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.     

Thermonuclear processes in the core is the main source of energy of geodynamic evolution and degassing of the earth

Based on some additional clarifications of the cosmological model of the formation of the Solar System it was shown that the main source of the Earth’s energy are thermonuclear processes in the inner Earth’s core consisting of metallic hydrides. This energy is quite significant, but it is substantially smaller (by about three orders of magnitude) than the energy received from the Sun. The proposed hypothesis suggests a presence of hydrogen fluxes or deep fluids propagating from the Earth’s core and transporting thermal energy from the thermonuclear reactions to the Earth’s surface. This energy has been a primary reason for the endogenic, geodynamic and tectonic processes over the course of the Earth’s whole history.     

Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth

Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.     

Precession/nutation solution consistent with the general planetary theory

In the present paper the equations of the translatory motion of the major planets and the Moon and the Poisson equations of the 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 is presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients.     

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.     

Is there a Nuclear Reactor at the Center of the Earth?

In this paper we discuss the Herndon hypothesis that a nuclear reactor is operating at the center of the Earth. Recent experimental evidence shows that some uranium can have partitioned into the core. There is no viable mechanism for the small amount of uranium that is dissolved in the molten metal to crystallize as a separate uranium phase (uranium metal or uranium sulfide) and migrate to the center of the core. There is no need for an extra heat source, as the total heat leaving the core can be easily provided by “classical” heat sources, which are also more than adequate to maintain the Earth’s magnetic field. It is unlikely that nuclear georeactors (fast breeder reactors) are operating at the Earth’s center.     

Preparing For Hyperseed MAC: An Observing Campaign To Monitor The Entry Of The Genesis Sample Return Capsule

The imminent return of the Genesis Sample Return Capsule (SRC) from the Earth’s L1 point on September 8, 2004, represents the first opportunity since the Apollo era to study the atmospheric entry of a meter-sized body at or above the Earth’s escape speed. Until now, reentry heating models are based on only one successful reentry with an instrumented vehicle at higher than escape speed, the 22 May 1965 NASA “FIRE 2” experiment. In preparation of an instrumented airborne and ground-based observing campaign, we examined the expected bolide radiation for the reentry of the Genesis SRC. We find that the expected emission spectrum consists mostly of blackbody emission from the SRC surface (T∼ ∼2630 K@peak heating), slightly skewed in shape because of a range of surface temperatures. At high enough spectral resolution, shock emission from nitrogen and oxygen atoms, as well as the first positive and first negative bands of N₂⁺, will stand out above this continuum. Carbon atom lines and the 389-nm CN band emission may also be detected, as well as the mid-IR 4.6-μm CO band. The ablation rate can be studied from the signature of trace sodium in the heat shield material, calibrated by the total amount of matter lost from the recovered shield. A pristine collection of the heat shield would also permit the sampling of products of ablation.     

Infrasonic Observations of Meteoroids: Preliminary Results from a Coordinated Optical-radar-infrasound Observing Campaign

Recent observations using the newly installed Elginfield infrasound array in coordination with the Southern Ontario all-sky meteor camera network and Canadian Meteor Orbit Radar (CMOR) has shown that the number of meteors producing infrasound at the Earth’s surface is more frequent than previously thought. These data show the flux of meteoroids capable of producing infrasound at the ground is at least 1/month and is limited to meteors with peak visual brightness above −2. Comparisons to current meteor infrasound theory show excellent agreement with amplitude and period predictions for weakly non-linear shock waves using a realistic vertically inhomogeneous atmosphere. Similar predictions show isothermal assumptions underestimate the amplitude by orders of magnitude.     

Position and velocity perturbations for the determination of geopotential from space geodetic measurements

Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting (LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values, our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic measurements for the determination of geopotential.     

PHOKA experiment: Description of the equipment and first results

The CORONAS-PHOTON Russian satellite intended to study the Sun was successfully launched into orbit on January 30, 2009. Scientific equipment of the satellite includes the PHOKA radiometer of soft X-ray and extreme UV radiation. The PHOKA instrument is intended to measure the absolute flux of solar electromagnetic radiation in the spectral windows of 0.5–7 nm, 0.5–11 nm, 27–37 nm, and 116–125 nm. When leaving and entering the Earth’s shadow, the instrument aboard the spacecraft measures absorption of radiation by various layers of the Earth’s atmosphere. Before the launch, photodiodes of the instrument had been calibrated using a synchrotron radiation source. In-flight stability of sensitivity of main channels is controlled using calibration channels. The paper describes the PHOKA instrument and presents its capabilities and main characteristics, as well as some results of its operation in orbit.     

Trap with ultracold neutrons as a detector of dark matter particles with long-range forces

The possibility of using a trap with ultracold neutrons as a detector of dark matter particles with long-range forces is considered. The main advantage of the proposed method lies in the possibility of detecting a recoil energy of ∼10⁻⁷ eV. Constraints on the parameters of an interaction potential of the form φ (r) = ae ^−r/b /r between dark matter particles and a neutron are presented at various dark matter densities on Earth. The assumption about the long-range interaction of dark matter particles and ordinary matter is shown to lead to a significant increase in the elastic scattering cross section at low energies. As a consequence, it becomes possible to capture and accumulate dark matter in the Earth’s gravitational field. The accumulated dark matter in the Earth’s gravitational field is roughly estimated. The first experimental constraints on the existence of dark matter with long-range forces on Earth are presented.     

Optimal low-thrust transfers between libration point orbits

Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute the invariant tori and their manifolds in this dynamical model.     

Disturbance compensating control of orbit radially aligned two-craft Coulomb formation

This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an Earth–Moon collinear libration point.     

Influence of geomagnetic field on the motion of low satellites

The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1 satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis.     

A second order analytical atmospheric drag theory based on the TD88 thermospheric density model

A second order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order in terms of TD88 small parameters K _n,j . The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites ROHINI (1980 62A), and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument of perigee due to the Earth’s gravity are taken into account up to the second order in Earth’s oblateness.     

Towards Earth AntineutRino TomograpHy (EARTH)

The programme Earth AntineutRino TomograpHy (EARTH) proposes to build ten underground facilities each hosting a telescope. Each telescope consists of many detector modules, to map the radiogenic heat sources deep in the interior of the Earth by utilising direction sensitive geoneutrino detection. Recent hypotheses target the core-mantle boundary (CMB) as a major source of natural radionuclides and therefore of radiogenic heat. A typical scale of the processes that take place at the CMB is about 200 km. To observe these processes from the surface requires an angular resolution of about 3°. EARTH aims at creating a high-resolution 3D-map of the radiogenic heat sources in the Earth’s interior. It will thereby contribute to a better understanding of a number of geophysical phenomena observed at the Earth’s surface. This condition requires a completely different approach from the monolithic detector systems as e.g. KamLAND. This paper presents, for such telescopes, the boundary conditions set by physics, the estimated count rates, and the first initial results from Monte-Carlo simulations and laboratory experiments. The Monte-Carlo simulations indicate that the large volume telescope should consist of detector modules each comprising a very large number of detector units, with a cross section of roughly a few square centimetres. The signature of an antineutrino event will be a double pulse event. One pulse arises from the slowing down of the emitted positron, the other from the neutron capture. In laboratory experiments small sized, ¹⁰B-loaded liquid scintillation detectors were investigated as candidates for direction sensitive, low-energy antineutrino detection.     

Micrometeorites and Their Implications for Meteors

Micrometeorites (MMs) are extraterrestrial dust particles, in the size range 25–400 μm, recovered from the Earth’s surface. They have experienced a wide range of heating during atmospheric entry from completely molten spherules to particles heated to temperatures <300°C that have retained low temperature minerals. The majority of MMs have mineralogies, textures and compositions that strongly resemble components from chondritic meteorites suggesting these correspond to sporadic, low geocentric velocity meteors. Changes in MMs due to entry heating, however, have implications for meteoric processes in general that may allow the observed behaviour of meteors to be directly related to the material properties of their meteoroids.     

The past,present and future supernova threat to Earth’s biosphere

A brief review of the threat posed to Earth’s biosphere via near-by supernova detonations is presented. The expected radiation dosage, cosmic ray flux and expanding blast wave collision effects are considered, and it is argued that a typical supernova must be closer than ∼10-pc before any appreciable and potentially harmful atmosphere/biosphere effects are likely to occur. In contrast, the critical distance for Gamma-ray bursts is of order 1-kpc. In spite of the high energy effects potentially involved, the geological record provides no clear-cut evidence for any historic supernova induced mass extinctions and/or strong climate change episodes. This, however, is mostly a reflection of their being numerous possible (terrestrial and astronomical) forcing mechanisms acting upon the biosphere and the difficulty of distinguishing between competing scenarios. Key to resolving this situation, it is suggested, is the development of supernova specific extinction and climate change linked ecological models. Moving to the future, we estimate that over the remaining lifetime of the biosphere (∼2 Gyr) the Earth might experience 1 GRB and 20 supernova detonations within their respective harmful threat ranges. There are currently at least 12 potential pre-supernova systems within 1-kpc of the Sun. Of these systems IK Pegasi is the closest Type Ia pre-supernova candidate and Betelgeuse is the closest potential Type II supernova candidate. We review in some detail the past, present and future behavior of these two systems. Developing a detailed evolutionary model we find that IK Pegasi will likely not detonate until some 1.9 billion years hence, and that it affords absolutely no threat to Earth’s biosphere. Betelgeuse is the closest, reasonably well understood, pre-supernova candidate to the Sun at the present epoch, and may undergo detonation any time within the next several million years. The stand-off distance of Betelgeuse at the time of its detonation is estimated to fall between 150 and 300-pc—again, affording no possible threat to Earth’s biosphere. Temporally, the next most likely, close, potential Type Ic supernova to the Sun is the Wolf-Rayet star within the γ ² Velorum binary system located at least 260-pc away. It is suggested that evidence relating to large-scale astroengineering projects might fruitfully be looked for in those regions located within 10 to 30-pc of any pre-supernova candidate system.     

On the Near-One-Year Variation of the Sun’s Mean Magnetic Field

The mean magnetic field (MMF) of the Sun-as-a-star was measured over the last 38 years by six observatories (about 17 000 MMF daily records, 1968 – 2005). The MMF power spectrum reveals the presence of an enigmatic 1.029(7) year periodicity whose origin requires explanation. We show that this quasi-annual variation is not produced by modulation of the MMF signal due to the annual change of the Earth’s helio-latitude (one-year change of visibility of the Sun’s polar regions) as commonly accepted. The nature of this new solar phenomenon is open for discussion.