The constrained normal form algorithm

This paper describes an algorithm which brings a regularizable polynomial perturbation of a three degree of freedom Kepler problem into a normal form which Poisson commutes with the Kepler Hamiltonian. We illustrate the alogrithm with an example: the quadratic Zeeman effect. For other applications of this algorithm see [1],[4], and [5]. The authors have written a program in MAPLE which implements the constrained normal form.     

The formation of Mg i 4571 Å in the solar atmosphere

An analysis of the 4571 Å line of neutral magnesium is presented in which one-dimensional macroscopic velocity fields are included. It is shown that gradients over restricted heights in the vertical and horizontal components of the velocity field of order -0.005 s^–1 and -0.004 s^–1 (such that velocity towards the observer decreases as height increases), respectively, result in asymmetries in the computed line profile similar to those observed. The heights in the solar atmosphere at which these velocity gradients exist are shown to be very critical in reproducing the observations. It was found that the best results were obtained when the gradients existed in the height range from 200 km to 300 km below the temperature minimum. The results indicate that for the Mg i 4571 Å line model calculations that do not include one-dimensional flow velocities may safely be compared with frequency-averaged observations.     

Solar soft X-rays and solar activity

Flare-associated soft X-ray bursts (8–12 Å) are examined for 283 events observed by OSO-III. These bursts are shown to be predominantly thermal in nature. Their time-profiles are roughly similar to those of the associated H flares, although the X-ray burst begins about two minutes earlier, on the average. The strength of the soft X-ray burst is directly related to the area and brilliance of the flare, the age and flare-richness of the associated plage, and the general level of solar activity at the time of the burst. The peak enhancements in the soft X-ray and H emission rates during flares are of the same order of magnitude, as are the total flare energies radiated at these wavelengths. We estimate that soft X-radiation accounts for up to 10% of a flare's total electromagnetic emission.NRC/NAS Resident Research Associate.     

Gravity-gradient stabilization of gyrostat satellites with rotor axes in principal planes

Three special classes of equilibrium orientations of gyrostat satellites subject to gravitational torques have been treated in the literature. Here we find the set of all equilibria for a restricted class of gyrostat configurations. Those configurations for which the internal angular momentum vector (or the rotor axis) is aligned with a principal axis have been treated in a separate work, where it is shown that at one, and only one, rotor speed there exists a continuum of equilibrium orientations. When the rotor axis is moved away from a principal axis in such a way that it is contained in a plane formed by two principal axes, it is shown that the continuum disappears, and we have a new set of eight equilibrium orientations which have not previously been described. The stability of these orientations is then investigated using the Hamiltonian as a Liapunov testing function. For properly chosen satellite inertia ratios some of these orientations are stable, and might be used in future gravitygradient stabilized satellites.This research is sponsored by the United States Air Force under Project RAND-Contract No. F44620-67-C-0045-monitored by the Directorate of Operational Requirements and Development Plans, Deputy Chief of Staff, Research and Development, Hq. USAF. Views or conclusions contained in this study should not be interpreted as representing the official opinion or policy of the United States Air Force. The material presented here was originally published in RAND Corporation Memorandum RM-5921-PR. The author wishes to acknowledge his indebtedness to Dr. R. E. Roberson for helpful discussions, and for suggesting a research area, part of which is treated here.     

Soft solar X-rays and solar activity

Soft X-radiation between 8–12 Å was found to be emitted from the Sun at the time of four optically-identified major systems of loop prominences. The peak emission rates and time-integrated X-ray energies are very similar for three of the events while the fourth appeared to emit X-rays only weakly. The data are not consistent with a compression-condensation model for the loops, and support the fast-proton injection model. Proton injection may take place on a long time scale.     

Radar observations at 3.5 and 12.6 cm wavelength of asteroid 433 Eros

A study of the asteroid 433 Eros using 3.5 and 12.6 cm radar waves indicates that the surface is very much rougher than any planetary or lunar surface observed by this method. A surface completely covered with sharp edges, pits, subsurface holes, or embedded chunks with scale sizes on the order of our wavelengths seems to be indicated. A model based on a rough rotating triaxial ellipsoid having radii in the rotation equator of 18.6 and 7.9 km agrees well with our data, although a strong wobble in the apparent center frequency of the spectra as rotation progresses indicates that one side may be more reflective than the other, or more likely, that the projected axis of rotation does not equally divide the projected area.     

The infrared spectrum of asteroid 433 Eros

The mineralogical composition of asteroid Eros has been determined from its infrared spectrum (0.9–2.7μm; 28cm^?1 resolution). Major minerals include metallic NiFe and pyroxene; no spectroscopic evidence for olivine or plagioclase feldspar was found. The IR spectrum of Eros is most consistent with a stony-iron composition.     

Optimal configurations for dual-spin satellites subject to gravitational torques

Dual-spin or gyrostat satellites subject to gravitational torques can adopt an infinite number of possible equilibria obtained by adjusting the magnitude and direction of the rotor angular momentum within the satellite. This paper seeks to answer the question, which of these equilibria is best — and best is chosen here to mean most stable in the sense that the energy required to perturb the orientation by any prescribed amount is maximized, i.e. the smallest eigenvalue of the Hessian matrix of the dynamic potential energy is maximized. Using this criterion, it is shown that the conventional configuration for dual-spin satellites with the angular momentum of the rotor, the spacecraft principal axis of maximum moment of inertia, and the perpendicular to the orbital plane coincident is not always the best orientation. The optimal configuration is shown to have the minimum moment of inertia always aligned with the local vertical, but the principal axis of maximum moment of inertia, shifts from the perpendicular to the orbital plane to lying in-plane as the angular momentum of the rotor is increased from zero (corresponding to a rigid gravity gradient satellite) to some sufficiently large value which is determined as a function of parameters. For angular momentum greater than this value, global optimality is established analytically, and otherwise local optimality is proved analytically with global optimality demonstrated numerically.     

The nature of cosmic ray sources

The limitations on the nature of cosmic ray acceleration regions and processes, as deduced from cosmic ray measurements and propagation studies, are reviewed. The power requirements for these acceleration regions are estimated from measurements of the local cosmic ray energy density, anisotropy and spallation-deduced pathlength. Possible constraints on the acceleration spectrum of the cosmic rays and on a charge dependence of the acceleration process, implied by the measured cosmic ray spectrum and composition, are considered. Various suggested sources and processes of cosmic ray acceleration are discussed in the light of these limitations.Astrophysics and Space Science Review Paper.     

A SPATIAL ANALYSIS OF AGRICULTURAL INTENSITY IN A BASOTHO VILLAGE OF SOUTHERN AFRICA

The effect of distance upon agricultural production should be as apparent among primitive subsistence agriculturalists as in market-oriented societies. This analysis of yield variations among the Basotho of southern Africa attempts to determine the frictional effect of distance. The results show that distance does not explain variations in yield even when other physical factors are held constant. Perhaps such variables as household characteristics, not included in the analysis, would provide a better explanation.