Three-dimensional subsatellite motion under air drag and oblateness perturbations

The three-dimensional relative motion of a subsatellite with respect to a reference station in an elliptical orbit is studied. A general theory based on the variation of the relative elements, i.e. the instantaneous differences between the orbital parameters of the subsatellite and those of the station, is formulated in order to incorporate arbitrary perturbing forces acting on both satellites. The loss of precision inherent in the subtraction of almost identical quantities is avoided by the consistent use of difference variables. In the absence of perturbations exact analytical representations can be obtained for the relative state parameters. The influences of air drag and Earth's oblateness on the relative motion trajectories are investigated and illustrated graphically for a number of cases.     

A technique for modeling the Earth’s gravity field on the basis of satellite accelerations

A technique is proposed for Earths gravity field modeling on the basis of satellite accelerations that are derived from precise orbit data. The functional model rests on Newtons second law. The computational procedure is based on the pre-conditioned conjugate-gradient (PCCG) method. The data are treated as weighted average accelerations rather than as point-wise ones. As a result, a simple three-point numerical differentiation scheme can be used to derive them. Noise in the orbit-derived accelerations is strongly dependent on frequency. Therefore, the key element of the proposed technique is frequency-dependent data weighting. Fast convergence of the PCCG procedure is ensured by a block-diagonal pre-conditioner (approximation of the normal matrix), which is derived under the so-called Colombo assumptions. Both uninterrupted data sets and data with gaps can be handled. The developed technique is compared with other approaches: (1) the energy balance approach (based on the energy conservation law) and (2) the traditional approach (based on the integration of variational equations). Theoretical considerations, supported by a numerical study, show that the proposed technique is more accurate than the energy balance approach and leads to approximately the same results as the traditional one. The former finding is explained by the fact that the energy balance approach is only sensitive to the along-track force component. Information about the cross-track and the radial component of the gravitational potential gradient is lost because the corresponding force components do no work and do not contribute to the energy balance. Furthermore, it is shown that the proposed technique is much (possibly, orders of magnitude) faster than the traditional one because it does not require the computation of the normal matrix. Hints are given on how the proposed technique can be adapted to the explicit assembling of the normal matrix if the latter is needed for the computation of the model covariance matrix.Acknowledgments. Professor R. Klees is thanked for support of the project and for numerous fruitful discussions. The authors are also thankful to Dr. J. Kusche for useful remarks and to Dr. E. Schrama, his solid background in satellite geodesy proved to be very helpful. A large number of valuable comments were made by Dr. S.-C. Han, Dr. P. Schwintzer, and an anonymous reviewer; their contribution is greatly acknowledged. The satellite orbits used in the numerical study were kindly provided by Dr. P. Visser (Aerospace Department, Delft University of Technology). Access to the SGI Origin 3800 computer was provided by Stichting Nationale Computerfaciliteiten (NCF), grant SG-027.     

Post‐orogenic evolution of the southern Pyrenees: constraints from inverse thermo‐kinematic modelling of low‐temperature thermochronology data

The late‐stage evolution of the southern central Pyrenees has been well documented but controversies remain concerning potential Neogene acceleration of exhumation rates and the influence of tectonic and/or climatic processes. A popular model suggests that the Pyrenees and their southern foreland were buried below a thick succession of conglomerates during the Oligocene, when the basin was endorheic. However, both the amount of post‐orogenic fill and the timing of re‐excavation remain controversial. We address this question by revisiting extensive thermochronological datasets of the Axial Zone. We use an inverse approach that couples the thermo‐kinematic model Pecube and the Neighbourhood inversion algorithm to constrain the history of exhumation and topographic changes since 40 Ma. By comparison with independent geological data, we identified a most probable scenario involving rapid exhumation (>2.5 km Myr^?1) between 37 and 30 Ma followed by a strong decrease to very slow rates (0.02 km Myr^?1) that remain constant until the present. Therefore, the inversion does not require a previously inferred Pliocene acceleration in regional exhumation rates. A clear topographic signal emerges, however: the topography has to be infilled by conglomerates to an elevation of 2.6 km between 40 and 29 Ma and then to remain stable until ca. 9 Ma. We interpret the last stage of the topographic history as recording major incision of the southern Pyrenean wedge, due to the Ebro basin connection to the Mediterranean, well before previously suggested Messinian ages. These results thus demonstrate temporally varying controls of different processes on exhumation: rapid rock uplift in an active orogen during late Eocene, whereas base‐level changes in the foreland basin control the post‐orogenic evolution of topography and exhumation in the central Pyrenees. In contrast, climate changes appear to play a lesser role in the post‐orogenic topographic and erosional evolution of this mountain belt.     

Hyperspectral remote sensing of evaporate minerals and associated sediments in Lake Magadi area, Kenya

Pleistocene to present evaporitic lacustrine sediments in Lake Magadi, East African Rift Valley, Kenya were studied and mapped using spectral remote sensing methods. This approach incorporated surface mineral mapping using space-borne hyperspectral Hyperion imagery together with laboratory analysis, including visible, near-infrared diffuse reflectance spectroscopy (VNIR) measurements and X-ray diffraction for selected rock and soil samples of the study area. The spectral signatures of Magadiite and Kenyaite, which have not been previously reported, were established and the spectral signatures of trona, chert series, volcanic tuff and the High Magadi bed were also analyzed.Image processing techniques, MNF (Minimum Noise Fraction) and MTMF (Mixture Tuned Matched Filtering) using a stratified approach (image analysis with and without the lake area), were used to enhance the mapping of evaporates. High Magadi beds, chert series and volcanic tuff were identified from the Hyperion image with an overall mapping accuracy of 84.3%. Even though, the spatial distribution of evaporites and sediments in Lake Magadi area change in response to climate variations, the mineralogy of this area has not been mapped recently. The results of this study shows the usefulness of the hypersspectral remote sensing to map the surface geology of this kind of environment and to locate promising sites for industrial open-pit trona mining in a qualitative and quantitative manner.     

Spectral properties of simulated impact glasses produced from martian soil analogue JSC Mars-1

To simulate the formation of impact glasses on Mars, an analogue of martian bright soil (altered volcanic soil JSC Mars-1) was melted at relevant oxygen fugacities using a pulsed laser and a resistance furnace. Reduction of Fe³⁺ to Fe²⁺ and in some cases formation of nanophase Fe⁰ in the glasses were documented by Mössbauer spectroscopy and TEM studies. Reflectance spectra for several size fractions of the JSC Mars-1 sample and the glasses were acquired between 0.3 and 25 μm. The glasses produced from the JSC Mars-1 soil show significant spectral variability depending on the method of production and the cooling rate. In general, they are dark and less red in the visible compared to the original JSC Mars-1 soil. Their spectra do not have absorption bands due to bound water and structural OH, have positive spectral slopes in the near-infrared range, and show two broad bands centered near 1.05 and 1.9 μm, typical of glasses rich in ferrous iron. The latter bands and low albedo partly mimic the spectral properties of martian dark regions, and may easily be confused with mafic materials containing olivine and low-Ca pyroxene. Due to their disordered structures and vesicular textures, the glasses show relatively weak absorption features from the visible to the thermal infrared. These weak absorption bands may be masked by the stronger bands of mafic minerals. Positive near-infrared spectral slopes typical of fresh iron-bearing impact or volcanic glasses may be masked either by oxide/dust coatings or by aerosols in the Mars' atmosphere. As a result, impact glasses may be present on the surface of Mars in significant quantities that have been either misidentified as other phases or masked by phases with stronger infrared features. Spectrometers with sufficient spatial resolution and wavelength coverage may detect impact glasses at certain locations, e.g., in the vicinity of fresh impact craters. Such dark materials are usually interpreted as accumulations of mafic volcanic sand, but the possibility of an impact melt origin of such materials also should be considered. In addition, our data suggest that high contents of feldspars or zeolites are not necessary to produce the transparency feature at 12.1 μm typical of martian dust spectra.     

History of solar telescopes

Solar observations have been done with telescopes since their invention—already Galileo looked at the Sun. Despite the Sun’s unusual brightness, telescopes which specialize in solar observations are fairly recent, dating from the late nineteenth century onwards. Today, many solar telescopes have rather little in common with nighttime telescopes. They are adapted to high light flux, a limited range of declination, and to the specifications of solar spectrographs and polarimeters. This paper presents the history of the modern optical solar telescope on the ground and in space, the accompanying evolution of scientific capabilities, and a brief outlook into the future.     

Spatial geochemistry of a Carboniferous platform-margin-to-basin transect: Balancing environmental and diagenetic factors

Conventional (one-dimensional) chemostratigraphy of marine carbonates assesses the chemical archive of individual stratigraphic sections and their correlation in space and time. Whereas this approach has shown to be of value when linking isobathymetric domains, usually characterised by similar facies, more caution is needed when correlations are extended across different physiographic settings and hence different facies belts. Here, the spatial geochemical record of Pennsylvanian platform-margin-to-basin transects across a bathymetric range of about 800 m is documented and discussed in a process-oriented context. Particularly, the presence of layered palaeo-water masses and their potential control on slope facies distribution and geochemical properties requires attention. Whereas Carboniferous thermo- and/or chemo-clines most likely affected depth-related slope facies zonation, it was facies change and hence, variances in porosity–permeability properties, that controlled differential early burial diagenetic alteration. Specifically, the lower-slope related breccia facies is characterised by higher volumes of early burial carbonate cements. This implies that these sediments entered the shallow-burial domain with a considerable open pore space and gave way to an increased rock:fluid ratio. Whereas the δ¹³C record is invariant with bathymetry, the more diagenesis-sensitive δ¹⁸O proxy, records pronounced shifts observed across major facies boundaries. From this it is concluded that although the primary controlling factor of slope facies distribution with depth is probably palaeoceanographic in nature, it is differential rock:fluid ratios that control the first-order, spatial shifts in δ¹⁸O composition. These findings show that one-dimensional chemostratigraphy will severely underestimate the complexity of three-dimensional (bathymetric) data sets across platform margins. This is of relevance for the interpretation of the geochemical archive of fossil carbonate platforms in general.     

Dynamical and collisional evolution of Halley-type comets

The number of observed Halley-type comets is hundreds of times less than predicted by models (Levison, H.F., Dones, L., Duncan, M.J. [2001]. Astron. J. 121, 2253–2267). In this paper we investigate the impact of collisions with planetesimals on the evolution of Halley-type comets. First we compute the dynamical evolution of a sub-set of 21 comets using the Mercury integrator package over 100 Myr. The dynamical lifetime is determined to be of the order of 10⁵–10⁶ years in agreement with previous work. The collisional probability of Halley-type comets colliding with known asteroids, a simulated population of Kuiper-belt objects, and planets, is calculated using a modified, Öpik-based collision code. Our results show that the catastrophic disruption of the cometary nucleus has a very low probability of occurring, and disruption through cumulative minor impacts is concluded to be negligible. The dust mantle formed from ejected material falling back to the comet’s surface is calculated to be less than a few centimeters thick, which is insignificant compared to the mantle formed by volatile depletion, while planetary encounters were found to be a negligible disruption mechanism.     

Late Holocene flood magnitudes in the Lower Rhine river valley and upper delta resolved by a two-dimensional hydraulic modelling approach

Palaeoflood hydraulic modelling is essential for quantifying ‘millennial flood’ events not covered in the instrumental record. Palaeoflood modelling research has largely focused on one-dimensional analysis for geomorphologically stable fluvial settings because two-dimensional analysis for dynamic alluvial settings is time consuming and requires a detailed representation of the past landscape. In this study, we make the step to spatially continuous palaeoflood modelling for a large and dynamic lowland area. We applied advanced hydraulic model simulations (1D–2D coupled set-up in HEC-RAS with 950 channel sections and 108 × 10³ floodplain grid cells) to quantify the extent and magnitude of past floods in the Lower Rhine river valley and upper delta. As input, we used a high-resolution terrain reconstruction (palaeo-DEM) of the area in early mediaeval times, complemented with hydraulic roughness values. After conducting a series of model runs with increasing discharge magnitudes at the upstream boundary, we compared the simulated flood water levels with an inventory of exceeded and non-exceeded elevations extracted from various geological, archaeological and historical sources. This comparison demonstrated a Lower Rhine millennial flood magnitude of approximately 14,000 m³/s for the Late Holocene period before late mediaeval times. This value exceeds the largest measured discharges in the instrumental record, but not the design discharges currently accounted for in flood risk management.