The eccentric case of a fast-rotating,gravity-gradient-perturbed satellite attitude solution

A closed-form first-order perturbation solution for the attitude evolution of a triaxial space object in an elliptical orbit is presented. The solution, derived using the Lie–Deprit method, takes into account gravity-gradient torque and is facilitated by an assumption of fast rotation of the object. The formulation builds on the earlier implementation of Lara and Ferrer, which assumes a circular orbit. The previously presented work—which assumes spin about an object’s axis of maximum inertia—is further extended by the explicit presentation of the transformations required to apply the solution to an object spinning about its axis of minimum inertia. Additionally, several numerical analyses are presented to more completely assess the utility of the solution. These studies (1) validate the elliptical solution, (2) assess the impact of varying the small parameter of the perturbation procedure, (3) analyze the assumption of fast rotation, and (4) apply the solution to the common and important scenario of a tumbling rocket body.     

A satellite relative motion model including $$J_2$$ and $$J_3$$J3 via Vinti’s intermediary

Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.     

Fe and O isotope composition of meteorite fusion crusts: Possible natural analogues to chondrule formation?

Meteorite fusion crust formation is a brief event in a high‐temperature (2000–12,000 K) and high‐pressure (2–5 MPa) regime. We studied fusion crusts and bulk samples of 10 ordinary chondrite falls and 10 ordinary chondrite finds. The fusion crusts show a typical layering and most contain vesicles. All fusion crusts are enriched in heavy Fe isotopes, with δ⁵⁶Fe values up to +0.35‰ relative to the solar system mean. On average, the δ⁵⁶Fe of fusion crusts from finds is +0.23‰, which is 0.08‰ higher than the average from falls (+0.15‰). Higher δ⁵⁶Fe in fusion crusts of finds correlate with bulk chondrite enrichments in mobile elements such as Ba and Sr. The δ⁵⁶Fe signature of meteorite fusion crusts was produced by two processes (1) evaporation during atmospheric entry and (2) terrestrial weathering. Fusion crusts have either the same or higher δ¹⁸O (0.9–1.5‰) than their host chondrites, and the same is true for Δ¹⁷O. The differences in bulk chondrite and fusion crust oxygen isotope composition are explained by exchange of oxygen between the molten surface of the meteorites with the atmosphere and weathering. Meteorite fusion crust formation is qualitatively similar to conditions of chondrule formation. Therefore, fusion crusts may, at least to some extent, serve as a natural analogue to chondrule formation processes. Meteorite fusion crust and chondrules exhibit a similar extent of Fe isotope fractionation, supporting the idea that the Fe isotope signature of chondrules was established in a high‐pressure environment that prevented large isotope fractionations. The exchange of O between a chondrule melt and an ¹⁶O‐poor nebula as the cause for the observed nonmass dependent O isotope compositions in chondrules is supported by the same process, although to a much lower extent, in meteorite fusion crusts.     

Drained cavity expansions in soils of finite radial extent subjected to two boundary conditions

The problem of drained cavity expansion in soils of finite radial extent is investigated. Cylindrical and spherical cavities expanded from zero radius subjected to either constant stress or zero displacement at the finite boundary are considered. The generalised analytical solution procedure presented enables more advanced constitutive models to be implemented than have been possible in previous studies. Results generated for Sydney quartz sand highlight substantial differences between cavity limit pressures for the two boundary conditions and for boundaries of finite and infinite radial extent. This is of significance in accounting for boundary effects when interpreting cone penetration tests conducted in calibration chambers. Copyright © 2011 John Wiley & Sons, Ltd.     

Jari: A pulp plantation in the Brazilian Amazon

Jari plantation is the largest pulp growing operation in the humid tropics, and occupies about 1000 sqkm previously covered by tropical forest. A study of five sites at Jari in 1980 indicated declining soil fertility, and low productivity of pulpwood. Low pulp production at Jari was caused by several factors, one of which appeared to be low soil fertility. The sams sites were re-evaluated in 1987. There was no discernable trend in either nutrients or productivity since 1980.Although productivity and nutrient stocks may have stabilized, low profitability caused by low pulp production resulted in the sale of Jari in 1982, for a $ 720 million loss. Despite growth rates at Jari which were too low to produce a profit on original investment, another plantation is planned for the eastern Amazon which is 10 times the size of Jari.     

Lightning fatalities in Australia, 1824–1991

Information on fatalities from lightning strikes has been extracted from a specially compiled database on natural hazards in Australia. Records dating from 1803–1991 indicate that at least 650 persons have been killed by lightning strikes. Maps and charts show the percentages of victims with respect to age, sex, locality, activity, and other circumstances of the strike. The majority of the 650 fatalities recorded have occurred along the more populous southeastern coast. The overall death rate, from 1910–1989, is 0.08 per 100 000 population. The annual number of lightning fatalities has decreased with time, from a death rate of 0.21 in 1910–1919 to 0.01 in 1980–1989. This trend is more pronounced when population figures are taken into account. The group that has been most at risk in Australia is that of males aged 15–19, followed by males aged 20–34. The male:female ratio of victims has decreased with time but is not approaching equality, being 11.6 in 1910–1919 and 5.3 in 1980–1989. The diurnal and monthly occurrences of lightning fatalities peak at 12.00–18.00 hours and November-February respectively. About 86% of fatalities have occurred outdoors and 14% have occurred indoors. Approximately three-fifths of fatalities have been work-related, and the group of workers that has traditionally been most at risk is that of land-workers. Approximately one-fifth of fatalities have been recreation-related, although this proportion has been increasing with time. The recreational activities of water sports, golf, and cricket have had the greatest number of lightning fatalities. Comparisons are made between these data and the results of other similar studies, both in Australia and overseas.     

Single-crystal x-ray diffraction of brucite to 14 GPa

Single-crystal brucite, Mg(OH)₂, was studied to 14 GPa in a quasi-hydrostatic pressure medium using a diamond anvil cell and energy-dispersive synchrotron x-ray diffraction. The parameters of a third-order Birch-Murnaghan equation of state fit to the data are: K _OT=42(2) GPa, and (?K _OT/?P)_T= 5.7(5). The bulk modulus is significantly lower than that obtained in recent shock compression and powder x-ray diffraction experiments under non-hydrostatic conditions. No evidence was found for a transition involving the Mg -O sub-structure over the pressure range of these experiments. This implies that the structural change previously identified at high pressure by Raman spectroscopy probably involves rearrangement of hydrogen atoms, leaving the Mg — O substructure largely unaffected.     

Comparison of intertidal habitat use and growth rates of two northern Puget Sound cohorts of 0+ age Dungeness crab,Cancer magister

Density, habitat use, and growth of intertidal 0+ age Dungeness crabs, Cancer magister, were examined at five northern Puget Sound (Washington, USA) sites between June 1984 and September 1987. Sampling was conducted biweekly during settlement, from June to September, and approximately monthly or bimonthly thereafter. Northern Puget Sound Dungeness crab populations appear to be largely supported by recruitment from inland parental stocks, but a smaller proportion of recruits originate from coastal or oceanic stocks, as evidenced by earlier settlement and larger size of the first instar. Settlement of Dungeness crabs in inland waters typically peaked in August, and interannual variation in year-class strength at settlement (measured as intertidal density) was low relative to that reported for coastal crab populations. Spatial and interannual differences in settlement densities were mediated by high postsettlement mortality, which varied inversely with habitat complexity. Seasonal densities were highest in mixed sand and gravel with an overstory of attached or drift macroalgae, intermediate in eelgrass (Zostera marina), and lowest on open sand. Postsettlement growth rates corresponded to seasonal water temperatures and were greatest for the coastal cohort that settled in May and June. This cohort was larger as first juvenile instars (7.2 mm carapace width, CW) and grew rapidly at summer temperatures in excess of 15°C to a size (>30 mm CW) that allowed emigration from intertidal to subtidal areas by September. The late summer cohort settled in August at 5.3 mm CW and soon after was subjected to decreasing autumn water temperatures. There crabs experienced little growth while over wintering in the intertidal, but growth rates increased in March, and the crabs emigrated in April and May, approximately 10 mo after settlement.     

Physical,chemical, and biological conditions associated with the early stages of the Lake Michigan vernal thermal front

An investigation of the thermal front in southeastern Lake Michigan during April 1988 revealed a dynamic physical, chemical, and biological environment. The front was observed approximately 4 km from the coast as a distinct gradient separating cold open-lake waters from warmer nearshore waters. Surface isotherms near the front were generally parallel to one another but skewed with respect to shore. Comparison between April 22 and 29 showed that the surface isothern pattern was modulated by wind stress. The pattern from April 29 showed signs of flow instabilities with horizontal scales of 1 km to 5 km. Surface drifter trajectories provided estimates of horizontal convergence at the fron which varied from 7×10^?6 s^?1 to 20×10^?6 s^?1. Inferred rates of downwelling, which ranged from 9.5 m d^?1 to 20.7 m d^?1, were sufficient to move a water parcel from the surface to the bottom in 2 to 6 d at the front. Convergent circulation was observed on both sampling dates despite contrasts in wind stress. Concentrations of chloride, soluble silica, and chlorophyll, which were always higher inshore, were 5% to 82% larger than offshore mean values. The aquatic environment just inshore of the thermal front was characterized by chlorphyll concentrations which exceeded 5.0 μg 1^?1 while concentrations offshore were between 1.0 μg 1^?1 and 2.0 μg 1^?1. A relatively uniform vertical structure in chlorophyll concentrations in the frontal zone was consistent with the observed convergence and inferred downwelling near the front.