Note on Mercury’s rotation: the four equilibria of the Hamiltonian model

Mercury is observed in a stable Cassini’s state, close to a 3:2 spin-orbit resonance, and a 1:1 node resonance. This present situation is not the only possible mathematical stable state, as it is shown here through a simple model limited to the second-order in harmonics and where Mercury is considered as a rigid body. In this framework, using a Hamiltonian formalism, four different sets of resonant angles are computed from the differential Hamiltonian equations, and each of them corresponds to four values of the obliquity; thanks to the calculation of the corresponding eigenvalues, their linear stability is analyzed. In this simplified model, two equilibria (one of which corresponding to the present state of Mercury) are stable, one is unstable, and the fourth one is degenerate. This degenerate status disappears with the introduction of the orbit (node and pericenter) precessions. The influence of these precession rates on the proper frequencies of the rotation is also analyzed and quantified, for different planetary models.     

Martian perched craters and large ejecta volume: Evidence for episodes of deflation in the northern lowlands

Abstract— The northern lowland plains, such as those found in Acidalia and Utopia Planitia, have high percentages of impact craters with fluidized ejecta. In both regions, the analysis of crater geometry from Mars Orbiter Laser Altimeter (MOLA) data has revealed large ejecta volumes, some exceeding the volume of excavation. Moreover, some of the crater cavities and fluidized ejecta blankets of these craters are topographically perched above the surrounding plains. These perched craters are concentrated between 40 and 70°N in the northern plains. The atypical high volumes of the ejecta and the perched craters suggest that the northern lowlands have experienced one or more episodes of resurfacing that involved deposition and erosion. The removal of material, most likely caused by the sublimation of ice in the materials and their subsequent erosion and transport by the wind, is more rapid on the plains than on the ejecta blankets. The thermal inertia difference between the ejecta and the surrounding plains suggests that ejecta, characterized by a lower thermal inertia, protect the underneath terrain from sublimation. This results in a decreased elevation of the plains relative to the ejecta blankets. Sublimation and eolian erosion can be particularly high during periods of high obliquity.     

Optical constants of Titan’s stratospheric aerosols in the 70–1500 cm−1 spectral range constrained by Cassini/CIRS observations

We utilized aerosol extinction coefficient inferred from Cassini/CIRS spectra in the far and mid infrared region to derive the extinction cross-section near an altitude of 190 km at 15°S (from far-IR) and 20°S (from mid-IR). By comparing the extinction cross section that are derived from observations with theoretical calculations for a fractal aggregate of 3000 monomers, each having a radius of 0.05 μm, and a fractal dimension of 2, we are able to constrain the refractive index of Titan’s aerosol between 70 and 1500 cm^?1 (143 and 6.7 μm). As the real and imaginary parts of the refractive index are related by the Kramers–Kronig equation, we apply an iterative process to determine the optical constants in the thermal infrared. The resulting spectral dependence of the imaginary index displays several spectral signatures, some of which are also seen for some Titan’s aerosol analogues (tholins) produced in laboratory experiments. We find that Titan’s aerosols are less absorbent than tholins in the thermal infrared. The most prominent emission bands observed in the mid-infrared are due to CH bending vibrations in methyl and methylene groups. It appears that Titan’s aerosols predominantly display vibrations implying carbon and hydrogen atoms and perhaps marginally nitrogen. In the mid infrared, all the aerosol spectral signatures are observed at three additional latitudes (56°S, 5°N and 30°N) and in the 193–274 km altitude range, which implies that Titan’s aerosols exhibit the same chemical composition in all investigated latitude and altitude regions.     

Co‐seismic deformation and post‐glacial slip rate along the Magallanes‐Fagnano fault,Tierra Del Fuego,Argentina

Across the extreme south of Patagonia, the Magallanes‐Fagnano Fault (MFF) accommodates the left‐lateral relative motion between South America and Scotia plates. In this paper, we present an updated view of the geometry of the eastern portion of the MFF outcropping in Tierra del Fuego. We subdivide the MFF in eight segments on the basis of their deformation styles, using field mapping and interpretation of high‐resolution imagery. We quantify coseismic ruptures of the strongest recorded 1949, M_w7.5 earthquake, and determine its eastern termination. We recognize several co‐seismic offsets in man‐made features showing a sinistral shift up to 6.5 m, greater than previously estimated. Using ¹⁰Be cosmogenic nuclides depth profiles, we date a cumulated offset in post‐glacial morphologies and estimate the long‐term slip rate of the eastern MFF. We quantify a 6.4 ± 0.9 mm/a left‐lateral fault slip rate, which overlaps geodetic velocity and suggests stable fault behaviour since Pleistocene.     

Planetary long periodic terms in Mercury’s rotation: a two dimensional adiabatic approach

The averaged spin-orbit resonant motion of Mercury is considered, with e the orbital eccentricity, and i _o the orbital inclination introduced as very slow functions of time, given by any secular planetary theory. The basis is our Hamiltonian approach (D’Hoedt, S., Lemaître, A.: Celest. Mech. Dyn. Astron. 89:267–283, 2004) in which Mercury is considered as a rigid body. The model is based on two degrees of freedom; the first one is linked to the 3:2 resonant spin-orbit motion, and the second one to the commensurability of the rotational and orbital nodes. Mercury is assumed to be very close to the Cassini equilibrium of the model. To follow the motion of rotation close to this equilibrium, which varies with respect to time through e and i _o , we use the adiabatic invariant theory, extended to two degrees of freedom. We calculate the corrections (remaining functions) introduced by the time dependence of e and i _o in the three steps necessary to characterize the frequencies at the equilibrium. The conclusion is that Mercury follows the Cassini equilibrium (stays in the Cassini forced state), in an adiabatic behavior: the area around the equilibrium does not change by more than ${\varepsilon}$ for times smaller than ${\frac{1}{\varepsilon}}$ . The role of the inclination and the eccentricity can be dissociated and measured in each step of the canonical transformation.     

Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal mission: I. Hydrocarbons, nitriles and CO2 vertical mixing ratio profiles

Observations of the Composite InfraRed Spectrometer (CIRS) during the entire nominal Cassini mission (2004-2008) provide us with an accurate global view of composition and temperature in the middle atmosphere of Titan (between 100 and 500 km). We investigated limb spectra acquired at resolution at nine different latitudes between 56°S and 80°N, with a better sampling in the northern hemisphere where molecular abundances and temperature present strong latitudinal variations. From this limb data acquired between February 2005 and May 2008, we retrieved the vertical mixing ratio profiles of C₂H₂, C₂H₄, C₂H₆, C₃H₈, CH₃C₂H, C₄H₂, C₆H₆, HCN, HC₃N and CO₂. We present here for the first time, the latitudinal variations of the C₂H₆, C₃H₈, CO₂, C₂H₄ and C₆H₆ vertical mixing ratios profiles. Some molecules, such as C₂H₆ or C₃H₈ present little variations above their condensation level. The other molecules (except CO₂) show a significant enhancement of their mixing ratios poleward of 50°N. C₂H₄ is the only molecule whose mixing ratio decreases with height at latitudes below 46°N. Regions depleted in C₂H₂, HCN and C₄H₂ are observed around 400 km (0.01 mbar) and 55°N. We also inferred a region enriched in CO₂ located between 30 and 40°N in the 2-0.7 mbar pressure range. At 80°N, almost all molecules studied here present a local minimum of their mixing ratio profiles near 300 km (∼0.07 mbar), which is in contradiction with Global Circulation Models that predict constant-with-height vertical profiles due to subsidence at the north pole.     

The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model

The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant, the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational) on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained by Rambaux and Bois [Astron. Astrophys. 413, 381–393]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mechanisms and Model Diversity of Trade-Wind Shallow Cumulus Cloud Feedbacks: A Review

Shallow cumulus clouds in the trade-wind regions are at the heart of the long standing uncertainty in climate sensitivity estimates. In current climate models, cloud feedbacks are strongly influenced by cloud-base cloud amount in the trades. Therefore, understanding the key factors controlling cloudiness near cloud-base in shallow convective regimes has emerged as an important topic of investigation. We review physical understanding of these key controlling factors and discuss the value of the different approaches that have been developed so far, based on global and high-resolution model experimentations and process-oriented analyses across a range of models and for observations. The trade-wind cloud feedbacks appear to depend on two important aspects: (1) how cloudiness near cloud-base is controlled by the local interplay between turbulent, convective and radiative processes; (2) how these processes interact with their surrounding environment and are influenced by mesoscale organization. Our synthesis of studies that have explored these aspects suggests that the large diversity of model responses is related to fundamental differences in how the processes controlling trade cumulus operate in models, notably, whether they are parameterized or resolved. In models with parameterized convection, cloudiness near cloud-base is very sensitive to the vigor of convective mixing in response to changes in environmental conditions. This is in contrast with results from high-resolution models, which suggest that cloudiness near cloud-base is nearly invariant with warming and independent of large-scale environmental changes. Uncertainties are difficult to narrow using current observations, as the trade cumulus variability and its relation to large-scale environmental factors strongly depend on the time and/or spatial scales at which the mechanisms are evaluated. New opportunities for testing physical understanding of the factors controlling shallow cumulus cloud responses using observations and high-resolution modeling on large domains are discussed.     

A secondary resonance in Mercury’s rotation

The resonant rotation of Mercury can be modelised by a kernel model on which we can add perturbations. Our kernel model is a two-degree of freedom one written in Hamiltonian formalism. For this kernel, we consider that Mercury is solid and rotates on a Keplerian orbit. By introducing the perturbations due to the other planets of the Solar System, it appears that, in a particular case, our slow degree of freedom may enter into a 1:1 resonance with the Great Inequality of Jupiter and Saturn. Actually, as the moments of inertia of Mercury are still poorly known, this phenomenon cannot be excluded.