. A method for the efficient gravity field recovery is presented using in situ satellite-to-satellite observations at altitude and results on static as well as temporal gravity field recovery are shown. Considering the energy relationship between the kinetic energy of the satellite and the gravitational potential, the disturbing potential observations can be computed from the orbital state vector, using high-low GPS tracking data, low–low satellite-to-satellite GRACE measurements, and data from 3-axis accelerometers. The solution method is based on the conjugate gradient iterative approach to efficiently recover the gravity field coefficients and approximate error covariance up to degree and order 120 every month. Based on the monthly GRACE noise-only simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 6–7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The temporal gravity field, representing the monthly mean continental water mass redistribution, was recovered in the presence of measurement noise and high frequency temporal variation. The resulting recovered temporal gravity fields have about 0.3 mm errors in terms of geoid height with a resolution of 670 km.     

Future Satellite Gravimetry for Geodesy

After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is shown based on the analysis of spectral signal power of various gravity field components and on the comparison with current knowledge and expected performance of GRACE and GOCE. Both, accuracy and resolution can be improved by future dedicated gravity satellite missions. For applications in geodesy, the spectral omission error due to the limited spatial resolution of a gravity satellite mission is a limiting factor. The recommended strategy is to extend as far as possible the spatial resolution of future missions, and to improve at the same time the modelling of the very small scale components using terrestrial gravity information and topographic models.We discuss the geodetic needs in improved gravity models in the areas of precise height systems, GNSS levelling, inertial navigation and precise orbit determination. Today global height systems with a 1 cm accuracy are required for sea level and ocean circulation studies. This can be achieved by a future satellite mission with higher spatial resolution in combination with improved local and regional gravity field modelling. A similar strategy could improve the very economic method of determination of physical heights by GNSS levelling from the decimeter to the centimeter level. In inertial vehicle navigation, in particular in sub-marine, aircraft and missile guidance, any improvement of global gravity field models would help to improve reliability and the radius of operation.     

The Impact of the Static Part of the Earth's Gravity Field on Some Tests of General Relativity with Satellite Laser Ranging

In this paper we calculate explicitly the classical secular precessions of the node and the perigee of an Earth artificial satellite induced by the even zonal harmonics of the static part of the geopotential up to degree l = 20. Subsequently, their systematic errors induced by the mismodelling in the even zonal spherical harmonics coefficients J _l are compared to the general relativistic secular gravitomagnetic and gravitoelectric precessions of the node and the perigee of the existing laser-ranged geodetic satellites and of the proposed LARES. The impact of the future terrestrial gravity models from CHAMP and GRACE missions is discussed as well. Preliminary estimates with the recently released EIGEN-1S gravity model including the first CHAMP data are presented.     

GOCE: The Earth Gravity Field by Space Gradiometry

An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers are flown in the same satellite, they naturally eliminate (to some extent) the common perturbational accelerations and their differences are affected by the second derivatives of the gravity fields only (gradiometry). The mission GOCE is based on this principle. Its peculiar dynamical observation equations are reviewed. The possibility of estimating the gravity field up to some harmonic degree (200) is illustrated.     

Future Benefits of Time-Varying Gravity Missions to Ocean Circulation Studies

A summary is offered of the potential benefits of future measurements of temporal variations in gravity for the understanding of ocean dynamics. Two types of process, and corresponding amplitudes are discussed: ocean basin scale pressure changes, with a corresponding amplitude of order 1 cm of water, or 1 mm of geoid height, and changes in along-slope pressure gradient, at cross-slope length scales corresponding to topographic slopes, with a corresponding amplitude of order 1 mm of water, or a maximum of about 0.01 mm of geoid. The former is feasible with current technology and would provide unprecedented information about abyssal ocean dynamics associated with heat transport and climate. The latter would be a considerable challenge to any foreseeable technology, but would provide an exceptionally clear, quantitative window on the dynamics of abyssal ocean currents, and strong constraints on ocean models. Both options would be limited by the aliassing effect of rapid mass movements in the earth system, and it is recommended that any future mission take this error source explicitly into account at the design stage. For basin-scale oceanography this might involve a higher orbit than GRACE or GOCE, and the advantages of exact-repeat orbits and multiple missions should be considered.     

一种计算垂线偏差的抗差最小二乘严密解法

针对当前利用大地水准面模型求解垂线偏差精度不高、稳健性差的问题,设计了一种严密的垂线偏差抗差最小二乘解法.首先,基于大地水准面与垂线偏差的关系,采用EGM2008 (Earth Gravity Model 2008)重力场模型计算参数初始解;然后,引入中位数抗差法,并选用Huber权函数计算等价权,迭代计算出稳健的垂线偏差最小二乘解;最后,结合两个实测算例对设计方法进行验证.试验结果表明,该方法计算的垂线偏差分量与约定真值最大偏差在0.5′′左右,相较于对比方法精度更高;同时,该方法能有效抵抗粗差值的影响,具有较强的稳健性.     

Challenges From Solid Earth Dynamics for Satellite Gravity Field Missions in the Post-Goce Era

Examples from four main categories of solid-earth deformation processes are discussed for which the GOCE and GRACE satellite gravity missions will not provide a high enough spatial or temporal resolution or a sufficient accuracy. Quasi-static and episodic solid-earth deformation would benefit from a new satellite gravity mission that would provide a higher combined spatial and temporal resolution. Seismic and core periodic motions would benefit from a new satellite mission that would be able to detect gravity variations with a higher temporal resolution combined with very high accuracies.     

Ice Mass Balance and Ice Dynamics from Satellite Gravity Missions

An overview of advances in ice research which can be expected from future satellite gravity missions is given. We compare present and expected future accuracies of the ice mass balance of Antarctica which might be constrained to 0.1–0.3 mm/year of sea level equivalent by satellite gravity data. A key issue for the understanding of ice mass balance is the separation of secular and interannual variations. For this aim, one would strongly benefit from longer uninterrupted time series of gravity field variations (10 years or more). An accuracy of 0.01 mm/year for geoid time variability with a spatial resolution of 100 km would improve the separability of ice mass balance from mass change due to glacial isostatic adjustment and enable the determination of regional variations in ice mass balance within the ice sheets. Thereby the determination of ice compaction is critical for the exploitation of such high accuracy data. A further benefit of improved gravity field models from future satellite missions would be the improvement of the height reference in the polar areas, which is important for the study of coastal ice processes. Sea ice thickness determination and modelling of ice bottom topography could be improved as well.