Magnetohydrodynamic modelling of interplanetary disturbances between the Sun and Earth

A time-dependent, nonplanar, two-dimensional magnetohydrodynamic computer model is used to simulate a series, separately examined, of solar flare-generated shock waves and their subsequent disturbances in interplanetary space between the Sun and the Earth's magnetosphere. The ‘canonical’ or ansatz series of shock waves include initial velocities near the Sun over the range 500 to 3500 km s^?1. The ambient solar wind, through which they propagate, is taken to be a steady-state homogeneous plasma (that is, independent of heliolongitude) with a representative set of plasma and magnetic field parameters. Complete sets of solar wind plasma and magnetic field parameters are presented and discussed. Particular attention is addressed to the MHD model's ability to address fundamental operational questions vis-à-vis the long-range forecasting of geomagnetic disturbances. These questions are: (i) will a disturbance (such as the present canonical series of solar flare shock waves) produce a magnetospheric and ionospheric disturbance, and, if so, (ii) when will it start, (iii) how severe will it be, and (iv) how long will it last? The model's output is used to compute various solar wind indices of current interest as a demonstration of the model's potential for providing ‘answers’ to these questions.     

The solution for seasonal variations in the Earth's rate of rotation

New physical principles for an explanation of seasonal variations in the Earth's rate of rotation are proposed. It is thought that the variations are caused by a variation of the total energy of the Earth's atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. Jacobi's virial equation for the Earth's atmosphere is derived from the Eulerian equations. The virial theorem is obtained. The existence of the relationship between Jacobi's function and potential energy of the atmosphere is confirmed. In the framework of this relationship, Jacobi's equation is reduced to the equation of unperturbed virial oscillations. The solution of the above-mentioned equation expresses the periodic virial oscillations of Jacobi's function (moment of inertia) of the Earth's atmosphere with time. The solution of the perturbed virial oscillation problem of the atmosphere-solid Earth system is obtained. The perturbation term in Jacobi's virial equation regards, in explicit form, the energy changes occurring in the atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. The annual and semi-annual periodic variations in the Earth's rate of rotation can be considered as an astrometrical result following from the obtained solution. A satisfactory accord of the theoretical results with experimental data is shown.     

The internal evolution of planetary-sized objects

The importance of ‘creep’ in controlling the internal thermal state of large objects with physical properties corresponding to a roughly homogeneous meteoritic composition is reviewed. Some results of this study are used to justify a picture of evolution as a quasistatic process. An attempt is made to show that the viscous dissipation of the motions that occur in the lifetime of such bodies formed about 4.5 × 10⁹ yr ago gives them an innate capacity to chemically differentiate if their external radius exceeds a few hundred kilometres. The capacity to differentiate increases rapidly with external radius and for objects of lunar size and greater, the process is not yet complete. During the ‘active’ stage of evolution the convective cores of these objects tend to grow smaller and hotter with time, giving a secular change in the composition of the differentiating phases. It is suggested that by a curious coincidence of dehydration curves and the horizontally averaged temperature distribution, water of dehydration can still be present at depth in the planets and is the cause of the observed seismic attenuation at the Moon's centre and in the Earth's upper mantle. It is also noted that if water is present at tenths of a percent level the temperature within objects with radii < 3000 km is kept below the Curie point of pure iron for long periods - a situation that could have significant bearing on the present magnetisation of the planetary objects in this size range.     

Theoretische Betrachtungen zum Verhalten des Magnetfeldes in einem sphärischen Erdmodell

The theoreticl treatment of several geophysical problems presupposes the solution of field equations of the magnetic field in the Earth's mantle. The field equations are given in a scalar form for a spherical model of the Earth. It will be shown that analytical solutions are possible in all cases. The boundary conditions are discussed with regard to the dynamo process in the Earth's core and the existence of a field representation, which is investigated on the Earth's surface. The question is discussed, to what extend the mantle's field is given by this field representation, when some special assumptions about the Earth's model are made.     

A New Ionosphere Monitoring Technology Based on GPS

Although global positioning system (GPS) was originally planned as a satellite-based radio-navigation system for military purposes, civilian users have significantly increased their access to the system for both, commercial and scientific applications. Almost 400 permanent GPS tracking stations have been stablished around the globe with the main purpose of supporting scientific research. In addition, several GPS receivers on board of low Earth orbit satellites fitted with special antennas that focus on Earth's horizon, are tracking the radio signals broadcasted by the high-orbiting GPS satellites, as they rise and set on Earth horizon. The data of these ground and space-born GPS receivers, readily accessible through Internet in a ‘virtual observatory’ managed by the International GPS Service, are extensively used for many researches and might possibly ignite a revolution in Earth remote sensing. By measuring the changes in the time it takes for the GPS signals to arrive at the receiver as they travel through Earth's atmosphere, scientists can derive a surprising amount of information about the Earth's ionosphere, a turbulent shroud of charged particles that, when stimulated by solar flares, can disrupt communications around the world. This contribution presents a methodology to obtain high temporal resolution images of the ionospheric electron content that lead to two-dimensional vertical total electron content maps and three-dimensional electron density distribution. Some exemplifying results are shown at the end of the paper.     

Magnetization of celestial bodies with special application to the primeval Earth and Moon

The magnetic fields of celestial bodies are usually supposed to be due to a ‘hydromagnetic dynamo’. This term refers to a number of rather speculative processes which are supposed to take place in the liquid core of a celestial body. In this paper we shall follow another approach which is more closely connected with hydromagnetic processes well-known from the laboratory, and hence basically less speculative. The paper should be regarded as part of a general program to connect cosmical phenomena with phenomena studied in the laboratory. As has been demonstrated by laboratory experiments, a poloidal magnetic field may be increased by the transfer of energy from a toroidal magnetic field through kink instability of the current system. This mechanism can be applied to the fluid core of a celestial body. Any differential rotation will produce a toroidal field from an existing poloidal field, and the kink instability will feed toroidal energy back to the poloidal field, and hence amplify it. In the Earth-Moon system the tidal braking of the Earth's mantle acts to produce a differential angular velocity between core and mantle. The braking will be transferred to the core by hydromagnetic forces which at the same time give rise to a strong magnetic field. The strength of the field will be determined by the rate of tidal braking. It is suggested that the magnetization of lunar rocks from the period ?4 to ?3 Gyears derives from the Earth's magnetic field. As the interior of the Moon immediately after accretion probably was too cool to be melted, the Moon could not produce a magnetic field by hydromagnetic effects in its core. The observed lunar magnetization could be produced by such an amplified Earth field even if the Moon never came closer than 10 or 20 Earth's radii. This hypothesis might be checked by magnetic measurements on the Earth during the same period.     

Comparing analytical and numerical approaches to meteoroid orbit determination using Hayabusa telemetry

Fireball networks establish the trajectories of meteoritic material passing through Earth's atmosphere, from which they can derive pre‐entry orbits. Triangulated atmospheric trajectory data require different orbit determination methods to those applied to observational data beyond the Earth's sphere of influence, such as telescopic observations of asteroids. Currently, the vast majority of fireball networks determine and publish orbital data using an analytical approach, with little flexibility to include orbital perturbations. Here, we present a novel numerical technique for determining meteoroid orbits from fireball network data and compare it to previously established methods. The re‐entry of the Hayabusa spacecraft, with its known pre‐Earth orbit, provides a unique opportunity to perform this comparison as it was observed by fireball network cameras. As initial sightings of the Hayabusa spacecraft and capsule were made at different altitudes, we are able to quantify the atmosphere's influence on the determined pre‐Earth orbit. Considering these trajectories independently, we found the orbits determined by the novel numerical approach to align closer to JAXA's telemetry in both cases. Using simulations, we determine the atmospheric perturbation to become significant at ~90 km—higher than the first observations of typical meteorite dropping events. Using further simulations, we find the most substantial differences between techniques to occur at both low entry velocities and Moon passing trajectories. These regions of comparative divergence demonstrate the need for perturbation inclusion within the chosen orbit determination algorithm.     

A noncanonical analytic solution to theJ 2 perturbed two-body problem

The motion of a satellite subject to an inverse-square gravitational force of attraction and a perturbation due to the Earth's oblateness as theJ ₂ term is analyzed, and a uniform, analytic solution correct to first-order inJ ₂, is obtained using a noncanonical approach. The basis for the solution is the transformation and uncoupling of the differential equations for the model. The resulting solution is expressed in terms of elementary functions of the independent variable (the ‘true anomaly’), and is of a compact and simple form. Numerical results are comparable to existing solutions.     

The Earth's core formation due to the Rayleigh-Taylor instability

The recent theories of planetary formation lead to a gravitationally unstable structure of the proto-Earth in the accretion stage, which is composed of three layers: an innermost undifferentiated solid core, an intermediate metal-melt layer, and an outermost silicate-melt layer. Taking this configuration as an initial state, we investigate the Earth's core formation due to the Rayleigh-Taylor instability by using the quantitative results on the instability in a self-gravitating fluid sphere obtained from another paper (S. Ida, Y. Nakagawa, and K. Nakagawa, submitted). We find that the instability occurs through the translational mode on a time scale of about 10 hr if the thickness of the metal-melt layer ⪆1 km. This leads to the conclusion that the Earth's core began to form through the translation of the innermost undifferentiated solid core as soon as the outer layer was melted and differentiated in the late accretion stage. In addition, we examine the rotational effects of the instability; the translation occurs most often along the rotational axis. But this preference is weak, since the rotational energy is small compared to the gravitational one.     

The rate of small impacts on Earth

Abstract— Asteroids tens to hundreds of meters in diameter constitute the most immediate impact hazard to human populations, yet the rate at which they arrive at Earth's surface is poorly known. Astronomic observations are still incomplete in this size range; impactors are subjected to disruption in Earth's atmosphere, and unlike the Moon, small craters on Earth are rapidly eroded. In this paper, we first model the atmospheric behavior of iron and stony bodies over the mass range 1–10¹² kg (size range 6 cm‐1 km) taking into account deceleration, ablation, and fragmentation. Previous models in meteoritics deal with rather small masses (<10⁵–10⁶ kg) with the aim of interpreting registered fireballs in atmosphere, or with substantially larger objects without taking into account asteroid disruption to model cratering processes. A few earlier attempts to model terrestrial crater strewn fields did not take into account possible cascade fragmentation. We have performed large numbers of simulations in a wide mass range, using both the earlier “pancake” models and also the separated fragments model to develop a statistical picture of atmosphere‐bolide interaction for both iron and stony impactors with initial diameters up to ?1 km. Second, using a compilation of data for the flux at the upper atmosphere, we have derived a cumulative size‐frequency distribution (SFD) for upper atmosphere impactors. This curve is a close fit to virtually all of the upper atmosphere data over 16 orders of magnitude. Third, we have applied our model results to scale the upper atmosphere curve to a flux at the Earth's surface, elucidating the impact rate of objects <1 km diameter on Earth. We find that iron meteorites >5 times 10⁴ kg (2.5 m) arrive at the Earth's surface approximately once every 50 years. Iron bodies a few meters in diameter (10⁵–10⁶ kg), which form craters ?100 m in diameter, will strike the Earth's land area every 500 years. Larger bodies will form craters 0.5 km in diameter every 20,000 years, and craters 1 km in diameter will be formed on the Earth's land area every 50,000 years. Tunguska events (low‐level atmospheric disruption of stony bolides >10⁸ kg) may occur every 500 years. Bodies capable of producing hazardous tsunami (?200 m diameter projectiles) should strike the Earth's surface every ?100,000 years. This data also allows us to assess the completeness of the terrestrial crater record for a given area over a given time interval.     

Testing materials to mitigate terrestrial organic contamination of meteorites: Implications for collection,curation, and handling of astromaterials

Organic matter in astromaterials can provide important information for understanding the chemistry of our solar system and the prebiotic conditions of the early Earth. However, once astromaterials reach the Earth's surface, they can be readily contaminated through contact with the Earth's surface as well as during processing and curation. Here, we investigate how typical handling and curation materials interact with meteorite specimens by documenting hydrophobic organic compound contamination in the laboratory environment and on materials that might be used for their collection and storage. We use gas chromatography–mass spectrometry analysis of soluble organic compounds in dichloromethane extracts of these materials to gain insights into what materials and methods are best for the collection and curation of astromaterials. Our results have implications for how extraterrestrial samples—especially those containing significant intrinsic organic matter—are handled and curated to preserve them in their most pristine states. Following recommendations of other researchers in the area of returned sample curation, we advocate for a thorough investigation into the materials used in handling and curation of meteorites to create a contamination baseline to inform soluble organic analyses on astromaterials and enable the discrimination of terrestrial and extraterrestrial compounds.     

On the Origin of the Tektites

The conclusion that tektite falls were restricted in time to an earlier era in Earth history is supported by all known facts, in particular, by the results of critical examinations of various reported falls, including 2 australite falls described not long ago by the late Dr. E. S. Simpson. On the contrary, if the tektites originate as “lunar impactites,” as Dr. H. H. Nininger has recently suggested, it seems evident that they would have continued to fall onto the Earth right up to the present time. Furthermore, the probability that the distribution of “lunar impactite” falls over the Earth's surface would exhibit the alinement along 3 great circles, which is characteristic of all known tektite deposits, is vanishingly small.     

On lagrange solutions in the problem of three rigid bodies

The present paper is a direct continuation of the paper (Duboshin, 1973) in which was proved the existence of one kind of Lagrange (triangle) and Euler (rectilinear) solutions of the general problem of the motion of three finite rigid bodies assuming different laws of interaction between the elementary particles of the rigid bodies. In particular, Duboshin found that the general problem of three rigid bodies permits such solutions in which the centres of mass of the bodies always form an equilateral triangle or always remain on one straight line, and each body possesses an axial symmetry and a symmetry with respect to the plane of the centres of mass and rotates uniformly around its axis orthogonal to this plane. The conditions for the existence of such solutions have also been found. The results in Duboshin's paper have greatly interested the author of the present paper. In another paper (Kondurar and Shinkarik, 1972) considering a more special problem, when two of the three bodies are spheres, either homogeneous or possessing a spherically symmetric distribution of the densities or of the material points, and the third is an axially symmetrical body possessing equatorial symmetry, the present author obtained analogous solutions of the ‘float’ type describing the motion of the indicated dynamico-symmetrical body in assuming its passive gravitation. In the present paper new Lagrange solutions of the considered general problems of three rigid bodies of ‘level’ type are found when the axes of geometrical and mechanical symmetry of all three bodies always lie in the triangle plane, and the bodies themselves rotate inertially around the symmetry axis, independently of the parameters of the orbital motion of the centres of mass as in the ‘float’ case. The study of particular solutions of the general problem of the translatory-rotary motion of three rigid bodies, which are a generalization of Lagrange solutions, is in the author's opinion, a novelty of some interest for both theoretical and practical divisions of celestial mechanics. For example, in recent times the problem of the libration points of the Earth-Moon system has acquired new interest and value. A possible application which should be mentioned is that to the orbits of artificial satellites near the triangular libration points to serve as observation stations with the aim of specifying the physical parameters in the Earth-Moon system (e.g., the relation of the Earth's mass to the Moon's mass for investigating the orientation of the satellite, solar radiation, etc.).     

Decameter storm radiation,II

The physical properties of six decametric storms, observed at Clark Lake Radio Observatory are studied. The height of the storm continuum sources was determined from the rotation rate. Assuming that the radiation originates at the plasma frequency we computed the gradient of electron density for the regions where the storms originate. The mean angular size of the decametric continuum sources is large; it increases with decreasing frequency. The storm continuum is found to be strongly directive toward the disk center. The east-west asymmetry, well observed at meter wavelengths is also observed at decameter wavelengths. The occurrence of two distinct classes of type III bursts in storms is discussed: ‘off-fringe’ and ‘onfringe’ type Ill's. The ‘off-fringe’ Ill's are found to be displaced in position from the continuum source ; on the other hand, the ‘on-fringe’ ones coincide in position with the continuum. These two kinds of bursts differ in other properties as well. A model of the storm region is proposed. The continuum radiation and the ‘on-fringe’ type III's are believed to originate above closed magnetic loops, in regions of diverging field lines; the ‘offfringe’ type Ill's are thought to be excited by energetic electron streams, having access to open magnetic field lines at the base of the loops.     

Stabilization of Kepler's problem

A regularization of Kepler's problem due to Moser is used to ‘stabilize’ the equations of motion, that is, imbed a particular solution of Kepler's problem in a Lyapounov stable system.     

Turbulence in cosmology

Principles of the theory of turbulence in relativistic cosmology are developed. By averaging Einstein's equations over stochastic fields a self-consistent system of equations is obtained which describes statistically: (1) the influence of the turbulence on the ‘basic state of the Universe (the background) on which the turbulence develops; (2) the behaviour of the turbulence on the background ‘distorted’ by it. By means of a qualitative study of exact equations in the region of a strong turbulence at an early stage of cosmological expansion conditions of the absence of singularity are found and the possibility of stationary solutions in the homogeneous, isotropic, on the average, Universe (the cosmological constantA=0) is shown. The rate of cosmological expansion increases if the energy density of the turbulence is positive, and decreases if it is negative. The latter alternative takes place if the absolute value of the energy density of excitations, which will change into potential motions in the future, exceeds the energy density of the remaining part of the turbulence.