Motion of test particles in parabolic density distributions

A detailed study of the motion of test-particles [either having a nonzero rest-mass or zero rest-mass] has been carried out for Tolman's type VII solution with vanishing surface density, which is one of the few physically relevant exact solutions of Einstein's field equations for static and spherically symmetric mass distributions.The trapping angles, 0, at which the test-particles escape these configurations are calculated and the trajectories of test-particles are studied in detail. The types of trajectories found for this spacetime geometry are: (1) arc-like trajectories, (2) spiral-like trajectories ending into a circle of constant radius, (3) trajectories with a cusp at the minimum distance, (4) double-bounded trajectories, and (5) double-bounded trajectories with a cusp at the minimum distance. The test-particles following the trajectories of type (1) and type (3) escape the configuration while others are trapped within the structure. Besides the advancement of periastron of the orbits the retrogradation of periastrons are also observed.The stability of the structures is considered by using the variational method (Chandrasekhar, 1964a,b), and its is seen that the structures remain stable at least for a central redshift,z0, as large as 5.09.These studies may distinguish relativistic cluster from a Newtonian one and may find application to the local models of quasi-stellar objects (QSOs).     

Wound magnetostatics and flaring

We discuss the winding of a force-free axisymmetric magnetic field rooted on a heavy conductor onz=0. In quadrupolar symmetry the field expands in the half-spacez>0 and the toroidal flux concentrates on a conical surface. After a mean twist of 208°, the conical layer hosts large toroidal current loops with reversal of the magnetic flux on either side. The evolution of the field structure is described by scale-free static solutionsBr ^–(p+2), withp taking values between 0 and 2. The large expansion factor of the field structure is suggestive of flaring originating on the solar photosphere.     

Height dependence of the amplitudes of solar oscillations viewed with a potassium resonance scattering spectrometer

Over the course of the year, the variation in the solar line-of-sight velocity causes a change in the heights in the photosphere which are analysed by the red and blue passbands of a resonance scattering spectrometer. This in turn would be expected to produce a variation in the ratio of acoustic amplitudes measured in each passband. Using data from the Tenerife spectrometer of the Birmingham Solar Oscillations Network (BiSON), we demonstrate such a seasonal change. We then use the Eddington-Barbier approximation and an atmospheric model to convert the magnitude of this trend in velocity ratio with line-of-sight velocity into an approximate value of 580 km for the velocity-amplitude scale height. However, a simple argument suggests that Doppler imaging causes this to be an overestimate of the true value.     

Brief description of bare essentials of surface transfer and results from simulations with the HAPEX-MOBILHY data

The Bare Essentials of Surface Transfer (BEST) land surface scheme is briefly described and the key physical parameterisations discussed. Results are then presented to illustrate how the model performs, with forcing data for HAPEX-MOBILHY, compared to a series of other schemes in the simulation of evaporation and sensible heat. The implications of the models performance, and some indications of the future development of the scheme are provided. The basic version of BEST was found to overestimate evaporation for the HAPEX-MOBILHY data, simulating 816 mm yr⁻¹ compared to a range of 550 to 816 mm yr⁻¹ for all models. A modification to the β parameterisation reduced the evaporation to 759 mm yr⁻¹ which, although an improvement, is still probably too high.     

Mariner 9 ultraviolet spectrometer experiment: Vertical distribution of ozone on Mars

The vertical distribution of ozone in the atmosphere of Mars is computed from ultraviolet spectra obtained by the Mariner 9 spacecraft. In the Northern Hemisphere the ozone scale height is much smaller than the atmospheric scale height in midlatitudes and increases rapidly to a maximum farther north. At high latitudes (above 60°) there is no significant difference between the scale heights of ozone in the Northern (winter) Hemisphere and the Southern (summer) Hemisphere. Comparison of the ozone distribution with atmospheric temperature structure indicates that at some locations in the North, the density of water vapor increases with altitude, and the time for vertical mixing is about 3 days or more.     

General features of the magnetic field of the equatorial electrojet measured by the POGO satellites

The magnitude of the equatorial electrojet signature, S, is a measure of its magnetic field at the location of the satellite recording the signature. The general features of the large quantity of the magnetic field data of the electrojet observed by the series of POGO satellites from 1967 to 1970 have been studied here. We have compared the position of the axis of the electrojet as indicated by the position of the minimum of the electrojet signature with the position of the dip equator on the Earth's surface, and we find no significant latitudinal shift of the electrojet axis from the dip equator on the Earth. Apart from the expected decrease of the magnetic field of the electrojet with altitude above the electrojet, we have found unexpected cases in which the field increases with altitude. More surprisingly, we have discovered that the magnitude of S oscillates with altitude having maxima at about 460km and 635km and minima at about 580km and 725km, with a mean wavelength of 160 ± 29 km. It is suggested that this could be caused by additional weak current layers flowing above the main electrojet at about 110 km altitude. It is also pointed out that Onwumechili's model based on a single current system of the equatorial electrojet predicts field oscillation with altitude. The model therefore shows that a field oscillating with altitude can also result from a single complicated system of current unaided by additional current layers.     

The identification of the 3μ spectral feature in galactic infrared sources

We show that a 3 extinction feature in galactic infrared sources cannot be due to water-ice grains. Infrared spectra with a resolution of /=0.015 are in remarkably close agreement with the 2.5–4 extinction properties calculated for bacterial grains.     

Solar gravitational redshift

Wavelengths of solar spectrum lines should be shifted toward the red by the Sun's gravitational field as predicted by metric theories of gravity according to the principle of equivalence. Photographic wavelengths of 738 solar Fe i lines and their corresponding laboratory wavelengths have been studied. The measured solar wavelength minus the laboratory wavelength (_observed) averaged for the strong lines agrees well with the theoretically predicted shift (_theoretical). Studies show that the departures depend on line strength. No dependence of the departures on wavelength was found within the existing data.By studying strong lines over a wide spectral range, velocity shifts caused by the complex motions in the solar atmosphere seem to affect the results in a minimal fashion.     

Solar flares and the cosmic ray intensity

The relationship between the cosmic ray intensity and solar activity during solar cycle 20 is discussed. A model is developed whereby it is possible to simulate the observed cosmic ray intensity from the observed number of solar flares of importance 1. This model leads to a radius for the modulation region of 60–70 AU. It is suggested that high speed solar streams also made a small contribution to the modulation of cosmic rays during solar cycle 20.     

Optimal station keeping by electric propulsion with thrust operation constraints

The orbit of a geostationary satellite has to be corrected from time to time in order to compensate for the effects of various perturbations. This is usually done by means of a system of thrusters mounted on the satellite. In this paper a method is developed to find the optimal thrusting strategy for the case of an electric propulsion system under given limitations on thrust magnitude and operation times. Optimization techniques are applied to minimize a cost function which is a weighted combination of fuel consumption and station keeping errors.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.