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Celestial Mechanics (Tatum)

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    This book provides a mathematically rigorous and computation-focused introduction to celestial mechanics, guiding the reader from essential numerical methods and geometric foundations through the physical theory of gravitation and orbital motion. It develops the tools needed to describe and compute celestial trajectories, beginning with numerical analysis, conic sections, trigonometry, and three-dimensional coordinate geometry, then applying Newtonian gravity to a wide range of mass distributions. The text bridges theory and observation through detailed treatments of the celestial sphere, time, planetary motion, and the two-body problem, leading to practical methods for ephemeris computation and orbit determination. Advanced topics such as perturbation theory, the restricted three-body problem, and Lagrangian points extend the analysis beyond idealized systems, while applications to photographic and CCD astrometry and to visual and spectroscopic binary stars demonstrate how observational data are used to derive orbital elements, masses, and velocities in real astronomical systems.

    Thumbnail: Deep exposures of Nebulae (CC BY-SA 4.0 Intermational; Ngc1535 via Wikipedia; Adam Block/Mount Lemmon SkyCenter/University of Arizona).​​​​​​

    This page titled Celestial Mechanics (Tatum) is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.