On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.     

A low-dimensional subsurface model for saturated and unsaturated flow processes: ability to address heterogeneity

A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes.     

GETEMME—a mission to explore the Martian satellites and the fundamentals of solar system physics

GETEMME (Gravity, Einstein??s Theory, and Exploration of the Martian Moons?? Environment), a mission which is being proposed in ESA??s Cosmic Vision program, shall be launched for Mars on a Soyuz Fregat in 2020. The spacecraft will initially rendezvous with Phobos and Deimos in order to carry out a comprehensive mapping and characterization of the two satellites and to deploy passive Laser retro-reflectors on their surfaces. In the second stage of the mission, the spacecraft will be transferred into a lower 1500-km Mars orbit, to carry out routine Laser range measurements to the reflectors on Phobos and Deimos. Also, asynchronous two-way Laser ranging measurements between the spacecraft and stations of the ILRS (International Laser Ranging Service) on Earth are foreseen. An onboard accelerometer will ensure a high accuracy for the spacecraft orbit determination. The inversion of all range and accelerometer data will allow us to determine or improve dramatically on a host of dynamic parameters of the Martian satellite system. From the complex motion and rotation of Phobos and Deimos we will obtain clues on internal structures and the origins of the satellites. Also, crucial data on the time-varying gravity field of Mars related to climate variation and internal structure will be obtained. Ranging measurements will also be essential to improve on several parameters in fundamental physics, such as the Post-Newtonian parameter ?? as well as time-rate changes of the gravitational constant and the Lense-Thirring effect. Measurements by GETEMME will firmly embed Mars and its satellites into the Solar System reference frame.     

Multiscale approach to geo‐composite cellular structures subjected to rock impacts

Geo‐composite cellular structures are an efficient technological solution for various applications in civil engineering. This type of structure is particularly well adapted to resisting rockfalls and can act as a defensive structure. However, the design of such structures is for the most part empirically based; this lack of research‐based design stagnates optimization and advanced development. In this paper, the mechanical behaviour of a geo‐composite cellular structure is investigated using a multi‐scale approach, from the individual cell made up of an assembly of rocky particles contained in a wire netting cage to the entire structure composed of a regular array of cells. Based on discrete modelling of both the cell and structure scales, a computational tool has been developed for design purposes. Copyright © 2007 John Wiley & Sons, Ltd.     

Calibrating a glaciological model of the Greenland ice sheet from the Last Glacial Maximum to present-day using field observations of relative sea level and ice extent

We constrain a three-dimensional thermomechanical model of Greenland ice sheet (GrIS) evolution from the Last Glacial Maximum (LGM, 21 ka BP) to the present-day using, primarily, observations of relative sea level (RSL) as well as field data on past ice extent. Our new model (Huy2) fits a majority of the observations and is characterised by a number of key features: (i) the ice sheet had an excess volume (relative to present) of 4.1 m ice-equivalent sea level at the LGM, which increased to reach a maximum value of 4.6 m at 16.5 ka BP; (ii) retreat from the continental shelf was not continuous around the entire margin, as there was a Younger Dryas readvance in some areas. The final episode of marine retreat was rapid and relatively late (c. 12 ka BP), leaving the ice sheet land based by 10 ka BP; (iii) in response to the Holocene Thermal Maximum (HTM) the ice margin retreated behind its present-day position by up to 80 km in the southwest, 20 km in the south and 80 km in a small area of the northeast. As a result of this retreat the modelled ice sheet reaches a minimum extent between 5 and 4 ka BP, which corresponds to a deficit volume (relative to present) of 0.17 m ice-equivalent sea level. Our results suggest that remaining discrepancies between the model and the observations are likely associated with non-Greenland ice load, differences between modelled and observed present-day ice elevation around the margin, lateral variations in Earth structure and/or the pattern of ice margin retreat.     

Alteration geochemistry of the Nopal I uranium deposit (Sierra Peña Blanca,Mexico), a natural analogue for a radioactive waste repository in volcanic tuffs

Natural analogues provide an approach to characterize and test the long‐term modelling of a repository performance. This article presents geochemical information about the alteration conditions of the Nopal I uranium deposit, Mexico, an analogue for the proposed Yucca Mountain radioactive waste repository. Mineralization and hydrothermal alteration of volcanic tuffs are contemporaneous, according to petrographic observations. Trace element geochemistry (U, Th, REE) provides evidence for local mobilization of uranium under oxidizing conditions and further precipitation under reducing conditions. O‐ and H‐isotope geochemistry of kaolinite, smectite, opal and calcite suggests that argillic alteration proceeded at shallow depth with meteoric water at 25–75 °C, a low‐temperature context, unusual for volcanic‐hosted uranium deposits. This temperature range is compatible with some post‐closure evolution models of the proposed Yucca Mountain repository.     

Biogenic carbon flows through the planktonic food web of the Amundsen Gulf (Arctic Ocean): A synthesis of field measurements and inverse modeling analyses

Major pathways of biogenic carbon (C) flow are resolved for the planktonic food web of the flaw lead polynya system of the Amundsen Gulf (southeast Beaufort Sea, Arctic Ocean) in spring-summer 2008. This period was relevant to study the effect of climate change on Arctic marine ecosystems as it was characterized by unusually low ice cover and warm sea surface temperature. Our synthesis relied on a mass balance estimate of gross primary production (GPP) of 52.5 ± 12.5 g C m⁻² calculated using the drawdown of nitrate and dissolved inorganic C, and a seasonal f-ratio of 0.64. Based on chlorophyll a biomass, we estimated that GPP was dominated by phytoplankton (93.6%) over ice algae (6.4%) and by large cells (>5 μm, 67.6%) over small cells (<5 μm, 32.4%). Ancillary in situ data on bacterial production, zooplankton biomass and respiration, herbivory, bacterivory, vertical particle fluxes, pools of particulate and dissolved organic carbon (POC, DOC), net community production (NCP), as well as selected variables from the literature were used to evaluate the fate of size-fractionated GPP in the ecosystem. The structure and functioning of the planktonic food web was elucidated through inverse analysis using the mean GPP and the 95% confidence limits of every other field measurement as lower and upper constraints. The model computed a net primary production of 49.2 g C m⁻², which was directly channeled toward dominant calanoid copepods (i.e. Calanus hyperboreus 20%, Calanus glacialis 10%, and Metridia longa 10%), other mesozooplankton (12%), microzooplankton (14%), detrital POC (18%), and DOC (16%). Bacteria required 29.9 g C m⁻², a demand met entirely by the DOC derived from local biological activities. The ultimate C outflow comprised respiration fluxes (82% of the initial GPP), a small sedimentation (3%), and a modest residual C flow (15%) resulting from NCP, dilution and accumulation. The sinking C flux at the model limit depth (395 m) supplied 60% of the estimated benthic C demand (2.8 g C m⁻²), suggesting that the benthos relied partly on other C sources within the bottom boundary layer to fuel its activity. In summary, our results illustrate that the ongoing decline in Arctic sea ice promotes the growth of pelagic communities in the Amundsen Gulf, which benefited from a ∼80% increase in GPP in spring-summer 2008 when compared to 2004 – a year of average ice conditions and relatively low GPP. However, 53% of the secondary production was generated within the microbial food web, the net ecological efficiency of zooplankton populations was not particularly high (13.4%), and the quantity of biogenic C available for trophic export remained low (6.6 g C m⁻²). Hence it is unlikely that the increase in lower food web productivity, such as the one observed in our study, could support new harvestable fishery resources in the offshore Beaufort Sea domain.