Gravitational and magnetic fields of some simple solids of revolution

Summary. Exact spherical harmonic expansions are given for calculating the gravitational and magnetic fields associated with certain uniform solids of revolution. The figures are those made by rotating a conic section about one of its principal axes. The coefficients in the expansions can be computed accurately and efficiently and this approach leads to a very satisfactory method for calculating the fields of geological bodies with approximate circular symmetry about a vertical axis. A complete theory of convergence is given for the expansions. Somewhat unexpectedly, the sphere of convergence is determined by the location of a number of equivalent point or line sources that lie within the body or on its edges.     

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 2: Variations in orbital eccentricity

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the eccentricity, e, combining the effects of air drag with those of the Earth's gravitational field is given. This is solved numerically using as initial conditions 310 computed orbits of 1964-52B.The observed values of eccentricity are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure and low-order long-periodic tesseral harmonic perturbations. The method of removal of these effects is given in some detail. The behaviour of the orbital eccentricity predicted by the numerical solution is compared with the modified observed eccentricity to obtain values of atmospheric parameters at heights between 310 and 430 km. The daytime maximum of air density is found to be at 14.5 hours local time. Analysis of the eccentricity near 15th order resonance with the geopotential yielded values of four lumped geopotential harmonics of order 15, namely: $\text{10}{}^9\text{C}{}^{\mathrm{1,0}}{}_{15}\text{= ?78.8 ± 7.0}$, $\text{10}{}^9\text{S}{}^{\mathrm{1,0}}{}_{15}\text{= ?69.4 ± 5.3}$, $\text{10}{}^9\text{C}{}^{\mathrm{?1,2}}{}_{15}\text{= ?41.6 ± 3.5}$$\text{10}{}^9\text{S}{}^{\mathrm{?1,2}}{}_{15}\text{= ?26.1 ± 8.9}$, at inclination 98.68°.     

Umbral Three-Minute Oscillations and Running Penumbral Waves

We present results of investigations into chromospheric velocity oscillations in sunspots, carried out at the Sayan Solar Observatory. It is shown that the “chevron” structures in the space-time diagrams demonstrate wavetrain properties. Such structures are indicators of a propagating wave process and they are typical of many sunspots. In the authors’ opinion, three-minute umbral oscillations are not the source of running penumbral waves (RPW). It is very likely that umbral oscillations and RPW initially propagate along different magnetic field lines. We explain the decrease in RPW propagation velocity and frequency in the outer penumbra, as compared with the inner, by the combined action of different frequency modes. To better reveal the properties of these modes, frequency filtering was used. Our measurements of the RPW (five-minute mode) wavelength and RPW propagation velocity in different sunspots vary from 12^″ to 30^″ and from 28 to 60 – 70 km s⁻¹ correspondingly.     

Magneto-gravitational instability of a rotating and finitely-conducting fluid

The gravitational instability of an infinite homogeneous finitely conducting viscid fluid through porous medium is studied in the presence of a uniform vertical magnetic field and finite ion Larmor radius (FLR) effects. The medium is considered uniformly rotating along and perpendicular to the direction of the prevalent magnetic field. A general dispersion relation is obtained from the relevant linearized perturbation equations of the problem. Furthermore, the wave propagation along and perpendicular to the direction of existing magnetic field has been discussed for each direction of the rotation. It is found that the simultaneous presence of viscosity finite conductivity, rotation, medium porosity, and FLR corrections does not essentially change the Jeans's instability condition. The stabilizing influence of FLR in the case of transverse propagation is reasserted for a non-rotating and inviscid porous medium. It is shown that the finite conductivity has destabilizing influence on the transverse wave propagation whereas for longitudinal propagation finite conductivity does not affect the Jean's criterion.     

Noctilucent cloud formation and the effects of water vapor variability on temperatures in the middle atmosphere

To investigate the occurrence of low temperatures and the formation of noctilucent clouds in the summer mésosphere a one-dimensional time-dependent photochemical-thermal numerical model of the atmosphere between 50 and 120 km has been constructed. The model includes the important chemistry of the hydrogen and oxygen species and transport by eddy and molecular processes. The thermal balance incorporates: heating by solar ultraviolet radiation; transport of chemical potential energy; eddy diffusion and dissipation; molecular conduction; airglow emissions; and infrared cooling by carbon dioxide. A non- LTE parameterization is used to calculate 15 μm band cooling by carbon dioxide. The model self-consistently solves the coupled photochemical and thermal equations as perturbation equations from a reference state assumed to be in equilibrium and is used to consider the effect of variability in water vapor in the lower mesosphere on the temperature in the region of noctilucent cloud formation. It is found that change in water vapor from an equilibrium value of 5 ppm at 50 km to a value of 10 ppm, a variation consistent with observations, can produce a ~ 15 K drop in temperature at 82 km. It is suggested that this process may produce long periods (weeks) of cold temperatures and influence noctilucent cloud formation.     

Alkali elemental and potassium isotopic compositions of Semarkona chondrules

Abstract— We report measurements of K isotope ratios in 28 Semarkona chondrules with a wide range of petrologic types and bulk compositions as well as the compositions of CPX‐mesostasis pairs in 17 type I Semarkona chondrules, including two chondrules with radial alkali zonation and 19 type II chondrules. Despite the wide range in K/Al ratios, no systematic variations in K isotopic compositions were found. Semarkona chondrules do not record a simple history of Rayleigh‐type loss of K. Experimentally determined evaporation rates suggest that considerable alkali evaporation would have occurred during chondrule formation. Nevertheless, based on Na CPX‐mesostasis distribution coefficients, the alkali contents of the cores of most chondrules in Semarkona were probably established at the time of final crystallization. However, Na CPX‐mesostasis distribution coefficients also show that alkali zonation in type I Semarkona chondrules was produced by entry of alkalis after solidification, probably during parent body alteration. This alkali metasomatism may have gone to completion in some chondrules. Our preferred explanation for the lack of systematic isotopic enrichments, even in alkali depleted type I chondrule cores, is that they exchanged with the ambient gas as they cooled.     

Four-element CODAR beam forming

An HF radar called the Coastal Ocean Dynamics Applications Radar (CODAR) is presently being used in several forms to measure ocean surface parameters. The original version was developed by the National Oceanic and Atmospheric Administration (NOAA) and utilizes a four-element receive array. The array consists of four equally spaced elements arranged on a circle with a radius of 0.2151 wavelengths (at 25.4 MHz). It was designed to measure ocean currents using a direction-finding technique based on an extension to a simple two-element interferometer. The problem of determining the bearing of a radiating source can be readily shown to be equivalent to that incurred in spectral estimation. In an attempt to improve upon the processing of existing data, modern nonlinear spectral estimation techniques are applied in a beam-forming bearing estimation procedure and compared against several direction-finding algorithms. Enhancement of bearing estimators via analysis of the eigenstructure of a spatial correlation matrix is included. Antenna response patterns are calculated and used to investigate properties of direction-finding algorithms. Simulated data are used for a comparison of direction finding and beam forming. The asymmetrical bias of each method is investigated to determine its effect on the error in estimating the angle of arrival of a radar target.