This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, and the Vinti (Earth-satellite) problems. The analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions and the work highlights shared features in the unified treatment of the three problems. The work will be of interest to graduate students in mathematics and physics (including physical chemistry) and researchers concerned with the general areas of dynamical systems, statistical mechanics, and mathematical physics and has direct application to celestial mechanics, astronomy, orbital mechanics, and aerospace engineering.

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