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.     

Emission line shapes produced by dissociative excitation of atmospheric gases

Special line shapes are derived fro the λ 1356 Å (${}^5\text{S}{}^0\text{-}{}^3\text{P}$) transition of atomic oxygen from metastable (${}^5\text{S}{}^0\text{-}{}^3\text{P}$) time-of-flight spectra produced by electron impact dissociative excitation of O₂, CO₂, CO, and NO, and they are compared with the broadened λ 1304 A resonance line shapes deduced by Poland and Lawrence (1973) from atomic oxygen absorption studies. The non-thermal line shapes for both airglow emission features are shown to have an effective width comparable to a 60,000 K thermal doppler line shape for an electron impact energy of 100eV. The variation of the effective line width with electron-impact energy from threshold to 300 eV is given. Since the effective line width of the resonance radiation produced by dissociative excitation is very large compared with the doppler absorption widths of the ambient O atoms at normal exospheric temperatures, the anomalously broadened resonance lines will propagate through a planetary atmosphere as though they were optically thin. Thus, electron-impact dissociation of CO and CO₂ will contribute to the observed optically thin component of the λ 1304 Å emission in the upper atmospheres of Venus and Mars. However, the process cannot account for more than 10% of the observed optically thin emission because of the small magnitude of the excitation cross-section and the comparatively high-energy threshold for the process. The possibility that the source of the kinetically energetic $\text{O}\text{(}{}^3\text{S}$) atoms is the dissociative recombination of vibrationally excited CO₂⁺ ions is discussed.     

Higher order curvature terms in theories with creation

In two theories involving continuous creation higher order curvature terms are added to the field equations. At high gravitational curvatures the creation of matter depends critically on these extra terms.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

The thermal continuum in coronal loops: The influence of finite resistivity on the continuous spectrum

The normal mode spectrum for the linearized MHD equations is investigated for a cylindrical equilibrium. This spectrum is examined for zero perpendicular thermal conduction, with both zero and non-zero scalar resistivity. Particular attention is paid to the continuous branches of this spectrum, or continuous spectra. For zero resistivity there are three types of continuous spectra present, namely the Alfvén, slow, and thermal continua. It is shown that when dissipation due to resistivity is included, the slow and Alfvén continua are removed and that the thermal continuum is shifted to a different position (where the shift is independent of the exact value of resistivity). The old location of the thermal continuum is covered by a dense set of nearly singular discrete modes called a quasi-continuum. The quasi-continuum is investigated numerically, and the eigenfunctions are shown to have rapid spatial oscillating behaviour. These oscillations are confined to the most unstable part of the equilibrium based on the Field criterion, and may be the cause of fine structure in prominences.     

Nonlinear curvature Lagrangians and extended inflation in the early universe

Theories with Lagrangians nonlinear in the curvature scalar can be reduced by appropriate transformations to a form similar to the Brans-Dicke model. This may enable us to have extended inflation in the early universe without the difficulties of introducing scalar fields.     

Numerical simulations of granular dynamics II: Particle dynamics in a shaken granular material

Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties.We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration.We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments.     

The Opportunities and Challenges in the Use of Extra-Terrestrial Acoustics in the Exploration of the Oceans of Icy Planetary Bodies

Acoustic radiation is the signal of choice for exploring Earth??s oceans. Its potential application for the oceans of icy moons requires investigation. However acoustic technology needs to be treated with care for extra-terrestrial purposes. Instruments, calibrations, and predictive codes that have served well on Earth may require fundamental redesign for use on other worlds. However when such an assessment is achieved, acoustic signals open up the possibility of exploring volumes exceeding one million cubic kilometres in a few minutes. This paper begins at tutorial level for novice acousticians, illustrating the principles by which acoustics can be used to monitor the environment at great distances from the source, both by projecting out signals and by using natural signals of opportunity. It then progresses to calculations for a generic icy moon (which resembles, but does not model Europa), proceeding from tutorial calculations of ??flat world?? models to calculate the propagation times for pulses to circumpropagate around the entire moon. Given that a single emitted pulse can produce multiple arrivals from different propagation paths, the paper discusses how the structure of the received time history can be used to monitor changes in the temperature profile in the ocean, position of the water/ice layer and the asphericity of the moon during orbit.     

PKS2250-41 and the Role of Jet Cloud Interactions in Powerful Radio Galaxies

We have studied the effects of the interaction between the radio jet and the ambient gas in the powerful radio galaxy PKS2250-41 (z = 0.31). Our results show that the gas has been accelerated, compressed, heated and collisionally ionized by the shock. This study helps us to understand the processes which determine the observed properties of many high redshift radio galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.