Velocity-space maps and transforms of tracking observations for orbital trajectory state analysis

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies.     

A coordinated effort for observations and theories of the natural satellites

It was recognized over a year ago that a requirement to improve the ephemerides of the natural satellites existed and that it might be satisfied by a coordinated effort. Both the national ephemeris offices, which publish the satellite ephemerides, and NASA, which plans to send spacecraft to observe the satellites, require improved ephemerides of the natural satellites, but individually none of the organizations has the personnel or finances to undertake the task alone. At that time a few people and institutions had become interested in or were beginning to work on the theories and to make observations of the satellites. It was apparent that if the efforts of the various people and institutions were coordinated and others were encouraged to contribute, it might be possible in the next five years to satisfy the requirement for improved ephemerides. The coordinated effort includes personnel from the University of Texas, Smithsonian Astrophysical Center, University of Cincinnati, Bureau des Longitudes, Jet Propulsion Laboratory, University of Virginia, Vanderbilt University, Lowell Observatory, NASA Headquarters, and the U.S. Naval Observatory, with the latter institution serving as the coordinator.     

Relationship of intertidal surface sediment chlorophyll concentration to hyperspectral reflectance and chlorophyll fluorescence

Estimating biomass of microphytobenthos (MPB) on intertidal mud flats is extremely difficult due to their patchy occurrence, especially at the scale of an entire mud flat. We tested two optical approaches that can be applied in situ: spectral reflectance and chlorophyll fluorescence. These two approaches were applied in 4 European estuaries with different sediment characteristics. At each site, paired replicate measurements of hyperspectral reflectance, chlorophyll fluorescence (after 15 min dark adaptation, F_o ¹⁵), sediment water content, and chlorophylla concentrations were taken (including breakdown products: [chla+phaeo]). Sediments were further characterized by grain size and organic content analysis. The spectral signatures of tidal flats dominated by benthic microalgae, mainly diatoms, could be easily distinguished from sites dominated by macrophytes; we present a 3 waveband algorithm that can be used to detect the presence of macrophytes. The normalized difference vegetation index (NDVI) was found to be most strongly correlated to sediment [chla+phaeo], except for the predominantly sandy Sylt stations. F_o ¹⁵ was also significantly correlated to sediment [chla+phaeo] in all but one grid (Sylt grid A). Our results suggest that the functional relationships (i.e., the slopes) between NDVI or fluorescence and [chla+ phaeo] were not significantly different in the muddier grids, although the intercepts could differ significantly, especially for F_o ¹⁵. This suggests a mismatch of the optical depth seen by the reflectometer or fluorometer and the depth sampled for pigment analysis. NDVI appears to be a robust proxy for sediment [chla+phaeo] and can be used to quantify MPB biomass in muddy sediments of mid latitude estuaries.     

Temperature and its control of isotope fractionation by a sulfate-reducing bacterium

A synthesis of previous results, which we dub the “standard model,” provides a prediction as to how isotope fractionation during sulfate reduction should respond to physiological variables such as specific rate of sulfate reduction and environmental variables such as substrate availability and temperature. The standard model suggests that isotope fractionation should decrease with increasing specific rates of sulfate reduction (rate per cell). Furthermore, the standard model predicts that low fractionations should be found at both high and low temperatures whereas the highest fractionations should be found in the intermediate temperature range. These fractionation trends are controlled, as a function of temperature, by the balance between the transfer rates of sulfate into and out of the cell and the exchange between the sulfur pools internal to the organism. We test this standard model by conducting experiments on the growth physiology and isotope fractionation, as a function of temperature, by the sulfate-reducing bacterium Desulfovibrio desulfuricans (DSMZ 642). Our results contrast with the “standard model” by showing a positive correlation between specific rates of sulfate reduction and fractionation. Also by contrast with the standard model, we found the highest fractionations at low and high temperatures and the lowest fractionations in the intermediate temperature range. We develop a fractionation model which can be used to explain both our results as well as the results of the “standard model.” Differences in fractionation with temperature relate to differences in the specific temperature response of internal enzyme kinetics as well as the exchange rates of sulfate in and out of the cell. It is expected that the kinetics of these processes will show strain-specific differences.     

The role of prokaryotes in subsurface weathering of hydrothermal sediments: A combined geochemical and microbiological investigation

A detailed geochemical and microbiological study of a ∼2 m sediment core from the inactive Alvin mounds within the TAG hydrothermal field was conducted to examine, for the first time, the role of prokaryotes in subsurface weathering of hydrothermal sediments. Results show that there has been substantial post-depositional remobilisation of metal species and diagenetic overprinting of the original high-temperature hydrothermal minerals, and aspects have involved prokaryotic processes. Prokaryotic enumeration demonstrates the presence of a population smaller than the average for deep sea sediments, probably due to the low organic carbon content, but not inhibited by (and hence adapted to) the metal rich environment. There was a small but significant increase in population size associated with the active redox boundary in an upper metal sulphide layer (50-70 cm) around which active metal remobilisation was concentrated (Cu, Au, Cd, Ag, U, Zn and Zn). Hence, subsurface prokaryotes were potentially obtaining energy from metal metabolism in this near surface zone. Close association of numbers of culturable Mn and Fe reducing prokaryotes with subsurface Fe²⁺ and Mn²⁺ pore water profiles suggested active prokaryotic metal reduction at depth in core CD102/43 (to ∼175 cm). In addition, a prokaryotic mechanism, which is associated with bacterial sulphate reduction, is invoked to explain the U enrichment on pyrite surfaces and Zn and Pb remobilisation in the upper sediment. Although prokaryotic populations are present throughout this metalliferous sediment, thermodynamic calculations indicated that the inferred low pH of pore waters and the suboxic/anoxic conditions limits the potential energy available from Fe(II) oxidation, which may restrict prokaryotic chemolithotrophic biomass. This suggests that intense prokaryotic Fe oxidation and weathering of seafloor massive sulphide deposits may be restricted to the upper portion of the deposit that is influenced by near neutral pH and oxic seawater unless there is significant subsurface fluid flow.     

Kinetics of arsenopyrite oxidative dissolution by oxygen

We used a mixed flow reactor system to determine the rate and infer a mechanism for arsenopyrite (FeAsS) oxidation by dissolved oxygen (DO) at 25 °C and circumneutral pH. Results indicate that under circumneutral pH (6.3-6.7), the rate of arsenopyrite oxidation, 10^{−10.14±0.03} mol m⁻² s⁻¹, is essentially independent of DO over the geologically significant range of 0.3-17 mg L⁻¹. Arsenic and sulfur are released from arsenopyrite in an approximate 1:1 molar ratio, suggesting that oxidative dissolution by oxygen under circumneutral pH is congruent. Slower rates of iron release from the reactor indicate that some of the iron is lost from the effluent by oxidation to Fe(III) which subsequently hydrolyzes and precipitates. Using the electrochemical cell model for understanding sulfide oxidation, our results suggest that the rate-determining step in arsenopyrite oxidation is the reduction of water at the anodic site rather than the transfer of electrons from the cathodic site to oxygen as has been suggested for other sulfide minerals such as pyrite.     

Diffusion induced Li isotopic fractionation during the cooling of magmatic rocks: The case of pyroxene phenocrysts from nakhlite meteorites

Ion-microprobe was used to measure Li abundances and isotopic compositions in pyroxenes from three Martian meteorites belonging to the nakhlite family. The profiles performed across augite crystals from Northwest Africa 817 show a large isotopic zoning from crystal cores (δ⁷Li ∼ 0‰) to rims (δ⁷Li ∼ +20‰) while Li abundances are almost constant (∼9.2 μg/g). Unlike NWA 817, the pyroxene studied in the Miller Range 03346 nakhlite shows a zoning in Li abundance, with concentrations increasing from ∼2.5 μg/g in the core to ∼9 μg/g in the rim. The augite rim (δ⁷Li = +7‰) is slightly enriched in ⁷Li with regard to the core (δ⁷Li = +4‰), but most of the isotopic variations observed occur at an intermediate position along the profile, where δ⁷Li falls down to ∼−11‰. In the case of Nakhla, Li concentrations in augite increase from cores (∼3.5 μg/g) to rims (∼6.5 μg/g), while the δ⁷Li variation is restricted (i.e., between δ⁷Li = +6.0 and +12.6‰). For the three meteorites the Li abundances were also measured in the groundmass, which was found to be enriched in lithium (∼10 μg/g). Conventional magmatic and post-magmatic processes such as alteration and fractional crystallization, fail to explain the dataset obtained on nakhlites. Degassing processes, which were previously proposed to explain the Li distribution in shergottite crystals, cannot result in the strong decoupling between Li abundances and isotopic composition observed in nakhlites. We suggest that the original magmatic Li distributions (concentrations and isotopic compositions) in nakhlites have been modified by diffusion of Li from the Li-rich groundmass towards the pyroxene crystals during sub-solidus cooling. Diffusion appears to have been efficient for NWA 817 and MIL 03346 but, apparently, did not produce a significant migration of Li in Nakhla, possibly because of the lower abundance of groundmass in the latter. Diffusion induced Li redistributions may also affect terrestrial porphyric rocks but very specific cooling rates are required to quench the diffusion profiles as observed in two of the present nakhlites.