Analytical method for perturbed frozen orbit around an asteroid in highly inhomogeneous gravitational fields: a first approach

This article provides a method for finding initial conditions for perturbed frozen orbits around inhomogeneous fast rotating asteroids. These orbits can be used as reference trajectories in missions that require close inspection of any rigid body. The generalized perturbative procedure followed exploits the analytical methods of relegation of the argument of node and Delaunay normalisation to arbitrary order. These analytical methods are extremely powerful but highly computational. The gravitational potential of the heterogeneous body is firstly stated, in polar-nodal coordinates, which takes into account the coefficients of the spherical harmonics up to an arbitrary order. Through the relegation of the argument of node and the Delaunay normalization, a series of canonical transformations of coordinates is found, which reduces the Hamiltonian describing the system to a integrable, two degrees of freedom Hamiltonian plus a truncated reminder of higher order. Setting eccentricity, argument of pericenter and inclination of the orbit of the truncated system to be constant, initial conditions are found, which evolve into frozen orbits for the truncated system. Using the same initial conditions yields perturbed frozen orbits for the full system, whose perturbation decreases with the consideration of arbitrary homologic equations in the relegation and normalization procedures. Such procedure can be automated for the first homologic equation up to the consideration of any arbitrary number of spherical harmonics coefficients. The project has been developed in collaboration with the European Space Agency (ESA).     

Sedimentary evolution of the Mesozoic continental redbeds using geochemical and mineralogical tools: the case of Upper Triassic to Lowermost Jurassic Monte di Gioiosa mudrocks (Sicily,southern Italy)

The continental redbeds from the Internal Domains of the central-western Mediterranean Chains have an important role in the palaeogeographic and palaeotectonic reconstructions of the Alpine circum-Mediterranean orogen evolution since these redbeds mark the Triassic-Jurassic rift-valley stage of Tethyan rifting. The composition and the sedimentary evolution of the Middle Triassic to Lowermost Jurassic continental redbeds of the San Marco d’Alunzio Unit (Peloritani Mountains, Southern Italy), based on mineralogical and chemical analyses, suggests that the studied mudrock sediments share common features with continental redbeds that constitute the Internal Domains of the Alpine Mediterranean Chains. Phyllosilicates are the main components in the mudrocks. The 10 Å-minerals (illite and micas), the I–S mixed layers, and kaolinite are the most abundant phyllosilicates. The amount of illitic layers in I–S mixed layers coupled with the illite crystallinity values (IC) are typical of high degree of diagenesis, corresponding to a lithostatic/tectonic loading of about 4–5 km. The mineralogical assemblage coupled with the A-CN-K plot suggest post-depositional K-enrichments. Palaeoweathering proxies (PIA and CIW) record intense weathering at the source area. Further, the studied sediments are affected by reworking and recycling processes and, as consequence, it is likely these proxies monitor cumulative effect of weathering. The climate in the early Jurassic favoured recycling and weathering occurred under hot, episodically humid climate with a prolonged dry season. The source-area is the low-grade Paleozoic metasedimentary basement. Mafic supply is minor but not negligible as suggested by provenance proxies.     

Active normal faulting along the Mt. Morrone south-western slopes (central Apennines,Italy)

In the present work we analyse one of the active normal faults affecting the central Apennines, i.e. the Mt. Morrone normal fault system. This tectonic structure, which comprises two parallel, NW-SE trending fault segments, is considered as potentially responsible for earthquakes of magnitude ≥ 6.5 and its last activation probably occurred during the second century AD. Structural observations performed along the fault planes have allowed to define the mainly normal kinematics of the tectonic structure, fitting an approximately N 20° trending extensional deformation. Geological and geomorphological investigations performed along the whole Mt. Morrone south-western slopes permitted us to identify the displacement of alluvial fans, attributed to Middle and Late Pleistocene by means of tephro-stratigraphic analyses and geomorphological correlations with dated lacustrine sequences, along the western fault branch. This allowed to evaluate in 0.4 ± 0.07 mm/year the slip rate of this segment. On the other hand, the lack of synchronous landforms and/or deposits that can be correlated across the eastern fault segment prevented the definition of the slip rate related to this fault branch. Nevertheless, basing on a critical review of the available literature dealing with normal fault systems evolution, we hypothesised a total slip rate of the fault system in the range of 0.4 ± 0.07 to 0.8 ± 0.09 mm/year. Moreover, basing on the length at surface of the Mt. Morrone fault system (i.e. 22–23 km) we estimated the maximum expected magnitude of an earthquake that might originate along this tectonic structure in the order of 6.6–6.7.     

X-rays from massive OB stars: thermal emission from radiative shocks

Chandra grating spectra of a sample of 15 massive OB stars were analysed under the basic assumption that the X-ray emission is produced in an ensemble of shocks formed in the winds driven by these objects. Shocks develop either as a result of radiation-driven instabilities or due to confinement of the wind by a relatively strong magnetic field, and since they are radiative, a simple model of their X-ray emission was developed that allows a direct comparison with observations. According to our model, the shock structures (clumps, complete or fractional shells) eventually become 'cold' clouds in the X-ray sky of the star. As a result, it is expected that for large covering factors of the hot clumps, there is a high probability for X-ray absorption by the 'cold' clouds, resulting in blueshifted spectral lines. Our analysis has revealed that such a correlation indeed exists for the considered sample of OB stars. As to the temperature characteristics of the X-ray emission plasma, the studied OB stars fall in two groups: (i) one with plasma temperature limited to ∼0.1–0.4 keV and (ii) the other with X-rays produced in plasmas at considerably higher temperatures. We argue that the two groups correspond to different mechanisms for the origin of X-rays: in radiation-driven instability shocks and in magnetically confined wind shocks, respectively.     

A sixth-order accurate scheme for solving two-point boundary value problems in astrodynamics

A sixth-order accurate scheme is presented for the solution of ODE systems supplemented by two-point boundary conditions. The proposed integration scheme is a linear multi-point method of sixth-order accuracy successfully used in fluid dynamics and implemented for the first time in astrodynamics applications. A discretization molecule made up of just four grid points attains a O(h ⁶) accuracy which is beyond the first Dahlquist’s stability barrier. Astrodynamics applications concern the computation of libration point halo orbits, in the restricted three- and four-body models, and the design of an optimal control strategy for a low thrust libration point mission.