Operational requirements and the geometry of a station-keeping maneuver

In this paper station-keeping is regarded as the specialization of relative motion referred to a moving, orbiting origin. For this study a well-known linear solution to this problem serves as a base formulation from which the investigation begins.Even though the overall problem could be separated into three parts—necessitating two distinct studies for coverage—this paper examines only the last phase of the operation. That is, it is the continuation, or retention, of a relative motion sub-orbit which is of interest in this analysis.The situation becomes one of determining what is needed to maintain the sub-orbit, and/or to adjust it. In addition, the consequences of these actions, and the results predicted from theory are established, examined, and commented upon. In the presentation of information gathered from this study, various graphs have been prepared; however, these are expressed in a dimensionless format so that the results apply equally to all reasonable reference orbits.For this analysis the separate and combined influences, due to both the initial relative motion state and to a thrusting condition, are examined. Also, the consequences of referencing the acquired sub-orbits to an inertially aligned frame of reference (rather than the familiar rotating one) are illustrated, discussed, and commented upon.Formerly: Sr. Analyst and Manager, Seabrook Office, AMA, Inc., Seabrook, Md., U.S.A.     

The absorption of energetic electrons by argon gas

The processes by which energetic electrons lose energy in a weakly ionized gas of argon are analysed and calculations are carried out taking into account the discrete nature of the excitation processes. The excitation, ionization and heating efficiences are computed for energies up to 200 eV absorbed in a gas with fractional ionizations varying up to 10^?2.     

A model for thinning of the plasma sheet

A one-dimensional model for thinning of the plasma sheet is developed on the basis of launching a fast mode MHD rarefaction wave propagating in the tailward direction along the plasma sheet. Behind the rarefaction wave the pressure is reduced, leading to thinning of the plasma sheet and also to an Earthward plasma flow with a speed on the order of the sound speed a₀. The plasma sheet thickness is reduced by a factor of 2 if an Earthward plasma flow speed of 0.8a₀ is induced. The predictions of the model are in reasonable agreement with observations.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

Auroral ion velocity distributions for a polarization collision model

We have calculated the effect that convection electric fields have on the velocity distribution of auroral ions at the altitudes where the plasma is weakly-ionized and where the various ion-neutral collision frequencies are much smaller than the ion cyclotron frequencies, i.e. between about 130 and 300 km. The appropriate Boltzmann equation has been solved by expanding the ion velocity distribution function in a generalized orthogonal polynomial series about a bi-Maxwellian weight factor. We have retained enough terms in the series expansion to enable us to obtain reliable quantitative results for electric field strengths as large as 90 mV m^?1. Although we have considered a range of ion-neutral scattering mechanisms, our main emphasis has been devoted to the long-range polarization interaction. In general, we have found that to lowest order the ion velocity distribution is better represented by a two-temperature or bi-Maxwellian distribution than by a one-temperature Maxwellian, with there being different ion temperatures parallel and perpendicular to the geomagnetic field. However, the departures from this zeroth-order bi-Maxwellian distribution become significant when the ion drift velocity approaches (or exceeds) the neutral thermal speed.     

The ion-composition of the plasma produced by impacts of fast dust particles

The composition of the impact plasma produced by fast dust particles (v > 1 km/sec) hitting an Au or W target was measured both with a model of the HELIOS micrometeoroid experiment (low electric field at the target) and a high field detector. The plasma composition and the total plasma charge depend strongly on the impact velocity and the electric field strength at the target. Spectra of 9 different projectile-target combinations were analysed. Two types of spectra could be observed, depending on the projectile material. (1) Spectra of metals and hard dielectrics (Mohs' hardness ? 5). Particle constituents of low ionisation energy (e · u ? 7eV, e.g. Na, K, Al) dominate the spectra of these materials at impact velocities below 10 km/sec. At higher speed the relative intensities change and new ions with higher ionisation energies appear. (2) Spectra of soft dielectrics (Mohs' hardness < 3). Below 9 km/sec these materials produced less total charge than did the others. The highest masses were detected at 74 amu. The relative abundance of ions with low ionization energies such as Li, Na, K, etc. is comparatively small. Negative ions were also observed in the impact plasma. Their total number was found to be approximately 3–6% of that of the positive ions at 6 km/sec particle speed.     

Fitting of hydrodynamic and kinetic solar wind models

In isothermal models of the expanding solar corona there exists in general an exobase level where the collision mean free path becomes equal to the density scale height. At this level the hydrodynamic approximations of the transport equations fail to be justified and a kinetic approach is more appropriate. This exobase is located below the altitude of the critical point proper to the hydrodynamic solutions. The bulk velocity at the exobase is subsonic and smaller than the expansion velocity at the critical point. Therefore the transition to a supersonic solar wind velocity occurs in the collisionless ion-exosphere.     

Distribution of minor constituents in a thermal interface

A non-steady, two-dimensional, compressible mathematical model of a fluid with constant viscosity and thermal conductivity is given in order to represent a thin atmospheric layer located at 60 km height, as a function of a known initial vertical distribution of temperature, chemical concentrations of minor components and assumed free boundary conditions.The purpose of this paper is to determine the influence of convective laminar processes in the vertical distribution of minor constituents in a thermal interface. Only three minor components are considered, atomic oxygen, molecular oxygen and ozone. Numerical solutions of the stated timedependent convection problem for different Rayleigh numbers show a marked influence of the established flow pattern upon the distribution of minor constituents. In all cases, an enhancement of mean concentration gradients in relatively small regions adjacent to the warmer and colder boundaries was observed.     

Mars surface properties observed by earth-based radar at 70-, 12.5-, and 3.8-cm wavelengths

A review of Mars radar data obtained through the 1973 opposition confirms that the surface of the planet has many diverse characteristics. Analysis of the quasi-specular echo component shows changes in apparent reflectivity of at least 5 to 1. If attributed entirely to variations in surface material, these correspond to dielectric constants between 1.6 and 4.0. Values of rms surface slope on 1- to 100-m scales range from as low as 0.5° in tablelands near Vlles Marineris to more than 3.0° (the upper limit for which these analysis techniques are appropriate) in certain other areas such as inside Coprates Chasma itself. There is weak correlation between the small-scale surface characteristics inferred from radar and those inferred from Mariner 9 images, geologic maps derived from those images, and other remote sensing data sets. Topography, a large-scale surface characteristic for which good correlation exists between radar and other data sets, was not considered in this study. A search for guidelines which would allow extrapolation of radar properties to new areas on the basis of those studied has been singularly unsuccessful. Data obtained during the 1973 opposition at Arecibo, Goldstone, and Haystack Observatories indicate that the scattering behavior of Mars varies little over the 70- to 3.8-cm wavelength range. Comparison of 1971 and 1973 Goldstone results shows no detectable variation with time.     

Infrared imaging of Jupiter in the 8–14-micrometer spectral region

High spatial resolution images of Jupiter were produced on the Hale 200-in. telescope in August 1974 and October 1975. A programmable wobbling secondary was used to raster scan the planet with 64 by 64 1-arsec pixels. Images were made with broadband (8–14 μm) and several 1- and 2-μm wide filters. All images reveal a belt and zone structure similar to visible pjotographs. Belts, in the broadband data, appear to be about 2°K hotter than the zones, but contrast varies markedly in different parts of the 8–14-μm spectral region. The lowest belt-zone contrast is found in the hydrogen opacity dominated region at 12.5 μm, while images at 9.5 μm exhibit the greatest contrast. Isolated areas are observed to be as much as 4°K hotter than surrounding areas at 9.5 μm. This large contrast is probably due to variations in the distribution of the ammonia clouds in the upper atmosphere.