Surfaces of section in the Miranda-Umbriel 3:1 inclination problem

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed.     

Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

The librations, shape, and icy shell of Europa

Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.     

Analytical and numerical results on the stability of a planetary precessional model

A model for planetary precession is investigated using analytical and numerical techniques. A Hamiltonian function governing the model is derived in terms of action-angle Andoyer-Déprit variables under the assumption of equatorial symmetry. As a first approximation a simplified Hamiltonian with zero-eccentricity is considered and stability estimates are derived using KAM theory. A validation of the analytical results is performed computing Poincaré surfaces of section for the circular and elliptical model. We also investigate the role of the eccentricity and its connection with the appearance of resonances. Special attention is devoted to the particular case of the Earth–Moon system. This revised version was published online in July 2006 with corrections to the Cover Date.     

日本Mw9.0地震前的舒曼谐振异常分析

2011年3月11日日本本州岛东海岸附近海域发生了Mw9.0地震.基于中国云南的舒曼谐振(SR)观测站的磁场观测数据,分析了与该次地震有关的SR疑似异常现象.分析表明,震前3 4天低阶谐振开始出现比较明显的幅度增强现象,以2011年3月8日(北京时间)这一天的现象最明显,南北向在7:00-10:00和12:00-15:00异常比较明显,而东西向只在12:00-15:00异常相对比较强.根据对2011年3月1-11日及对应每天前后各15天共41天的数据的联合分析,3月8日部分时间段的低阶谐振磁场差明显高于一倍甚至两倍标准差;相比而言,正常的一天内各阶磁场差要明显低于一倍标准差.最后,根据一些日本地震学者提出的SR异常机理,进一步分析了在云南观测站能观测到日本地震异常的可能性.结果表明,在永胜观测站可以观测到日本地震引起的一阶到三阶SR异常,与发现的异常主要集中在低阶的现象比较吻合.     

母船垂荡导致ROV脐带缆参量共振的研究

研究有缆遥控潜水器(Remote Operated Vehicles)的脐带缆受到轴向激励所产生的大幅横向振动,即参量共振.ROV脐带缆的参激现象发生会影响ROV的安全性.针对ROV脐带缆的结构特性,推导出其在轴向激励力下的非线性振动方程.运用希尔无穷行列式的方法分析脐带缆的参量不稳定性.以稳定性图为基准分析脐带缆在多...     

Current and Future Applications of 3-D Global Earth-Ionosphere Models Based on the Full-Vector Maxwell’s Equations FDTD Method

Advances in computing technologies in recent decades have provided a means of generating and performing highly sophisticated computational simulations of electromagnetic phenomena. In particular, just after the turn of the twenty-first century, improvements to computing infrastructures provided for the first time the opportunity to conduct advanced, high-resolution three-dimensional full-vector Maxwell’s equations investigations of electromagnetic propagation throughout the global Earth-ionosphere spherical volume. These models, based on the finite-difference time-domain (FDTD) method, are capable of including such details as the Earth’s topography and bathymetry, as well as arbitrary horizontal/vertical geometrical and electrical inhomogeneities and anisotropies of the ionosphere, lithosphere, and oceans. Studies at this level of detail simply are not achievable using analytical methods. The goal of this paper is to provide an historical overview and future prospectus of global FDTD computational research for both natural and man-made electromagnetic phenomena around the world. Current and future applications of global FDTD models relating to lightning sources and radiation, Schumann resonances, hypothesized earthquake precursors, remote sensing, and space weather are discussed.

A symplectic mapping approach to the study of the stochasticity in asteroidal resonances

In the case of the 2:1 and 3:2 resonances with Jupiter, it has not been yet possible to have a complete identification of all chaotic diffusion processes at work, mainly because the time scale of some of them are of an order still out of the reach of precise integrations. A planar Hadjidemetriou's mapping, using expansions valid for high eccentricities and scaled in order to accelerate the diffusion processes, was derived. The solutions obtained with the mapping show huge eccentricity variations in all orbits starting in the middle of the 2:I resonance, when the main short-period perturbations of Jupiter's orbit are considered. The solutions starting in the middle of the 3:2 resonance do not show any important diffusion.     

Variations in the accuracy of gravity recovery due to ground track variability: GRACE,CHAMP, and GOCE

Following an earlier recognition of degraded monthly geopotential recovery from GRACE (Gravity Recovery And Climate Experiment) due to prolonged passage through a short repeat (low order resonant) orbit, we extend these insights also to CHAMP (CHAllenging Minisatellite Payload) and GOCE (Gravity field and steady state Ocean Circulation Explorer). We show wide track-density variations over time for these orbits in both latitude and longitude, and estimate that geopotential recovery will be as widely affected as well within all these regimes, with lesser track density leading to poorer recoveries. We then use recent models of atmospheric density to estimate the future orbit of GRACE and warn of degraded performance as other low order resonances are encountered in GRACE’s free fall. Finally implications for the GOCE orbit are discussed.