The equilibrium of a rotating body of arbitrary density

This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.     

A New Light Curve Analysis of the Eclipsing Binary SX Aur

Using WOOD 's (1972) model, we have analysed BONDARENKO 's (1974) two-colour photoelectric observations – till now unsolved – of the eclipsing binary SX Aur. Our photometric solutions turn out to be in substantial agreement with those derived by CHAMBLISS and LEUNG (1979); they confirm that SX Aur is a post-mass exchange (case A) semi-detached system.     

Magnetic reversals of Jupiter and Saturn

We propose that the origin and behavior of the internal magnetic fields of Jupiter and Saturn should be much like the Sun's. Jupiter and Saturn are predominantly gaseous, they have significant internal heat sources, and their surface angular rotation rates vary with latitude. There is also empirical evidence showing that the rotation rates of their magnetic fields vary with latitude. This differential rotation is instrumental in producing solar-type dynamos, which are characterized by quasi-periodic field reversals. When we apply the theory and scaling parameters for the reversal period of the magnetic field of the Sun to Jupiter and Saturn, we derive an estimate for the time interval between magnetic reversals to be on the order of centuries. This time scale is consistent with observed changes in Jupiter's magnetic field over the last 2 decades.     

On particle acceleration and radiation output in stochastic electromagnetic fields

We demonstrate that when charged particles interact with a plane electromagnetic wave which possesses a random amplitude, then the particles are accelerated to high energy because they are pushed along by the wave's Poynting vector. Not only are they so accelerated, as they are carried along by the wave, but also they diffuse at right angles to the direction of the Poynting flux (i.e. in the direction of the wave's electric field). The ultimate energy that such particles can reach is determined when they radiate as much energyper unit time as they receive from the plane wave. For numbers believed typical of the Crab nebula this ultimate energy is of order 10¹⁰ mc ². We have done these calculations to show that turbulent electromagnetic waves are quite efficient in generating high energy particles from low energy particles. Thus when the low frequency coherent waves emitted by a magnetized rotating neutron star are turned into incoherent waves because of wave-plasma interactions in a surrounding nebula, they still accelerate particles to rather high energies. Accordingly, while it obviously takes less time to produce high energy particles with a coherent wave than with a turbulent wave, the calculations given here show that the bulk of the relativistic electrons in the Crab nebula could still be energized by the turbulent remnants of a coherent wave.     

Jovian seismology

Standing acoustic waves, with periods between about 4.5 and 9 min, may be trapped in a wave duct beneath Jupiter's tropopause. Detection of these oscillations by observations of Doppler shifting of infrared and ultraviolet absorption lines would offer a new important method for probing the giant planet's deep atmosphere and interior. Information would be revealed on Jupiter's thermal and density structure and the depth to which its zonal winds penetrate. Standing oscillations in the molecular hydrogen envelope are modeled and their theoretical eigenfrequencies are presented as they might appear in actual data analysis. Several forcing functions for wave generation are considered. These include coupling with turbulent and convective motions, thermal overstability due to radiative transfer, effects of wave propagation in a saturated atmosphere, and consequences of ortho- to parahydrogen conversion. Altjough the forcing mechanisms couple well with the acoustic waves, allowing for possible maintenance of the oscillations, the contribution they make to velocity amplitudes is very small, between 1.0 and 0.1 m sec⁻¹. This implies that the Doppler shifting caused by the waves may be unresolvable except, perhaps, by methods of superposing time records of oscillations to enhance acoustic signals and diminish random noise.     

The chronology of Mercury's geological and geophysical evolution: The vulcanoid hypothesis

Previous discussions of Mercury's evolution have assumed that its cratering chronology is tied to that of the Moon, i.e., with Caloris forming about 3.9 Gyr ago as part of a late heavy bombardment that affected all of the terrestrial planets. That assumption requires that Mercury's core formed very early, because associated expansion features are not visible, and must have been erased before the cratering flux declined. Moreover, the modest amount of global shrinkage inferred from visible compressional features on Mercury's surface implies that the core is either largely molten at present, or had largely solidified before the end of the bombardment. The former interpretation requires a significant volatile content or implausibly large internal heat sources, while the latter raises questions about how to generate the planet's magnetic field. We have investigated whether constraints on Mercury's chronology could be relaxed by effects of a Mercury-specific bombarding population of planetesimals interior to its orbit, encountering the planet only occasionally due to secular perturbations. Such “vulcanoids” could have been a significant source of early cratering. However, those in orbits that can cross Mercury's are depleted by mutual collisions in ⪅1 Gyr, and can provide at most a modest extension of the period of heavy bombardment. Further inside Mercury's orbit, lower collisional velocities might allow survival of vulcanoids to the present. We report on a search for such bodies and on observational limits to such a population. We also review evidence that Mercury's intercrater plains are of volcanic origin and mainly predate Caloris, and that scarp formation (and global contraction) mainly postdates Caloris and has continued to recent times. If global lineaments are the product of tidal despinning, they constrain core formation to the first half of the planet's lifetime. While some questions and inconsistencies remain, the preponderance of evidence suggests that Mercury differentiated early, and at least half of its core volume is presently molten, probably due to a significant content of some light element such as sulfur.     

Interpretation of the metric tensor components based on possible astrophysical implications

In this paper we shall consider the following question: ‘If the whole galactical system expands and if galaxies are separating away from one another just as much as they are separating from our galaxy, can we assume that such a reality will have repercussions on the formulation of basic physical laws in our surroundings?’ Considering a confirmative answer, we performed an attempt to find a physical interpretation of the perturbations of the metric tensor components. It was shown that they can be expressed in terms of the dilatation function which also appears to be one reason which prohibits the precise measurement of real time and distance. Considering that an observer in our wold knows nothing of the aperiodicity of atomic oscillations which ‘determine’ the unit of time, we discerned the meaning of time in two ways: (i) the time as it is accepted in special relativity and (ii) the ‘time’ based on the reading of clocks which suffer dilatation. The usual procedure for establishing equations of the gravitational field was then carried out. These equations reduce to those of the classical theory, if the dilatation function is proportional to Newtonian gravitational potential. On this basis, considering the Earth's expansion as a process which exists as a cosmological manifestation, we discussed the observed fact of the agreement between the rate of the Earth's radius and that of the universe, according to Hubble's law.     

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.     

Mercury's exosphere origins and relations to its magnetosphere and surface

Mariner 10, the only spacecraft that ever passed close to Mercury, revealed several unexpected characteristics: an intrinsic magnetosphere, the highest mean density of any Solar System terrestrial planet and a very thin non-collisional atmosphere. Mercury's atmosphere is very poorly explored since only three atomic elements, H, He and O, were observed during the three flybys of Mariner 10. The measurements done by radio and solar occultations provided upper limits on the neutral and ion densities. These measurements pointed out the close connection between species in Mercury's exosphere and its surface, which is also the case for the Moon. Mariner 10 observations also characterized the vertical distributions and the day to night contrasts of Mercury's exosphere for its lightest components H and He (Broadfoot, A.L., et al., 1976. Mariner 10: Mercury atmosphere. Geophys. Res. Lett. 3, 577–580).More than a decade later, the first observation from a ground-based observatory of Mercury's sodium (Na) exospheric component was reported (Potter, A.E., Morgan, T.H., 1985. Discovery of sodium in the atmosphere of Mercury. Science 229, 651–653). Since then, potassium and more recently calcium have been identified in Mercury's exosphere. The bright Na resonant scattering emission has been often observed since 1985. This large set of observations is now the best source of information on Mercury's exospheric mechanisms of ejection, dynamics, sources and sinks. In particular, several of these observations provided evidence of prompt and delayed effects, both localized and global, for the very inhomogeneous Mercury's Na exosphere. These inhomogenities have been interpreted as the trace of Mercury's magnetosphere–solar wind interaction and have highlighted some of the main sources of exospheric material. Some of these features have been also interpreted as the trace of a global dayside to night side circulation of Mercury's exosphere and therefore have highlighted also the relation between exospheric production and upper surface composition.Hopefully, new sets of in situ measurements will be obtained within the next decade thanks to Messenger and Bepi-Colombo missions. Until then, ground-based observations and modelling will remain the only approaches to resolve questions on Mercury's exosphere. Mercury's exospheric composition and structure as they are presently known are described in this paper. The principal models for the main short and long times terms variations and local and global variations of Mercury's exosphere are described. The mechanisms of production and their characteristics are also given. Mercury's exosphere can also be seen as part of the coupled magnetosphere–upper surface–exosphere system and several of the links between these elements are essential to the interpretation of most of the ground-based observations. The relation between Mercury's planet composition and its exospheric composition is also considered, as is the global recycling, sources and sinks of Mercury's exosphere.     

East-west asymmetry of Saturn's ring

A spectrophotometric comparison of the eastern and western parts of Saturn's ring was made using the photographs taken with the 50-in. reflector of the Crimean Astrophysical Observatory during 5 oppositions from 1968 to 1972. The excess of brightness, observable — sometimes at the east, sometimes at the west — appears to be due to the following effects: the eastern excess of brightness, which does not depend on wavelength but changes with time and decreases with opening the ring (the Schönberg-Fessenkov effect) and the western excess of brightness, which depends on wavelength, is best of all noticeable in the shortwave part of the spectrum but does not depend on the epoch of observations. The eastern effect can be explained by the fact that water vapour condensed on the ring particles during their transitions throughout the Saturn shadow and they become brighter at the east after going out of the shadow. The western effect is like to photometric peculiarities of Iapetus. This shows that one more field, non-gravitational one, influences the ring particles as well. It might be that the magnetic field provokes the orientation of the particles with respect to Saturn's surface. The difference in magnetic properties of particles can produce an asymmetry of settling dust and result in darkening the leading hemisphere of large particles.     

Impact-induced devolatilization of four ungrouped ataxites and the formation of a silica glass spherule in ALHA77255

Allan Hills A77255, Babb's Mill (Blake's Iron), Nordheim, and Chinga are ungrouped ataxitic iron meteorites that are similar to the IAB group of noncarbonaceous-type irons in their concentrations of common and refractory siderophile elements. Mo-isotopic data show that ALHA77255, Nordheim, and Chinga are carbonaceous-type (CC) irons. (The Mo-isotopic composition of Babb's Mill [Blake's Iron] has not yet been measured, but it also seems likely to be a CC iron.) Relative to mean IAB irons, these four ataxites are severely depleted in moderately volatile elements: Ga, >99%; Ge, >99%; Cu, 79%–97%; As, 70%–96%; P, 76%–90%. These samples were probably devolatilized by major collisions on separate parent asteroids (consistent with fractional crystallization modeling showing they are unlikely to be derived from the same metallic core). Collisionally induced devolatilization of ALHA77255 likely facilitated the formation of a 5-mm diameter silica–glass spheroid in this meteorite. The spheroid may have formed by a complex process involving impact-induced vaporization of mantle material in its parent asteroid, followed by fractional condensation.     

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.     

On the influence of nonlinearities on the eigenfrequencies of five-minute oscillations of the Sun

Fitting the results of linear normal-mode analysis of the solar five-minute oscillations to the observed k - ω diagram selects a class of models of the Sun's envelope. It is a property of all the models in this class that their convection zones are too deep to permit substantial transmission of internal g modes of degree 20 or more. This is in apparent conflict with Hill and Caudell's (1979) claim to have detected such modes in the photosphere. A proposal to resolve the conflict was made by Rosenwald and Hill (1980). They pointed out that despite the impressive agreement between linearized theory and observation, nonlinear phenomena in the solar atmosphere might influence the eigenfrequencies considerably. In particular, they suggested that a correct nonlinear analysis could predict a shallow convection zone. This paper is an enquiry into whether their hypothesis is plausible. We construct k - ω diagrams assuming that the modes suffer local nonlinear distortions in the atmosphere that are insensitive to the amplitude of oscillation over the range of amplitudes that are observed. The effect of the nonlinearities on the eigenfrequencies is parameterized in a simple way. Taking a class of simple analytical models of the Sun's envelope, we compute the linear eigenfrequencies of one model and show that no other model can be found whose nonlinear eigenfrequencies agree with them. We show also that the nonlinear eigenfrequencies of a particular solar model with a shallow convective zone, computed with more realistic physics, cannot be made to agree with observation. We conclude, therefore, that the hypothesis of Rosenwald and Hill is unlikely to be correct.     

A satellite-asteroid mystery and a possible early flux of scattered C-class asteroids

Spectrophotometric measurements of the subset of satellites thought to be of capture origin, orbiting Saturn, Jupiter, and Mars, indicate that they typically (all?) have neutral spectra and low albedo, indicating spectral class C. This finding is puzzling in light of evidence that class-C objects are native only to the outer half of the asteroid belt. How did C-like objects approach, and get captured by, planets? Probably Jupiter resonances scattered a high flux of C-type objects out of the belt and throughout much of the primordial solar system. Such scattering could occur only at the close of planet accretion when extended atmospheres could affect capture. The largest flux of scattered objects came from resonances in the most heavily populated regions of the belt near 2.8 AU: in particular, the 7:3 and 5:2 resonance regions primarily populated by C's. Hence, most captured satellites are C's, not D's, S's, etc. This scenario supports and expands upon the capture scenario involving extended protoatmospheres, proposed by J. B. Pollack, J. Burns, and M. Tauper (1979, Icarus 37, 587–611) and D. Hunten (1979, Icarus 37,113–123).     

The Ground-based Experiment of the Prototype of Planetary (& Lunar) Rotation Monitor Telescope

The scientific objective of the Planetary (& Lunar) Rotation Monitor (PRM) telescope is to study the terrestrial planet's (the Moon's) rotation and its interior structure and physics by in-situ observation. In order to verify the brand new principle of observations and the data processing method, the prototype of the telescope is designed and manufactured. The prototype's optical system consists of a commercial telescope and trihedron mirror set placed at the entrance of its light path to realize the capability of observing three fields of view (FOVs) simultaneously. The ground-based validation observation began in 2017, and the images containing the stars from three FOVs were achieved. Star images from different FOVs are initially mixed together, but they can be classified into the three FOVs respectively by calculating the displacement of star images on the CCD plate between two adjacent exposures, to make the observational effect be identical with three independent observations of the three FOVs respectively. After image processing, from the orientation variation of the three FOVs simultaneously in space due to the Earth's rotation, the direction of the rotation axis of the Earth in space can be derived. Its deviation from the theoretical value is about 1${}^{″}$ in average, indicating that the working principle and data processing method are effective. The main errors in observations are discussed, including the atmospheric refraction, the thermal deformation of the commercial telescope tube, the low optical resolution caused by the short focal length, the optical aberration in the multi-FOV observation, etc. It is indicated that the spatial resolution of the telescope can be enhanced with a longer focal length, and the observational reliability can be improved by optimizing the thermal deformation control. Improving the optical design in the simultaneous observation of multiple FOVs will also be helpful to the accuracy enhancement.     

Helium and neon isotopes in stratospheric particles

Abstract— Helium and neon isotope ratios were determined for 16 interplanetary dust particles (IDPs) collected in the stratosphere. The concentration of helium observed varied greatly from particle to particle, with the highest values approaching those found for lunar surface fines and some gas-rich meteorites. With the exception of one particle, for which the ³He/⁴He was (1.45 ± 0.05) × 10^?3, the remainder of the particles had ratios falling between 1.4 and 3.1 × 10^?4, with an average of (2.4 ± 0.3) × 10^?4, substantially less than is associated with the solar wind or observed in average lunar fines or in lunar fines having sizes comparable to those of the IDPs studied. The average ²⁰Ne/²²Ne found was 12.0 ± 0.5. Only three reasonably reliable ²¹Ne/²²Ne ratios could be determined, and for these the average was 0.035 ± 0.006. The isotopic ratios appear to preclude the presence of any appreciable amount of cosmic ray-produced spallogenic products. The high ⁴He concentrations observed for some of the particles, approaching those observed for lunar surface grains, suggest they were not heated to high temperatures and degassed as they descended in the earth's atmosphere. From Flynn's study of the dynamics of IDPs entering the earth's atmosphere this could mean they entered the atmosphere at relatively low velocities, and hence may be primarily of asteroidal rather than cometary origin.     

Reexamination of the correlation of galaxies and QSO's

It is shown that the correlation between the separation on the sky of certain QSO's and the nearest bright galaxy to them with the galaxy's redshift could be an artifact of the sampling procedure or small number statistics. The overall association between 3C QSO's and bright galaxies remains as suggestive, but not compelling, evidence for a physical relationship.     

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.