Eccentric lunar frozen orbits are analyzed in this study in relation to lunar navigation and communications missions, particularly the proposed Magnolia-1 mission. An overview of the Earth/Moon system, frozen orbits, and the Magnolia-1 mission is provided. A review of existing literature is presented, and potential limitations are discussed. Both preliminary and numerical perturbation analyses are presented, and a general set of perturbations for further analysis of high-altitude lunar orbits is identified. Analysis of potential orbits for the Magnolia-1 mission is performed through calculation of a maximum deviation metric and through visualization as a function of initial orbital elements. Trends are identified within a closed search space by varying elements individually and in combination. Potential orbit designs for the Magnolia-1 mission are selected and compared to established alternatives. A method of orbit refinement is used to improve behavior, and coverage and eclipse analyses are performed to establish suitability. Conclusions are made involving general trends related to eccentric lunar frozen orbits and the specific designs proposed for the Magnolia-1 mission, and a method for the design of similar orbits is suggested. Ideas for further study are also presented.

The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups, and those obtained for two-dimensional electron gas systems whenever it is possible. It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities. Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values, which may be observed experimentally, are found.