Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Sources of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent

Based on generalization of available geochronological data, Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent are divided into three groups: 142–125, 124–115, and <110 Ma. The age of these associations decreases with approaching the Pacific margin of Asia. In the same direction, they show a change in sources of their parental melts: continental crust (142–125 Ma) → continental crust + PREMA (DM) (124–115 Ma) → continental crust + PREMA (DM) + EMII (<110 Ma). Isotope-geochemical (Sr-Nd) study indicates that intrusive and volcanic rocks of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent were originated in geodynamic settings that provided access of enriched mantle sources to magma formation. The most probable of these settings are as follows: (1) plate sliding accompanying by the formation of slab window beneath continental margin; (2) passage of the Asian margin over the East Asian mantle hot field in the Late Mesozoic; (3) asthenospheric upwelling due to delamination of the lower crust during closure of the Mongolian-Okhotsk ocean caused by collision between the Amurian microcontinent, Dzhugdzhur-Stanovoy, and Selenga-Stanovoy superterranes in the Central Asian fold belt.     

Agpaitic magmatism at Norra Kärr? RbSr isotopic evidence

RbSr isotopic analyses of 10'whole-rock samples from the controversial peralkaline Norra Kärr complex of southern Sweden suggest an age (1580±62 m.y.) considerably older than had previously been anticipated, and indicate an initial ⁸⁷Sr/⁸⁶Sr ratio of 0.7072±0.0035 (errors at 2σ). The isotopic data are consistent with a primary magmatic origin for the Norra Kärr agpaites, but data from 8 mineral separates show that they have experienced at least one period of metamorphic disturbance since the original intrusion; the last episode of isotopic readjustment must have occurred after 1250 m.y. before present, and is attributed to the Sveconorwegian (Grenville) metamorphism.     

A comparison of the photospheric and interplanetary magnetic fields during the flight of Mariner IV

The polarity of the interplanetary magnetic field observed by the Mariner IV spacecraft is compared to the polarity of the photospheric magnetic field observed with the solar magnetograph at Mt. Wilson Observatory. Unlike the results obtained from observations during the flight of IMP-I, these polarities are not well correlated when the photospheric polarity is determined from data along a narrow latitudinal strip. It is suggested that the structure of the interplanetary field is often related to major features in the photospheric field that are observed over a broad range of solar latitudes.     

Inverse Analysis of Deep Excavation Using Differential Evolution Algorithm

This paper presents the applications of the differential evolution (DE) algorithm in back analysis of soil parameters for deep excavation problems. A computer code, named Python‐based DE, is developed and incorporated into the commercial finite element software ABAQUS, with a parallel computing technique to run an FE analysis for all trail vectors of one generation in DE in multiple cores of a cluster, which dramatically reduces the computational time. A synthetic case and a well‐instrumented real case, that is, the Taipei National Enterprise Center (TNEC) project, are used to demonstrate the capability of the proposed back‐analysis procedure. Results show that multiple soil parameters are well identified by back analysis using a DE optimization algorithm for highly nonlinear problems. For the synthetic excavation case, the back‐analyzed parameters are basically identical to the input parameters that are used to generate synthetic response of wall deflection. For the TNEC case with a total of nine parameters to be back analyzed, the relative errors of wall deflection for the last three stages are 2.2, 1.1, and 1.0%, respectively. Robustness of the back‐estimated parameters is further illustrated by a forward prediction. The wall deflection in the subsequent stages can be satisfactorily predicted using the back‐analyzed soil parameters at early stages. Copyright © 2014 John Wiley & Sons, Ltd.