Flowgraph Techniques for Closed Systems

A two-port with both generator and load constitutes a closed system; it can be defined as a system with only interdependent variables or as a system containing no independent variables. The flowgraph describes the relationships between variables in a closed system as determined by the topology of its components. The corresponding closed flowgraph represents a zero-port network from which N-port networks can be generated as subsets by truncation of the closed system. A constraint governing any closed system expressing the properties of its cut-sets and tie-sets is referred to as the topology equation. The topology equation can be computed from the sum of loops in the closed flowgraph, and forms the key for the derivation of properties of closed systems and derived N-port subsets. Oscillators analyzed as zero-ports are discussed in detail to illustrate the rationale for the flowgraph approach to closed systems. To exploit the closed system model conceptually and computationally for N-ports, an approach is suggested and illustrated for N = 1 by an analysis of transfer functions and for N = 2 by a sensitivity analysis of stochastic networks.     

The YORP effect on the GOES 8 and GOES 10 satellites: A case study

The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is a proposed explanation for the observed rotation behavior of inactive satellites in Earth orbit. This paper further explores the YORP effect for highly asymmetric inactive satellites. Satellite models are developed to represent the GOES 8 and GOES 10 satellites, both of which are currently inactive in geosynchronous Earth orbit (GEO). A simple satellite model for the GOES 8 satellite is used to analyze the short period variations of the angular velocity and obliquity as a result of the YORP effect. A more complex model for the rotational dynamics of the GOES 8 and GOES 10 satellites are developed to probe their sensitivity and to match observed spin periods and states of these satellites. The simulated rotation periods are compared to observations for both satellites. The comparison between YORP theory and observed rotation rates for both satellites show that the YORP effect could be the cause for the observed rotational behavior. The YORP model also predicts a novel state for the GOES 8 satellite, namely that it could periodically fall into a tumbling rotation state. Recent observations of this satellite are consistent with this prediction.     

On the Detectability and Use of Normal Modes for Determining Interior Structure of Mars

The InSight mission to Mars is well underway and will be the first mission to acquire seismic data from a planet other than Earth. In order to maximise the science return of the InSight data, a multifaceted approach will be needed that seeks to investigate the seismic data from a series of different frequency windows, including body waves, surface waves, and normal modes. Here, we present a methodology based on globally-averaged models that employs the long-period information encoded in the seismic data by looking for fundamental-mode spheroidal oscillations. From a preliminary analysis of the expected signal-to-noise ratio, we find that normal modes should be detectable during nighttime in the frequency range 5–15 mHz. For improved picking of (fundamental) normal modes, we show first that those are equally spaced between 5–15 mHz and then show how this spectral spacing, obtained through autocorrelation of the Fourier-transformed time series can be further employed to select normal mode peaks more consistently. Based on this set of normal-mode spectral frequencies, we proceed to show how this data set can be inverted for globally-averaged models of interior structure (to a depth of \(\sim 250~\mbox{km}\)), while simultaneously using the resultant synthetically-approximated normal mode peaks to verify the initial peak selection. This procedure can be applied iteratively to produce a “cleaned-up” set of spectral peaks that are ultimately inverted for a “final” interior-structure model. To investigate the effect of three-dimensional (3D) structure on normal mode spectra, we constructed a 3D model of Mars that includes variations in surface and Moho topography and lateral variations in mantle structure and employed this model to compute full 3D waveforms. The resultant time series are converted to spectra and the inter-station variation hereof is compared to the variation in spectra computed using different 1D models. The comparison shows that 3D effects are less significant than the variation incurred by the difference in radial models, which suggests that our 1D approach represents an adequate approximation of the global average structure of Mars.     

The Composition of Interstellar Molecular Clouds

We consider four aspects of interstellar chemistry for comparison with comets: molecular abundances in general, relative abundances of isomers (specifically, HCN and HNC), ortho/para ratios for molecules, and isotopic fractionation, particularly for the ratio hydrogen/deuterium. Since the environment in which the solar system formed is not well constrained, we consider both isolated dark clouds where low mass stars may form and the "hot cores" that are the sites of high mass star formation. Attention is concentrated on the gas phase, since the grains are considered elsewhere in this volume. This revised version was published online in June 2006 with corrections to the Cover Date.     

Economics of the solid rocket booster for space shuttle

Solid Rocket Boosters (SRB's) became viable contenders as the booster for the Space Transportation System (STS) early in the concept studies of Space Shuttle because of their low development cost compared with equivalent liquid propellant boosters. Program risks and costs have been held down by scaling and adapting existing technology to the 146 in. SRB selected for development. To retain this low cost edge for the operational phase, NASA has concentrated on maintaining or reducing the cost of expendables and has demonstrated the feasibility of reusing the expensive nonexpendable SRB hardware. Drop tests of Titan III motor cases and nozzles in 1973 proved that boosters could survive water impact at vertical velocities of approx. 100 ft/s. SRB components have been designed with reuse in mind. In most cases, hardware designed for ascent will withstand water impact loads with little modification.

Cost effective refurbishment is a foremost design consideration. Continuing review of each component assures that design for reusability and/or cost of refurbishment does not become so costly that a low-cost expendable approach may be more cost effective.

The cost of expendables has been minimized by selecting proven propellants, insulations, and nozzle ablatives whose costs are well known. The propellant, which is approx. 95% of the expendables, is the lowest cost composite formulation available. As lower cost ablative materials such as pitch carbon fibers become available in quantity and are reliably demonstrated, they will be introduced to reduce operations costs.

Thus, by use of proven technology, low cost expendables and reuse of more expensive non-expendables, the development and operations costs of SRB's are held to a level that make the SRB an economical booster for the Space Shuttle.