Topological properties of disjoint channel networks within enclosed regions

Enclosure of some portion of one or more natural stream-drainage basins by superposition of a rectangle on a map of drainage network results in fragmentation of the natural basins into a set of disjoint channel networks. Each of these may have some channel links and forks of the natural network plus truncated links intersected by the enclosure boundary. The topological properties of the network elements in the enclosure are used to set up a model of random network patterns, in which the number of disjoint channel networks is expressed as a function of the number of links and forks in the enclosures. This function is shown to be a multiplicative constant times the square root of the number of links or forks. Empirical data on square and rectangular enclosures of several sizes from the Inez (Kentucky)Quadrangle map showed that the predicted multiplicative constants do not agree with observation, but that the square-root relation seems to hold at least to a first approximation. The models thus can be used as a norm against which deviations of real-world enclosures from network pattern randomness can be studied.     

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Lunar nomenclature: A dissenting note

This note reviews the nature of the traditional (Mädler) lunar nomenclature and the recent developments based on the use of more than 2000 named provinces. It appears that the new nomenclature is less efficient than the old in many cases and may lead to an impossible publication situation. The unnecessary break with the past is especially critized.     

A model for solar oscillations at cm and mm wavelengths

It is suggested that large scale oscillations of the Sun give rise to the periodic fluctuations observed in the quiet Sun at radio wavelengths. These fluctuations would be most readily observed from regions where there is a large gradient of electron temperature with electron density, and are thus more readily observed at cm wavelengths than at millimetre wavelengths.     

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.