Probing the Earth’s Interior with the LENA Detector

A future large-volume liquid scintillator detector such as the proposed 50 kton LENA (Low Energy Neutrino Astronomy) detector would provide a high-statistics measurement of terrestrial antineutrinos originating from β-decays of the uranium and thorium chains. Additionally, the neutron is scattered in the forward direction in the detection reaction . Henceforth, we investigate to what extent LENA can distinguish between certain geophysical models on the basis of the angular dependence of the geoneutrino flux. Our analysis is based on a Monte-Carlo simulation with different levels of light yield, considering an unloaded PXE scintillator. We find that LENA is able to detect deviations from isotropy of the geoneutrino flux with high significance. However, if only the directional information is used, the time required to distinguish between different geophysical models is of the order of severals decades. Nonetheless, a high-statistics measurement of the total geoneutrino flux and its spectrum still provides an extremely useful glance at the Earth’s interior.     

Obtaining the free frequencies of the non‐rigid Earth

In this paper, the mathematical algorithm elaborated by González, Getino and Farto (1998) is applied to four different nonrigid Earth models, in order to obtain the analytical expressions of the corresponding free frequencies. The solutions are studied, and the contributions of the different considered effects are evaluated. A numerical integration is also carried out, showing the validity of the obtained analytical solutions.     

What was the Volatile Composition of the Planetesimals that Formed the Earth?

Is there an asteroid type or meteorite class that best exemplifies the materials that went into the Earth? Carbonaceous chondrites were once the objects of choice, and in the minds of many this choice is still valid. However, the origin of primitive chondritic meteorites is unclear. At the extremes they could either be fragments of very small parent bodies that never became hot enough to undergo geochemical modification other than mild lithification, or remnants of the uppermost layers of a body that had undergone a significant degree of internal differentiation, while the top layers remained cool due to radiative heat loss or loss of volatiles to space. This latter case is problematic if one considers these objects as precursors to the Earth since the timescale for the evolution of such a small body could be longer than the timescale for the accretion of the Earth. Large-scale circulation of materials in the primitive solar nebula could greatly increase the diversity of materials near 1 AU while also making the entire inner solar system both more homogeneous and much wetter than previously expected. The total mass of the nebula is an important, but poorly constrained factor controlling the growth of planetesimals. There is also a selection effect that dominates our sampling of the planetesimals that may have existed 4.5 billion years ago; namely, small fragile bodies are more likely to be lost from the system or ground down by collisions between small bodies, yet these are precisely those that may have dominated the population from which the Earth accreted. The composition of these aggregates could have played a very important role in the early chemical evolution of the Earth. In particular, the Earth may have been much wetter and richer in hydrocarbons and other reducing materials than previously suspected.     

Peculiarities of the variations in the coordinates of the Earth’s pole

The appearance of features with cusp points on the diagrams of changes in the coordinates of the Earth’s instantaneous pole (polhodes) is considered as the result of mapping onto the plane of its displacement over the surface during the Earth’s rotational-translational motion. The results of qualitative and quantitative analyses of the data on the coordinates of the Earth’s instantaneous pole are discussed. The basic principles of the theory of Whitney singularities and their application for explaining the bifurcations of the equilibrium positions for the Zeeman catastrophe machine (Arnold 1990) are used in the analyses.     

Study of the interannual variations of the Earth’s rotation

In this work we investigate the variations of the Earth’s rotation in the interval of periods from 2 to 8 years using the longest available observational series obtained both by means of astrometry and space geodesy. We found an abrupt change of the variation pattern in the middle of the 1980s, when classical ground-based astrometric facilities for studying the Earth Rotation Parameters (ERP) were replaced with space geodesy methods. Variations with a 6-year periodicity and ∼0.2-ms amplitude practically disappeared (space geodesy instruments did not detect these variations right from the start), but the 2- to 4-year periodicities increased in amplitude and began to dominate in this frequency range under consideration. In this study, we analyze some possible excitation sources and possible causes of the change in the variability pattern.     

Statistical interrelation of 22-yr-long variations in the data on parameters of the Earth’s rotation and magnetic fields of the Earth and the Sun

By means of spectral analysis, oscillations have been detected in many-year time series of deviations in the duration of days from the standard that cannot be explained within the framework of existing gravitational theory. The solution of the problem of the origin and structure of these oscillations is associated with the essence of the phenomena taking place inside the Earth and the mechanisms of energy transfer by external fields and the Sun. The effect of the Sun on the Earth’s rotation also leads to the formation of a unified cyclic background, resulting in correlated oscillations in all shells of the Earth, as well as in its atmosphere and its nucleus. Ground magnetic fields of the Earth and the Sun play the leading role in the abovementioned unified cyclic process. The results of spectral autoregressive and wavelet analyses of experimental data concerning deviations in the duration of days from the standard in the years 1832–2006, ground geomagnetic field intensities in 1832–2006, and the mean magnetic field of the Sun during the period from 1975 to 2005 have been discussed in this paper to reveal and compare correlating oscillations. To analyze a short-period (31-yr-long) series of daily data on the mean magnetic field of the Sun, the results of wavelet transformations (the Morlet wavelet) of the detected amplitude of a burst envelope with a carrier frequency of 13 cycles/yr have been obtained.     

Effect of the Earth’s compression on the physical libration of the Moon

The effect of the Earth??s compression on the physical libration of the Moon is studied using a new vector method. The moment of gravitational forces exerted on the Moon by the oblate Earth is derived considering second order harmonics. The terms in the expression for this moment are arranged according to their order of magnitude. The contribution due to a spherically symmetric Earth proves to be greater by a factor of 1.34 × 10⁶ than a typical term allowing for the oblateness. A linearized Euler system of equations to describe the Moon??s rotation with allowance for external gravitational forces is given. A full solution of the differential equation describing the Moon??s libration in longitude is derived. This solution includes both arbitrary and forced oscillation harmonics that we studied earlier (perturbations due to a spherically symmetric Earth and the Sun) and new harmonics due to the Earth??s compression. We posed and solved the problem of spinorbital motion considering the orientation of the Earth??s rotation axis with regard to the axes of inertia of the Moon when it is at a random point in its orbit. The rotation axes of the Earth and the Moon are shown to become coplanar with each other when the orbiting Moon has an ecliptic longitude of L _? = 90° or L _? = 270°. The famous Cassini??s laws describing the motion of the Moon are supplemented by the rule for coplanarity when proper rotations in the Earth-Moon system are taken into account. When we consider the effect of the Earth??s compression on the Moon??s libration in longitude, a harmonic with an amplitude of 0.03?? and period of T ₈ = 9.300 Julian years appears. This amplitude exceeds the most noticeable harmonic due to the Sun by a factor of nearly 2.7. The effect of the Earth??s compression on the variation in spin angular velocity of the Moon proves to be negligible.     

Comments on ‘the origin of the Earth—Moon system’

The main points are presented of a new hypothesis of the origin of the Earth—Moon system, developed on the basis of Savi's (1961) theory of the origin of rotation of celestial bodies. The cooling off and contraction due to gravitational attraction on vast particle systems, with the pushing out of electrons from atom shells result in a continually increasing density. Depending on the amount of mass, this pushing out can lead to the expulsion of electrons and the creation of a magnetic field by which a rotational motion is brought about. These conditions are satisfied for the Earth's mass and all larger masses. If the Earth and the Moon formed a unique body, the protoplanet, then once rotational motion had begun, the primeval spherical body must have taken the shape of a large Jacobi ellipsoid. New condensation followed, however no longer solely around the centre of the protoplanet, but also along the edge of the ellipsoid, the process leading to the creation of the dual Earth—Moon system.     

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Starting from 80 families of low-energy fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an Earth–Moon transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.     

On constructing the general Earth’s rotation theory

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.     

Dynamics of the Earth’s core from VLBI observations

The Earth’s rotation is accompanied by free circadian oscillations of its liquid core in the inner cavity of the lower mantle, which perturb the angular momentum of the entire Earth and produce an additional free nutation of the celestial pole called free core nutation (FCN). Since this nutation causes resonances in the diurnal tides and in the expansions of luni—solar nutation, its study, especially an improvement of the FCN period, is of fundamental importance for the theory of the Earth’s rotation. We have determined the FCN parameters from a joint analysis of equidistant series of coordinates of the celestial pole obtained from the combined processing of VLBI observations on global networks of stations for the interval 1984.0–2008.4 by IERS (International Earth Rotation and Reference System Service, Paris, France) and NEOS (National Earth Orientation Service, Washington, USA). Applying a moving least-squares filter (MLSF) to these data has shown that the FCN period averaged over this time interval differs significantly from the theoretical one and its phase varies over a wide range. Using the mean quadratic collocation (MQC) method, we have obtained a new, more accurate stochastic FCN model. Its analysis by the envelope method has revealed long-term linear phase trends, calling into question not only the adopted FCN period but also its stability and, hence, the stability of the resonant effects in the Earth’s luni—solar nutation.     

Dynamic Structure of Near-Earth Orbital Space in the 1 : 2 Resonance Region with the Speed of Earth’s Rotation

Solar System Research - The paper presents the results of a study of the dynamic structure of near-Earth orbital space in the 1 : 2 resonance region with Earth’s rotation speed. The results...     

Gamma-ray bursts and the production of cosmogenic radionuclides in the Earth’s atmosphere

An explanation is offered for the impulsive increase in the concentration of cosmogenic radiocarbon in annual tree rings (Δ¹⁴C ～ 12‰) from AD ?775. A possible cause of such an increase could be the high-energy emission from a Galactic gamma-ray burst. It is shown that such an event should not lead to an increase in the total production of ¹⁰Be in the atmosphere, as distinct from the effect of cosmic-ray fluxes on the atmosphere. At the same time, the production of an appreciable amount of ³⁶Cl, which can be detected in Greenland and Antarctica ice samples of the corresponding age, should be expected. This allows the effects caused by a gamma-ray burst and anomalously powerful proton events to be distinguished.     

Discrete ULF modes in the Earth’s magnetosphere near the Alfven frequency minimum

The equation of small oscillations of ULF waves in the Earth’s magnetosphere is derived accounting for a fast magnetosonic wave. The spectrum of discrete Alfven modes near the Alfven frequency minimum is studied on the basis of this equation.     

On the origin of energetic particles in the foreshock region of the Earth’s bow shock

We consider the processes related to the formation of the so-called foreshock region upstream of the Earth’s bow shock. We suggest a model based on the surfing of pick-up ions in the bow shock front in terms of which the ion acceleration mechanism in the front can be explained. We ascertain the physical conditions under which the accelerated ions lie upstream of the shock front and determine the direction of motion of the energetic ions. We conclude that it is this population of energetic ions (longitudinal beams) that plays a major role in forming the ion foreshock boundary.     

Influence of the hot oxygen corona on the satellite drag in the Earth’s upper atmosphere

Calculation results on the possible influence of the hot oxygen fraction on the satellite drag in the Earth’s upper atmosphere on the basis of the previously developed theoretical model of the hot oxygen geocorona are presented. Calculations have shown that for satellites with orbits above 500 km, the contribution from the corona is extremely important. Even for the energy flux Q ₀ = 1 erg cm⁻² s⁻¹, the contribution of the hot oxygen can reach tens of percent; and considering that real energy fluxes are usually higher, one can suggest that for extreme solar events, the contribution of hot oxygen to the atmospheric drag of the satellite will be dominant. For lower altitudes, the contribution of hot oxygen is, to a considerable degree, defined by the solar activity level. The calculations imply that for the daytime polar atmosphere, the change of the solar activity level from F _10.7 ∼ 200 to F _10.7 ∼ 70 leads to an increase in the ratio of the hot oxygen partial pressure to the thermal oxygen partial pressure by a factor of almost 30, from 0.85 to 25%. The transition from daytime conditions to nighttime conditions almost does not change the contribution from suprathermal particles. The decrease of the characteristic energy of precipitating particles, i.e., for the case of charged particles with a softer energy spectrum, leads to a noticeable increase of the contribution of the suprathermal fraction, by a factor of 1.5–2. It has been ascertained that electrons make the main contribution to the formation of the suprathermal fraction; and with the increase of the energy of precipitating electrons, the contribution of hot oxygen to the satellite drag also increases proportionally. Thus, for a typical burst, the contribution of the suprathermal fraction is 30% even at relatively high solar activity F _10.7 = 135.     

Dynamics of Earth‐crossing asteroids: the protected Toro orbits

Some asteroids in Earth‐crossing orbits avoid close approaches by entering in a mean motion resonance whenever the distance between the two orbits is small. These orbits are ‘Toro class’ according to the classification of (Milani et al., 1989). This protection mechanism can be understood by a semi‐averaged model, in which the fast variables are removed and the dynamical variables are the critical argument and the semimajor axis, with dependence upon a slow parameter. The adiabatic invariant theory can be applied to this model and accounts for all the qualitative features of the orbits in this class, including the onset of the libration when the orbit distance is small. Because of the neglected perturbations by the other planets, this theory is approximate and the adiabatic invariant is conserved only with low accuracy moreover, the Toro state can be terminated by a close approach to another planet (typically Venus). “Would you tell me, please, which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat. Alice in Wonderland, L. Carroll     

Indirect transfer to the Earth–Moon L1 libration point

The Earth–Moon L1 libration point is proposed as a human gateway for space transportation system of the future. This paper studies indirect transfer using the perturbed stable manifold and lunar flyby to the Earth–Moon L1 libration point. Although traditional studies indicate that indirect transfer to the Earth–Moon L1 libration point does not save much fuel, this study shows that energy efficient indirect transfer using the perturbed stable manifold and lunar flyby could be constructed in an elegant way. The design process is given to construct indirect transfer to the Earth–Moon L1 libration point. Simulation results show that indirect transfer to the Earth–Moon L1 libration point saves about 420 m/s maneuver velocity compared to direct transfer, although the flight time is about 20 days longer.