Theoretical calculation of the interannual variability of the Earth’s insolation with daily resolution

Based on the astronomical ephemerides DE-406, theoretical calculations have been performed of the interannual variability of the Earth’s insolation related to celestial-mechanical processes for 365 points of a tropical year in the time period from 1900 to 2050. It has been determined that the average amplitude of variations of the interannual insolation is 0.310 W/m² (0.023% of the solar constant). The calculated variations are characterized by strict periodicity that corresponds with the length of a synodic month. Connection between the extreme values of the calculated insolation variability and syzygies has been defined. The average amplitude of the calculated variability exceeds by 1.7 times (0.01% of the solar constant) the amplitude of the interannual variability in the 11-year variation of the total Earth’s insolation.     

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.     

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.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

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.     

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.     

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.     

Statistical Characteristics of Meteoroid Parameters in the Earth’s Atmosphere

Statistical characteristics of meteoroids with kinetic energy from 0.1 to 440 kt TNT are estimated based on NASA satellite observations made in 1994–2016. The distributions of the number of falling meteoroids are constructed and analyzed based on the values of their initial kinetic energy, initial velocity, initial mass, altitude, geographic coordinates of the maximum total radiated energy region, and the year of the fall. Correlation dependences “mass–initial kinetic energy,” “maximum total radiated energy region altitude–initial kinetic energy,” and “maximum total radiated energy region altitude–initial velocity (the square of the initial velocity)” are constructed.     

Properties of acoustic-gravity waves in the Earth’s polar thermosphere

The properties of acoustic-gravity waves in the polar regions of the Earth’s thermosphere have been studied. It has been shown that the change in AGW amplitudes occurs against the background of large-scale rotational movements of the medium in the polar thermosphere. The amplitudes of waves increase with AGW propagation against the motion of the medium and decrease when AGW propagate along rotation. An analytical expression for the gain coefficient of AGW perturbations is obtained; the wave’s amplification effect in the opposite wind given the characteristic parameters of the thermosphere is estimated. The results are consistent with the measurements of AGW parameters in the polar regions from the “Dynamic Explorer 2” satellite.)     

Analytical theory of Earth’s rotation

An analytical theory of the rotation of the rigid Earth is developed in a form compatible with the general planetary theory. Numerical estimates of the constants of integration of the Poisson equations, which are a particular case of the equations of the Earth’s rotation, are given.     

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.     

Toroidal quarter waves in the Earth’s magnetosphere: theoretical studies

An analytic model has been developed for toroidal quarter wave (QW) oscillations in the Earth’s magnetosphere using idealistic and highly asymmetric ionospheric boundary condition. The background magnetic field is dipolar and plasma density distribution is governed by a power law 1/r ^m where r is the geocentric distance of any point along the field line and m is the density index. The solution thus obtained has been compared with the numerical solutions. Earlier workers had developed the analytic model for trivial 1/r ⁶ (m=6) type of plasma density distribution along the field line for which the period of the fundamental is twice that of corresponding half wave (i.e. toroidal oscillation in the symmetric ionospheric boundary). The present analytic model does reproduce this feature. In addition, it is seen that this ratio decreases for lower values of m. Moreover, for a particular value of m, this ratio shows a decreasing trend with increased harmonic number. The spatial characteristics of QW obtained from present analytic model are in excellent agreement with those computed numerically, thereby validating the model. The departure of frequency computed analytically from that obtained numerically is significant only for the fundamental and this departure reduces sharply with the increased harmonic number. It should be noted that there is no such departure for 1/r ⁶ type of plasma density distribution and spatial structures as well as frequency computed from the present analytic model match perfectly with those computed numerically.     

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...     

Possible Effect of the Earth’s Inertial Induction on the Orbital Decay of LAGEOS

The theory of velocity dependent inertial induction, based upon extended Mach’s principle, has been able to generate many interesting results related to celestial mechanics and cosmological problems. Because of the extremely minute magnitude of the effect its presence can be detected through the motion of accurately observed bodies like Earth satellites. LAGEOS I and II are medium altitude satellites with nearly circular orbits. The motions of these satellites are accurately recorded and the past data of a few decades help to test many theories including the general theory of relativity. Therefore, it is hoped that the effect of the Earth’s inertial induction can have any detectable effect on the motion of these satellites. It is established that the semi-major axis of LAGEOS I is decreasing at the rate of 1.3 mm/d. As the atmospheric drag is negligible at that altitude, a proper explanation of the secular change has been wanting, and, therefore, this paper examines the effect of the Earth’s inertial induction effect on LAGEOS I. Past researches have established that Yarkovsky thermal drag, charged and neutral particle drag might be the possible mechanisms for this orbital decay. Inertial induction is found to generate a perturbing force that results in 0.33 mm/d decay of the semi major axis. Some other changes are also predicted and the phenomenon also helps to explain the observed changes in the orbits of a few other satellites. The results indicate the feasibility of the theory of inertial induction i.e. the dynamic gravitation phenomenon of the Earth on its satellites as a possible partial cause for orbital decay.     

A Simulation Study of the Plasma Wave Enhancements in the Earth’s Equatorial Plasmasphere

In the equatorial plasmasphere, plasma waves are frequently observed. To improve our understanding of the mechanism generating plasma waves from instabilities, a comparison of observations, linear growth-rate calculations, and simulation results is presented. To start the numerical experiments from realistic initial plasma conditions, we use the initial parameters inferred from observational data obtained around the plasma-wave generation region by the Akebono satellite. The linear growth rates of waves of different modes are calculated under resonance conditions, and compared with simulation results and observations. By employing numerical experiments by a particle code, we first show that upper hybrid-, Z-, and whistler-mode waves are excited through instabilities driven by a ring-type velocity distribution. The simulation results suggest a possibility that energetic electrons with energies of some tens of keV confined around the geomagnetic equator are responsible for the observed enhancements of Z- and whistler-mode waves. While the comparison between linear growth-rate calculations and observations shows the different tendency of wave amplitude of Z-mode and whistler-mode waves, the wave amplitude of these wave modes in the simulation results is consistent with the observation.     

Asymmetric effects on Earth’s polar motion

Differential equations ruling the Earth’s polar motion are slightly asymmetric with respect to the pole coordinates. This is not only associated with the lack of axial symmetry around the Earth figure axis (triaxiality) but also with the longitude dependency of the pole tide (the main contribution). We propose a consistent handling of both asymmetric contributions, formulating a unique equation in the complex equatorial plane, of which we derive a general solution. Difference with respect to the usual symmetric solution is discussed and found significant in light of the present accuracy of the observed pole coordinates. For the same geophysical excitation, the prograde Chandler wobble is accompanied by a retrograde component up to 2 milliarcseconds (mas), transforming it in a slight elliptic motion. The asymmetric contribution is relatively larger in the geodetic excitation function, for Chandler wobble excitation mixes prograde and retrograde components of comparable level (1 mas).     

Minicomets in the Solar system and in the Earth’s atmosphere and related phenomena

We consider the history of discovery and justify the existence in the Solar system of a new class of bodies—minicomets, i.e., bodies of cometary nature and composition but of low mass. Two classes of minicomets are distinguished: icy ones similar to the Tunguska meteorite, and snow ones, which break up at high altitudes.