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.     

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.     

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.)     

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.     

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.     

Study of space debris burning in Earth’s atmosphere via television meteor monitoring

The observations on ground-based facilities miss multitudes of small fragments of space debris. However, the intrusion of fine particles into the atmosphere and their subsequent burning can be observed along with the usual meteor phenomena. Since the solar system meteoric body velocities at the entry into the atmosphere are over 11.2 km/s, and the velocity of the space debris objects does not exceed 11.2 km/s, the selection of meteors by velocity is a reliable criterion for separating these bodies. The paper describes a method of selecting the space debris fragments using a technique of television meteor monitoring. The technique was adapted on the material of real television observations on the FAVOR wide-field monitoring camera with high temporal resolution, conducted in 2006 in the Arkhyz station of the Institute for Precision Instrumentation (North Caucasus).     

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.     

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.     

Role of the solar wind parameters in changing orbital motion of the Earth’s satellites

The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96.     

A Nonequilibrium Figure of Saturn’s Satellite Iapetus and the Origin of the Equatorial Ridge on Its Surface

The structure, dynamical equilibrium, and evolution of Saturn’s moon Iapetus are studied. It has been shown that, in the current epoch, the oblateness of the satellite ε₂ ≈ 0.046 does not correspond to its angular velocity of rotation, which causes the secular spherization behavior of the ice shell of Iapetus. To study this evolution, we apply a spheroidal model, containing a rock core and an ice shell with an external surface ε₂, to Iapetus. The model is based on the equilibrium finite-difference equation of the Clairaut theory, while the model parameters are taken from observations. The mean radius of the rock core and the oblateness of its level surface, ε₁ ≈ 0.028, were determined. It was found that Iapetus is covered with a thick ice shell, which is 56.6% of the mean radius of the figure. We analyze a role of the core in the evolution of the shape of a gravitating figure. It was determined that the rock core plays a key part in the settling of the ice masses of the equatorial bulge, which finally results in the formation of a large circular equatorial ridge on the surface of the satellite. From the known mean altitude of this ice ridge, it was found that, in the epoch of its formation, the rotation period of Iapetus was 166 times shorter than that at present, as little as T ≈ 11^h27^m. This is consistent with the fact that a driving force of the evolution of the satellite in our model was its substantial despinning. The model also predicts that the ice ridge should be formed more intensively in the leading (dark and, consequently, warmer) hemisphere of the satellite, where the ice is softer. This inference agrees with the observations: in the leading hemisphere of Iapetus, the ridge is actually high and continuous everywhere, while it degenerates into individual ice peaks in the opposite colder hemisphere.     

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.     

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.     

Monitoring the Dynamics of the Ionosphere–Plasmasphere System by Ground-Based ULF Wave Observations

Cross-spectral analysis of ULF wave measurements recorded at ground magnetometer stations closely spaced in latitude allows accurate determinations of magnetospheric field line resonance (FLR) frequencies. This is a useful tool for remote sensing temporal and spatial variations of the magnetospheric plasma mass density. The spatial configuration of the South European GeoMagnetic Array (SEGMA, 1.56 <  L <  1.89) offers the possibility to perform such studies at low latitudes allowing to monitor the dynamical coupling between the ionosphere and the inner plasmasphere. As an example of this capability we present the results of a cross-correlation analysis between FLR frequencies and solar EUV irradiance (as monitored by the 10.7-cm solar radio flux F10.7) suggesting that changes in the inner plasmasphere density follow the short-term (27-day) variations of the solar irradiance with a time delay of 1–2 days. As an additional example we present the results of a comparative analysis of FLR measurements, ionospheric vertical soundings and vertical TEC measurements during the development of a geomagnetic storm.     

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.     

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.     

A Search for the Secular Resonances in the Dynamics of the Numbered Asteroids Passing through the Earth’s Gravity Sphere in the Nearest 200 Years

Solar System Research - The paper presents the results of studying the dynamics of the numbered near-Earth asteroids (NEAs) passing through the Earth’s gravity sphere (256000 km from the...     

A Comparison of Solar Cycle Variations in the Equatorial Rotation Rates of the Sun’s Subsurface, Surface, Corona, and Sunspot Groups

Using the Solar Optical Observing Network (SOON) sunspot-group data for the period 1985?–?2010, the variations in the annual mean equatorial-rotation rates of the sunspot groups are determined and compared with the known variations in the solar equatorial-rotation rates determined from the following data: i) the plasma rotation rates at 0.94R_⊙,0.95R_⊙,…,1.0R_⊙ measured by the Global Oscillation Network Group (GONG) during the period 1995?–?2010, ii) the data on the soft-X-ray corona determined from Yohkoh/SXT full-disk images for the years 1992?–?2001, iii) the data on small bright coronal structures (SBCS) that were traced in Solar and Heliospheric Observatory (SOHO)/EIT images during the period 1998?–?2006, and iv) the Mount Wilson Doppler-velocity measurements during the period 1986?–?2007. A large portion (up to ≈?30^° latitude) of the mean differential-rotation profile of the sunspot groups lies between those of the internal differential-rotation rates at 0.94R_⊙ and 0.98R_⊙. The variation in the yearly mean equatorial-rotation rate of the sunspot groups seems to be lagging behind that of the equatorial-rotation rate determined from the GONG measurements by one to two years. The amplitude of the GONG measurements is very small. The solar-cycle variation in the equatorial-rotation rate of the solar corona closely matches that determined from the sunspot-group data. The variation in the equatorial-rotation rate determined from the Mount Wilson Doppler-velocity data closely resembles the corresponding variation in the equatorial-rotation rate determined from the sunspot-group data that included the values of the abnormal angular motions (>?|3^°|?day^?1) of the sunspot groups. Implications of these results are pointed out.     

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.     

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.