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.     

Tidal Models in a New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Magnetic Field of the Earth’s Lithosphere

The lithospheric contribution to the Earth’s magnetic field is concealed in magnetic field data that have now been measured over several decades from ground to satellite altitudes. The lithospheric field results from the superposition of induced and remanent magnetisations. It therefore brings an essential constraint on the magnetic properties of rocks of the Earth’s sub-surface that would otherwise be difficult to characterize. Measuring, extracting, interpreting and even defining the magnetic field of the Earth’s lithosphere is however challenging. In this paper, we review the difficulties encountered. We briefly summarize the various contributions to the Earth’s magnetic field that hamper the correct identification of the lithospheric component. Such difficulties could be partially alleviated with the joint analysis of multi-level magnetic field observations, even though one cannot avoid making compromises in building models and maps of the magnetic field of the Earth’s lithosphere at various altitudes. Keeping in mind these compromises is crucial when lithospheric field models are interpreted and correlated with other geophysical information. We illustrate this discussion with recent advances and results that were exploited to infer statistical properties of the Earth’s lithosphere. The lessons learned in measuring and processing Earth’s magnetic field data may prove fruitful in planetary exploration, where magnetism is one of the few remotely accessible internal properties.     

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.     

小卫星主动磁控制地球捕获姿态控制系统设计

分析了小卫星捕获阶段的客观条件要求,重力梯度杆的指向要求,捕获阶段视为大角度机动问题,采用欧拉动力学和四元数方法描述,建立小卫星捕获阶段的动力学模型。控制器采用大角度机动拟 PD控制,拟PD控制器参数采用了简化分析和经验调试设计,同时分析设计了磁力矩器的磁偶极子,最后给出某小卫星姿态捕获仿真结果,经过几个轨道周期后可以实现一定精度的对地捕获,验证了本文的设计方法的可行性。     

Global Gravity Field Recovery Using Solely GPS Tracking and Accelerometer Data from Champ

A new long-wavelength global gravity field model, called EIGEN-1, has been derived in a joint German-French effort from orbit perturbations of the CHAMP satellite, exploiting CHAMP-GPS satellite-to-satellite tracking and on-board accelerometer data over a three months time span. For the first time it becomes possible to recover the gravity field from one satellite only. Thanks to CHAMP'S tailored orbit characteristics and dedicated instrumentation, providing continuous tracking and on-orbit measurements of non-gravitational satellite accelerations, the three months CHAMP-only solution provides the geoid and gravity with an accuracy of 20 cm and 1 mgal, respectively, at a half wavelength resolution of 550 km, which is already an improvement by a factor of two compared to any pre-CHAMP satellite-only gravity field model. This revised version was published online in August 2006 with corrections to the Cover Date.     

A geopause satellite system concept

The forthcoming 10 cm range tracking accuracy capability holds much promise in connection with a number of Earth and ocean dynamics investigations. These include a set of earthquake-related studies of fault motions and the Earth's tidal, polar and rotational motions, as well as studies of the gravity field and the sea surface topography which should furnish basic information about mass and heat flow in the oceans. The state of the orbit analysis art is presently at about the 10 m level, or about two orders of magnitude away from the 10 cm range accuracy capability expected in the next couple of years or so. The realization of a 10 cm orbit analysis capability awaits the solution of four kinds of problems, namely, those involving orbit determination and the lack of sufficient knowledge of tracking system biases, the gravity field, and tracking station locations. The Geopause satellite system concept offers promising approaches in connection with all of these areas. A typical Geopause satellite orbit has a 14 hour period, a mean height of about 4.6 Earth radii, and is nearly circular, polar, and normal to the ecliptic. At this height only a relatively few gravity terms have uncertainties corresponding to orbital perturbations above the decimeter level. The orbit s, in this sense, at the geopotential boundary, i.e., the geopause. The few remaining environmental quantities which may be significant can be determined by means of orbit analyses and accelerometers. The Geopause satellite system also provides the tracking geometery and coverage needed for determining the orbit, the tracking system biases and the station locations. Studies indicate that the Geopause satellite, tracked with a 2 cm ranging system from nine NASA affiliated sites, can yield decimeter station location accuracies. Five or more fundamental stations well distributed in longitude can view Geopause over the North Pole. This means not only that redundant data are available for determining tracking system biases, but also that both components of the polar motion can be observed frequently. When tracking Geopause, the NASA sites become a two-hemisphere configuration which is ideal for a number of Earth physics applications such as the observation of the polar motion with a time resolution of a fraction of a day. Geopause also provides the basic capability for satellite-to-satellite tracking of drag-free satellites for mapping the gravity field and altimeter satellites for surveying the sea surface topography. Geopause tracking a coplanar, drag-free satellite for two months to 0.03 mm per second accuracy can yield the geoid over the entire Earth to decimeter accuracy with 2.5° spatial resolution. Two Geopause satellites tracking a coplanar altimeter satellite can then yield ocean surface heights above the geoid with 7° spatial resolution every two weeks. These data will furnish basic boundary condition information about mass and heat flows in the oceans which are important in shaping weather and climate.     

Planetary radio astronomy experiment for Voyager missions

The planetary radio astronomy experiment will measure radio spectra of planetary emissions in the range 1.2 kHz to 40.5 MHz. These emissions result from wave-particle-plasma interactions in the magnetospheres and ionospheres of the planets. At Jupiter, they are strongly modulated by the Galilean satellite Io.As the spacecraft leave the Earth's vicinity, we will observe terrestrial kilometric radiation, and for the first time, determine its polarization (RH and LH power separately). At the giant planets, the source of radio emission at low frequencies is not understood, but will be defined through comparison of the radio emission data with other particles and fields experiments aboard Voyager, as well as with optical data. Since, for Jupiter, as for the Earth, the radio data quite probably relate to particle precipitation, and to magnetic field strength and orientation in the polar ionosphere, we hope to be able to elucidate some characteristics of Jupiter auroras.Together with the plasma wave experiment, and possibly several optical experiments, our data can demonstrate the existence of lightning on the giant planets and on the satellite Titan, should it exist. Finally, the Voyager missions occur near maximum of the sunspot cycle. Solar outburst types can be identified through the radio measurements; when the spacecraft are on the opposite side of the Sun from the Earth we can identify solar flare-related events otherwise invisible on the Earth.     

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.     

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.     

Pico-satellite Autonomous Navigation with Magnetometer and Sun Sensor Data

This article presents a near-Earth satellite orbit estimation method for pico-satellite applications with light-weight and low-power requirements. The method provides orbit information autonomously from magnetometer and sun sensor, with an extended Kalman filter (EKF). Real-time position/velocity parameters are estimated with attitude independently from two quantities: the measured magnitude of the Earth’s magnetic field, and the measured dot product of the magnetic field vector and the sun vector. To guarantee the filter’s effectiveness, it is recommended that the sun sensor should at least have the same level of accuracy as magnetometer. Furthermore, to reduce filter’s computation expense, simplification methods in EKF’s Jacobian calculations are introduced and testified, and a polynomial model for fast magnetic field calculation is developed. With these methods, 50% of the computation expense in dynamic model propagation and 80% of the computation burden in measurement model calculation can be reduced. Tested with simulation data and compared with original magnetometer-only methods, filter achieves faster convergence and higher accuracy by 75% and 30% respectively, and the suggested simplification methods are proved to be harmless to filter’s estimation performance.     

Thermal Evolution and Magnetic Field Generation in Terrestrial Planets and Satellites

Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and Venus do not. Magnetic field data recorded at Ganymede have been interpreted as evidence of a self-generated magnetic field. The other icy Galilean satellites have magnetic fields induced in their subsurface oceans while Io and the Saturnian satellite Titan apparently are lacking magnetic fields of internal origin altogether. Parts of the lunar crust are remanently magnetized as are parts of the crust of Mars. While it is widely accepted that the magnetization of the Martian crust has been caused by an early magnetic field, for the Moon alternative explanations link the magnetization to plasma generated by large impacts. The necessary conditions for a dynamo in the terrestrial planets and satellites are the existence of an iron-rich core that is undergoing intense fluid motion. It is widely accepted that the fluid motion is caused by convection driven either by thermal buoyancy or by chemical buoyancy or by both. The chemical buoyancy is released upon the growth of an inner core. The latter requires a light alloying element in the core that is enriched in the outer core as the solid inner core grows. In most models, the light alloying element is assumed to be sulfur, but other elements such as, e.g., oxygen, silicon, and hydrogen are possible. The existence of cores in the terrestrial planets is either proven beyond reasonable doubt (Earth, Mars, and Mercury) or the case for a core is compelling as for Venus and the Moon. The Galilean satellites Io and Ganymede are likely to have cores judging from Galileo radio tracking data of the gravity fields of these satellites. The case is less clear cut for Europa. Callisto is widely taken as undifferentiated or only partially differentiated, thereby lacking an iron-rich core. Whether or not Titan has a core is not known at the present time. The terrestrial planets that do have magnetic fields either have a well-established inner core with known radius and density such as Earth or are widely agreed to have an inner core such as Mercury. The absence of an inner core in Venus, Mars, and the Moon (terrestrial bodies that lack fields) is not as well established although considered likely. The composition of the Martian core may be close to the Fe–FeS eutectic which would prevent an inner core to grow as long as the core has not cooled to temperatures around 1500 Kelvin. Venus may be on the verge of growing an inner core in which case a chemical dynamo may begin to operate in the geologically near future. The remanent magnetization of the Martian and the lunar crust is evidence for a dynamo in Mars’ and possibly the Moon’s early evolution and suggests that powerful thermally driven dynamos are possible. Both the thermally and the chemically driven dynamo require that the core is cooled at a sufficient rate by the mantle. For the thermally driven dynamo, the heat flow from the core into the mantle must by larger than the heat conducted along the core adiabat to allow a convecting core. This threshold is a few mW?m^?2 for small planets such as Mercury, Ganymede, and the Moon but can be as large as a few tens mW?m^?2 for Earth and Venus. The buoyancy for both dynamos must be sufficiently strong to overcome Ohmic dissipation. On Earth, plate tectonics and mantle convection cool the core efficiently. Stagnant lid convection on Mars and Venus are less efficient to cool the core but it is possible and has been suggested that Mars had plate tectonics in its early evolution and that Venus has experienced episodic resurfacing and mantle turnover. Both may have had profound implications for the evolution of the cores of these planets. It is even possible that inner cores started to grow in Mars and Venus but that the growth was frustrated as the mantles heated following the cessation of plate tectonics and resurfacing. The generation of Ganymede’s magnetic field is widely debated. Models range from magneto-hydrodynamic convection in which case the field will not be self-sustained to chemical and thermally-driven dynamos. The wide range of possible compositions for Ganymede’s core allows models with a completely liquid near eutectic Fe–FeS composition as well as models with Fe inner cores or cores in with iron snowfall.     

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.     

The contribution of observations of satellites to the determination of the Earth's gravitational potential

The history of the determination of the external gravitational potential of the Earth is sketched briefly. A discussion of the principles by which the potential may be derived from the observations of changes in the orbits of artificial satellites is followed by outlines of the principal theories and by detailed consideration of the formal differences between them that arise from differences in the ways that the orbits are described and it is shown that those formulae on which most of the numerical results depend are equivalent in the principal theories. The usual methods of treatment break down in certain special conditions and the analysis of these cases is also considered although they are not of great practical importance in the derivation of the potential; similarly a short account is given of the behaviour of a satellite having an orbital angular velocity commensurable with the spin angular velocity of the Earth. Methods by which satellites are observed are mentioned and the main numerical results on the external potential of the Earth are discussed critically. Finally the results are compared with those derived from observations of gravity on the surface of the Earth and the application of the results to problems of geodesy, of the physical state of the Earth and of the motion of the Moon are described.     

Coronal holes and solar magnetic fields

Since 1972, nearly continuous observations of coronal holes and their associated photospheric magnetic fields have been made using a variety of satellite and ground-based equipment. The results of comparisons of these observations are reviewed and it is demonstrated that the structure and evolution of coronal holes is basically governed by the large-scale distribution of photospheric magnetic flux. Non-polar holes form in the decaying remnants of bipolar magnetic regions in areas with a large-scale flux imbalance. There is strong indirect evidence that the magnetic field in coronal holes is always open to interplanetary space but not all open-field regions have associated coronal holes. The well-observed declining phase of the last solar cycle was characterized by stable magnetic field and coronal hole patterns which were associated with recurrent, high-speed wind streams and interplanetary magnetic field patterns at the Earth. The ascending phase of the current cycle has been characterized by transient magnetic field and coronal hole patterns which tend to occur at high solar latitudes. This shift in magnetic field and coronal hole patterns has resulted in a less obvious and more complicated association with high-speed wind streams at the Earth.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.Visiting Scientist, Kitt Peak National Observatory.     

The Cusp as a Source of Magnetospheric Energetic Particles, Currents, and Electric Fields: A New Paradigm

Energetic particle instrumentation on the Polar satellite has discovered that significant fluxes of energetic particles are continuously present in the region of the dayside magnetosphere where they cannot be stably trapped. This region is associated with either open magnetic field lines or a magnetic topology associated with pseudo-trapping. Two distinct features [Time-Energy Dispersion (TED) signatures and Cusp Energetic Particle (CEP) events] are observed in these energetic particle fluxes that strongly suggest a local acceleration of mostly shocked solar wind particles. As the solar wind particles ram themselves into the cusp geometry, they form diamagnetic cavities with strong turbulence that are capable of accelerating particles to energies of 100s and 1000s of kiloelectronvolts. This process forms a layer of energetic particles on the magnetopause as well as permits such particles to enter via drift the equatorial nightside magnetosphere to distances as close as six Earth radii under the influence of gradient and curvature effects in the local magnetic field. The fluxes of these particles have all of the properties associated with the ring current and can supply the magnitude of the cross tail current required. ISEE-1 energetic particle data and their pitch angle distributions [PAD] are examined at the magnetic equatorial plane on the night side to investigate and possibly validate the insights gains from the Polar data and energetic particle trajectory tracing in a realistic magnetic field. The existence and properties of butterfly-type PADs strongly supports the concept of a dayside high latitude source of energetic particle fluxes. Because the CEP process is impulsive and time variable the charge separation produced by the drifting electrons (eastward) and ions (westward) on the magnetospheric nightside may be responsible for the cross tail electric field that has been ascribed to the reconnection/convection process.     

Solar Pressure Attitude Stabilization of Earth-Pointing Spacecraft

The development of a solar pressure control system for three-axis attitude control of Earth-oriented spacecraft is presented. A controller configuration consisting of two rotatable mirrorlike surfaces, representing the minimum hardware implementation, is considered. Optimal control theory is applied to synthesize a feedback control law directly governing the differential rotation of the control surfaces. The system performance is evaluated through the response analysis of a satellite subject to destabilizing gravity gradient torques as well as external disturbances. Even under such adverse conditions, the results indicate a moderately sized controller to be quite effective in maintaining the desired Earth-pointing spacecraft orientation. The validity of the optimal control law is established for all times of the year, and the feasibility of implementing suboptimal control policies is also examined.     

估计飞行器羽流影响的点源流动模型和计算机程序

目前和今后使用火箭发动机进行轨道和姿态控制的空间飞行器都要遇到发动机排气羽流影响问题.本文讨论了一种迅速估算轴对称的羽流远流场对飞行器影响的近似分析方法和相应的计算机程序.这种点源分析方法考虑了排气气体和喷管的特性.通过计算发动机排气羽流场,计算排气羽流干扰力矩和推力损失,这些影响在飞行器设计中必须给予考虑和控制.利用该方法和计算机程序对一个卫星模型进行了羽流影响的计算.     

Combined Use of Altimetry and In Situ Gravity Data for Coastal Dynamics Studies

Accurate local geoids derived from in situ gravity data will be valuable in the validation of GOCE results. In addition it will be a challenge to use GOCE data in an optimal way, in combination with in situ gravity, to produce better local geoid solutions. This paper discusses the derivation of a new geoid over the NW European shelf, and its comparison with both tide gauge and altimetric sea level data, and with data from ocean models. It is hoped that over the next few years local geoid methods such as these can be extended to cover larger areas and to incorporate both in situ and satellite measured gravity data. This revised version was published online in August 2006 with corrections to the Cover Date.