Gravity gradient mapping from the lunar polar orbiter - a simulation study

Simulations of the gravity data to be expected from a Lunar Polar Orbiter spacecraft utilizing either a Doppler velocity tracking system or a gravity gradiometer instrument system are generated using a point mass model that gives an excellent representation of the types of gravity anomalies to be found on the Moon. If the state of the art in instrumentation of both systems remain at the level of ±1 mm/sec at 10 sec integration time for the Doppler velocity system accuracy and at ±1 Eotvos at 10 sec integration time for the gravity gradiometer system accuracy, inspection of the simulations indicates that a gravity gradiometer system will give science data with better resolution and higher amplitude-to-measurement noise ratio than the Doppler velocity system at altitudes below 100 km. The error model used in the study is one where the system errors are assumed to be dominated by the point measurement noise and data quantization noise. The effects of other, more controllable, systematic error sources are not considered in this simplified analysis. For example, both systems will be affected by errors in LPO orbital altitude and position knowledge, spacecraft maneuvers, and data reduction errors. In addition, a Doppler tracking system will be sensitive to errors produced by spacecraft acceleration (from outgassing or solar pressure) and poor relative position of the LPO, Relay Satellite and ground tracking station, while a gravity gradiometer system will be sensitive to errors from spacecraft attitude and angular rates. These preliminary study results now need to be verified by a more complete error analysis in which all the uncertainties of the data gathering process are formally mapped into uncertainties in the resulting gravity maps.     

Characterizing and navigating small bodies with imaging data

Abstract— Recent advances in the characterization of small body surfaces with stereophotoclinometry are discussed. The principal data output is an ensemble of landmark maps (L‐maps), high‐resolution topography/albedo maps of varying resolution that tile the surface of the body. Because they can have a resolution comparable to the best images, and can be located on a global reference frame to high accuracy, L‐maps provide a significant improvement in discriminatory power for studies of small bodies, ranging from regolith processes to interior structure. These techniques are now being used to map larger bodies such as the Moon and Mercury. L‐maps are combined to produce a standard global topography model (GTM) with about 1.57 million vectors and having a wide variety of applications. They can also be combined to produce high‐resolution topography maps that describe local areas with much greater detail than the GTM. When combined with nominal predictions from other data sources and available data from other instruments such as LIDAR or RADAR, solutions for the spacecraft position and camera pointing are the most accurate available. Examples are drawn from studies of Phobos, Eros, and Itokawa, including surface characterization, gravity analysis, spacecraft navigation, and incorporation of LIDAR or RADAR data. This work has important implications for potential future missions such as Deep Interior and the level of navigation and science that can be achieved.     

Direct conversion of los acceleration data to vertical gravity anomalies: A new approach

Most of the existing lunar and planetary gravity data are in the form of LOS (line-of-sight) components which cannot be used for conventional geophysical modelling. Current methods to invert LOS data yield non-unique or poorly constrained results or results of low spatial resolution. An alternate method presented here promises to produce unique, detailed and more reliable results. It utilizes the fact that three non-coplanar LOS acceleration vectors determined at different times at some point of observation uniquely define the total acceleration vector at that point. Vector analysis shows that the local cartesian componentsg _i of the total gravity anomaly vector may be obtained by inversion of the system $$a_{ij} g_j = A_i^2 $$ where thea _ij andA _i 's are, respectively, the local cartesian components and scalar magnitudes of the three required LOS acceleration vectors. In principle, the method is applicable to lunar as well as planetary LOS data.     

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.     

Venus gravity: Analysis of Beta Regio

Radio tracking data acquired over Beta Regio were analyzed to obtain a surface mass distribution from which a detailed vertical gravity field was derived. In addition, a corresponding vertical gravity field was evaluated solely from the topography of the Beta region. A comparison of these two maps confirms the strong correlation between gravity and topography which was previously seen in line-of-sight gravity maps. It also demonstrates that the observed gravity is a significant fraction of that predicted from the topography alone. The effective depth of complete isostatic compensation for the Beta region is estimated to be 330 km, which is somewhat deeper than that found for other areas of Venus.     

New analysis of Lunar Prospector radio tracking data brings the nearside gravity field of the Moon with an unprecedented resolution

A new analysis of the Doppler tracking data from the Lunar Prospector mission in 1999 revealed a number of previously-unseen gravity anomalies at spatial scales as small as 27 km over the nearside. The tracking data at low altitudes (50 km or below) were better analyzed to resolve the nearside features without dampening from a power law constraint, by partitioning the gravity parameters concentrated on either the nearside or farside. The resulting model presents gravity anomalies correlated with topography with a correlation coefficient of 0.7 or higher from degree 50 to 150, the widest bandwidth yet. The gravity-topography admittance of ∼70 mGal/km is found from numerous craters of which diameters are 60 km or less. In addition, the new model produces orbits that fit to independent radio tracking data from the Lunar Reconnaissance Orbiter and Kaguya (SELENE) better than previous gravity models. This high-resolution model can be of immediate use to geophysical analysis of small craters. Our technique could be applied to an upcoming mission, the Gravity Recovery And Interior Laboratory and useful to extract short wavelength signals from the MESSENGER Doppler data.     

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.     

High-Resolution Mapping of Flows in the Solar Interior: Fully Consistent OLA Inversion of Helioseismic Travel Times

To recover the flow information encoded in travel-time data of time?–?distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at horizontal spatial resolutions of 7?10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses.     

A lunar crustal gravity model across the Triesnecker-Hyginus area,Mare Tranquillitatis,and Mare Fecunditatis

LOS Bouguer gravity anomalies have been calculated from a low altitude LOS free air Doppler gravity profile across northern Mare Fecunditatis, southern Mare Tranquillitatis and the Aridaeus Rille. The Hyginus-Triesnecker area has been included in model calculations, though here only free air anomalies are present. A crustal density model has been fitted to the Bouguer anomalies and to the free air anomalies in the case of the Hyginus-Triesnecker area.On a regional scale northern Fecunditatis has Bouguer anomalies up to 80 mgal and lithostatic stresses of 29 bar and thus is nearly in isostatic equilibrium. Tranquillitatis can be divided into three regions of different crustal structure: (1) northern Tranquillitatis with only minor free air gravity anomalies is more or less in isostatic balance, (2) the southeastern region with Bouguer anomalies to –100 mgal and lithostatic stresses of –73 bar has a considerable mass deficit, (3) the southwestern basin is dominated by the local structure Lamont with a Bouguer maximum of 200 mgal and extremely high lithostatic stresses of 285 bar.The Bouguer minimum of –180 mgal of the Aridaeus area has been modelled by two alternative models: (i) a crustal thickening of 33 km and associated lithostatic stresses of –164 bar, and (ii) a crustal thickening of 20 km plus a low density intrusion. The free air maximum of the Hyginus-Triesnecker area has been fitted by a mantle plug connected with stresses of 116 bar.As the old irregular maria could not sustain large mascon stresses, it has been concluded that the local high stresses of Lamont, Aridaeus, and Hyginus-Triesnecker have been evolved after the impacts of the circular maria. Intrusional activities in these areas could have proceeded to fault zones generated by the large impacts.Contribution No. 211, Institut für Geophysik der Universität Kiel, F.R.G.     

Doppler Tomography of X‐ray binaries

The Space Telescope Imaging Spectrograph (STIS) on HST provides the first ultraviolet data that are of sufficient spectral and temporal resolution to generate Doppler tomograms of X‐ray binaries.We show both optical and ultraviolet maps constructed for the intermediate mass system Hercules X‐1/HZ Her and the massive wind‐fed system SMC X‐1/SK160. We have used the maps and corresponding lightcurves as diagnostics with which to test the validity of published models for Hercules X‐1. We find that although the models are mostly able to explain the light curves they are not consistent with the full phase maps. We present simulations of Doppler maps of X‐ray lines that will be possible with the spectral and temporal resolution and substantial effective area of the next major X‐ray mission, Con‐X. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tectonics of the southern escarpment of Ishtar Terra on venus from observations of morphology and gravity

Maxima of calculated topographical line-of-sight (LOS) gravity attractions caused by Ishtar Terra are shifted to the north with respect to the measured LOS free air gravity maxima south of the highland. This implies a tendency to isostatic compensation of central Ishtar and mass surpluses at the continental border and the southern forelands.The following scenario is compatible with the interpretation of the gravity anomalies and morphological features. Relative motions of the lowland Sedna Planitia against continental Ishtar Terra have caused buckling and flat subduction of the lowland lithospheric material. (Deep subduction can be ruled out by thermal reasons). The free air gravity high is modelled by surplus masses of the buckling and of the high density subducting plate. Evidence for this is given by several compressional features like Ut and Vesta Rupes at the southern continental border and ridges at the SW-flanks of Maxwell Montes. It is further supported by several possible volcanic-tectonic depressions located in the southern part of Ishtar. This local interpretation does not necessarily imply the existence of global plate tectonics on Venus like on Earth, but at least limited horizontal movements of the Venusian lithosphere seem to be likely. This result shows that plate recycling must be considered for heat transfer through the lithosphere beside conduction and hot spot volcanism.Contribution No. 273, Institut für Geophysik der Universität Kiel, F.R.G.     

Speckle spectro‐polarimetry of magnetic structures

Two‐dimensional spectrograms were obtained with the Vacuum Tower Telescope, Tenerife, in order to study small‐scale structures and faculae on the Sun. Using the speckle reconstruction method, we obtain high‐resolution images and wavelength scans. Magnetic fields can be studied from Stokes V profiles, and velocity maps are gained by the Doppler shift of the center of gravity of Stokes I. Here some results about small‐scale structures and their magnetic fields are shown.     

Lunar gravity derived from long-period satellite motion — A proposed method

A new method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate longpperiod Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the Earth, Sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are then ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.Pseudo Doppler data have been generated simulating two different lunar orbits. This analysis included the perturbing effects of the L1 lunar gravity field, the Earth, the Sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of this controlled experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.     

Apollo 15 gravity analysis from theS-band transponder experiment

TheS-Band Transponder experiment used precision doppler tracking data of the command and service module, the lunar module and the subsatellite to provide detailed information about the near side gravity field. No special instruments are required other than the existingS-Band transponder used for real time navigation. The data consists of variations in the spacecraft speed as measured by the earth-based radio tracking system, which has a resolution of 0.65 mm/s.Initial data reduction has been concentrated on the low altitude CSM data ( 20 km) which provides new detailed gravity profiles of the Serenitatis and Crisium mascons. The results are in good agreement with Apollo 14 analysis and strongly suggest that the mascons are near surface features with a mass distribution per unit area of approximately 800 kg/cm². The Apennines reveal themselves as a local gravity high of 85 mgal and Marius Hills likewise have a gravity high of 62 mgal.The subsatellite data is too sparse at present to definitely determine new gravity anomaly locations. The spacecraft is functioning well and a dense data block is being obtained, which will provide a new gravity map from ±95° longitude to ±30 latitude. Since periapsis altitudes are following relatively close to predicted altitudes, it seems fairly safe at this point to believe the subsatellite lifetime will be at least one year.     

Modeling and Interpreting the Effects of Spatial Resolution on Solar Magnetic Field Maps

Different methods for simulating the effects of spatial resolution on magnetic field maps are compared, including those commonly used for inter-instrument comparisons. The investigation first uses synthetic data, and the results are confirmed with Hinode/SpectroPolarimeter data. Four methods are examined, one which manipulates the Stokes spectra to simulate spatial-resolution degradation, and three “post-facto” methods where the magnetic field maps are manipulated directly. Throughout, statistical comparisons of the degraded maps with the originals serve to quantify the outcomes. Overall, we find that areas with inferred magnetic fill fractions close to unity may be insensitive to optical spatial resolution; areas of sub-unity fill fractions are very sensitive. Trends with worsening spatial resolution can include increased average field strength, lower total flux, and a field vector oriented closer to the line of sight. Further-derived quantities such as vertical current density show variations even in areas of high average magnetic fill fraction. In short, unresolved maps fail to represent the distribution of the underlying unresolved fields, and the “post-facto” methods generally do not reproduce the effects of a smaller telescope aperture. It is argued that selecting a method in order to reconcile disparate spatial resolution effects should depend on the goal, as one method may better preserve the field distribution, while another can reproduce spatial resolution degradation. The results presented should help direct future inter-instrument comparisons.     

Comparing the CO and HI Distributions in Nearby Spiral Galaxies at High Resolution

With wide-field CO maps of spiral galaxies at ～6′′resolution provided by the BIMA Survey of Nearby Galaxies (BIMA SONG),it is now feasible to compare the CO and HI distributions in disks onscales of ～1 kpc or less. The results of such a comparisonsuggest that, when azimuthally averaged, the ratio of CO to HIemission, and by implication the molecular-to-atomic gas ratio, isdetermined by the midplane interstellar pressure, with the ISMmetallicity as a secondary factor. A variety of observed phenomena,including the inhibition of molecular cloud and star formation in theouter disks of galaxies, can be understood in terms of thisdependence. We present recent data on the edge-on galaxy NGC 891 thatallow a comparison of the vertical distribution of CO and HI, and willtherefore provide an independent test of these ideas.     

Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration

Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, we extend this technique to mass points and mass discs in the gravity field. This required the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.     

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.     

On the Magnetic Field Orientation and Plasma Flows in Solar Filament Barbs

Speeds of vertical flows in quiescent solar filaments are typically much less than the local Alfvén speed. This is why the flows in filament barbs can be modeled by perturbing a magnetostatic solution describing a balance between the Lorentz force, gravity, and gas pressure in a barb. This approach explains why some of the flows are neither aligned with the magnetic field nor controlled by gravity. Both the observed upflows and the magnetic field dips in barbs are likely to be caused by photospheric magnetic reconnection.     

Jupiter's atmospheric temperatures: From Voyager IRIS to Cassini CIRS

Retrievals performed on Cassini Composite Infrared Spectrometer data obtained during the distant Jupiter flyby in 2000/2001 have been used to generate global temperature maps of the planet in the troposphere and stratosphere, but to higher latitudes than were shown previously by Flasar et al. [Flasar, F.M., 39 colleagues, 2004a. Nature 427, 132-135; Flasar, F.M., 44 colleagues, 2004b. Space Sci. Rev. 115, 169-297]. Similar retrievals were performed on Voyager 1 IRIS data to provide the first detailed IRIS map of the stratosphere, and high latitudes in the troposphere. Thermal winds were calculated for each data set and show strong vertical shears in the zonal winds at low latitudes, and meridional temperature gradients indicate the presence of circumpolar jets, as well. The temperatures retrieved from the two spacecraft were also compared with yearly ground-based data obtained over the intervening two decades. Tropospheric temperatures reveal gradual changes at low latitudes, with little obvious seasonal or short-term variation [Orton et al., 1994. Science 265, 625-631]. Stratospheric temperatures show much more complicated behavior over short timescales, consistent with quasi-quadrennial oscillations at low latitudes, as suggested in prior analyses of shorter intervals of ground-based data [Orton et al., 1991. Science 252, 537-542; Friedson, A.J., 1999. Icarus 137, 34-55]. A scaling analysis indicates that meridional motions, mechanically forced by wave or eddy convergence, play an important role in modulating the temperatures and winds in the upper troposphere and stratosphere on seasonal and shorter timescales. At latitudes away from the equator, the mechanical forcing can be derived simply from a temporal record of temperature and its vertical derivative. Ground-based observations with improved vertical resolution and/or long-term monitoring from spacecraft are required for this purpose, though the Voyager and Cassini data given indications that the magnitude of the forcing is very small.