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Lunar Elemental Analysis Obtained From the Apollo Gamma-Ray and X-Ray Remote Sensing Experiment

Gamma-ray and X-ray spectrometers carried in the Service Modules of the Apollo 15 and Apollo 16 spacecraft were employed for compositional mapping of the lunar surface. The measurements involved the observation of the intensity and characteristic energy distribution of gamma rays and X-rays emitted from the lunar surface. A large-scale compositional map of over 10 percent of the lunar surface was obtained from an analysis of the observed spectra. The Apollo 15 flight was at a lunar orbital inclination of 29 degrees as compared with a 9-degree inclination of the Apollo 16 flight; thus, the projected ground track of the Apollo 15 flight covered a larger projected surface area than that of the Apollo 16 flight. The objective of the X-ray experiment was to measure the K spectral lines from Mg, Al, and Si. Spectra were obtained and the data were reduced to Al/Si and Mg/Si intensity ratios and ultimately to chemical ratios. Analyses of the results have indicated (1) that the Al/Si ratios are highest in the lunar highlands and considerably lower in the maria, and (2) that the Mg/Si concentrations generally show the opposite relationship. There is a tendency for the Al/Si values to increase from the western mare areas to the eastern limb highlands. There are distinct chemical contrasts between such features: as the small mare basins and the highland rims. The objective of the gamma-ray experiment was to measure the natural and cosmic-ray-induced activity emission spectrum. At this time, the elemental abundances for Th, U, K, Fe, Ti, Si, and O have been determined over a number of major lunar regions. Regions of relatively high natural radioactivity were found in the Mare Imbrium and Oceanus Procellarum regions. High spots of natural radioactivity were also found south of Fra Mauro; somewhat southwest of Archimedes, and south of Aristarchus. An enhanced region of natural radioactivity was found around Van de Graaff on the far side of tile Moon. In regions other than Mare Imbrium and Oceanus Procellarum, an anticorrelation between natural radioactivity and lunar elevation, as determined from the Apollo laser, altimeter, has been found. From the combined results of the gamma-ray and X-ray spectrometer experiments almost complete information concerning the major element composition of over 10 percent of the lunar surface has been obtained. Distributions have also been mapped for K, Th, and Ti. Interesting correlations between lunar topography and magnetic and gravitational properties have been found.

J I Trombka

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry