Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lay in the equatorial plane (Sun or Jupiter for example) using a Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient J ₂ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect and the coefficient J ₃ determines a shift of the equilibria.     

High-order resonances in the restricted three-body problem

This paper consists in analyzing very simple resonance models for the j+i/j (i=2, 3, 4) resonance cases by averaging, truncating and scaling the restricted three body problem. The phase space, the equilibria, the critical areas and the probability of capture are analytically calculated for each case.     

A web of secondary resonances for large <Emphasis Type="Italic">A</Emphasis>/<Emphasis Type="Italic">m</Emphasis> geostationary debris

The dynamics of space debris with very high A/m near the geostationary orbit is dominated by the gravitational coefficient C ₂₂ and the solar radiation pressure. An analysis of the stability of the orbits by the chaos indicator MEGNO and frequency analysis map FAM shows chaotic layers around the separatrix and reveals a web of sub-structures associated to resonances with the annual period of the Sun. This succession of stable thin islands and chaotic layers can be reproduced and explained by a quite simple toy model, based on a pendulum approach, perturbed, through the eccentricity, by the external (Sun) frequency. The use of suitable action-angle variables in the circulation and libration regions of the pendulum allows to point out new resonances between the geostationary libration angle and the Sun’s longitude. They correspond very well (positions, shape, width) to the structures visible on the FAM representations.     

Planetary perturbations on Mercury’s libration in longitude

Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR.     

A mental picture of the greenhouse effect

The popular picture of the greenhouse effect emphasises the radiation transfer but fails to explain the observed climate change. An old conceptual model for the greenhouse effect is revisited and presented as a useful resource in climate change communication. It is validated against state-of-the-art data, and nontraditional diagnostics show a physically consistent picture. The earth’s climate is constrained by well-known and elementary physical principles, such as energy balance, flow, and conservation. Greenhouse gases affect the atmospheric optical depth for infrared radiation, and increased opacity implies higher altitude from which earth’s equivalent bulk heat loss takes place. Such an increase is seen in the reanalyses, and the outgoing long-wave radiation has become more diffuse over time, consistent with an increased influence of greenhouse gases on the vertical energy flow from the surface to the top of the atmosphere. The reanalyses further imply increases in the overturning in the troposphere, consistent with a constant and continuous vertical energy flow. The increased overturning can explain a slowdown in the global warming, and the association between these aspects can be interpreted as an entanglement between the greenhouse effect and the hydrological cycle, where reduced energy transfer associated with increased opacity is compensated by tropospheric overturning activity.     

A review of EU bio-economic models for fisheries: The value of a diversity of models

The lessons learned from a review of thirteen existing European bio-economic models used in the evaluation of EU policies are presented. How these models compare and differ in terms of their biological and economic components, the integration between the components, which indicators are selected and how they are used, are described and analysed. The article concludes that the multitude of construction differences reflects the necessity of adapting the modelling approach to answer different questions. Since real life questions in fisheries are so diverse, answering them requires a diversity of models.     

Water content and land use history controlling soil CO2 respiration and carbon stock in savanna soil and groundnut fields in semi-arid Senegal

Decomposition of soil organic carbon (SOC) regulates the partitioning between soil C-stock and release of CO₂ to the atmosphere and is vital for soil fertility. Agricultural expansion followed by decreasing amounts of SOC and soil fertility is a problem mainly seen in tropical agro-ecosystems where fertilizers are in short supply. This paper focuses on factors influencing temporal trends in soil respiration measured as CO₂ effluxes in grass savanna compared with groundnut (Arachis hypogaea L.) fields in the semi-arid part of Senegal in West Africa. Based on laboratory experiments, soil CO₂ production has been expressed as a function of temperature and soil water content by fit equations. Field measurements included soil CO₂ effluxes, soil temperatures and water contents. Effluxes in grass savanna and groundnut fields during the dry season were negligible, while effluxes during the rainy season were about 3–8 μmol CO₂ m^?2 s^?1, decreasing to less than 1 μmol by the end of the growing season. Annual soil CO₂ production was simulated to be in the range of 31–38 mol C m^?2. Furthermore, a controlled water addition experiment revealed the importance of rain during the dry season for the overall turnover of soil organic matter.     

Integrating lysimeter drainage and eddy covariance flux measurements in a groundwater recharge model

Abstract

Field-scale water balance is difficult to characterize because controls exerted by soils and vegetation are mostly inferred from local-scale measurements with relatively small support volumes. Eddy covariance flux and lysimeters have been used to infer and evaluate field-scale water balances because they have larger footprint areas than local soil moisture measurements. This study quantifies heterogeneity of soil deep drainage (D) in four 12.5-m² repacked lysimeters, compares evapotranspiration from eddy covariance (ET_EC) and mass balance residuals of lysimeters (ETwb_Lys), and models D to estimate groundwater recharge. Variation in measured D was attributed to redirection of snowmelt infiltration and differences in lysimeter hydraulic properties caused by surface soil treatment. During the growing seasons of 2010, 2011 and 2012, ETwb_Lys (278, 289 and 269 mm, respectively) was in good agreement with ET_EC (298, 301 and 335 mm). Annual recharge estimated from modelled D was 486, 624 and 613 mm for three calendar years 2010, 2011 and 2012, respectively. In summary, lysimeter D and ET_EC can be integrated to estimate and model groundwater recharge.

Editor D. Koutsoyiannis