Keplerian Ellipses (Second Edition)

Celestial mechanics is the crown jewel of Newtonian physics. Building on the observational and theoretical work of Galileo, Tycho Brahe, Copernicus, Kepler and others, Isaac Newton deployed his hypothesized law of universal gravitation and his newly-developed calculus to show why the orbits of the Moon and planets have the shapes they do: Kepler's three laws of planetary motion. Contrived systems of equants, deferents, and epicycles gave way to a single elliptical orbit for each planet. This new approach facilitated predictions of celestial phenomena to unprecedented levels of accuracy, and the realization that these orbits reflected an underlying universal physical law whose validity extended from the firmament of the Earth to the remotest cosmos marked the birth of modern science. This volume will be a concise but self-contained treatment of Kepler/Newton orbits for students at about the third-year undergraduate level. The aim is for a student-friendly volume by using brief sections, clear notation and diagrams, and keeping the mathematics to the level of vector calculus and spherical coordinates that such students will be comfortable with.

Key Features:

• Provides a compact, self-contained treatment of a universally-interesting topic

• Sections are brief, with emphasis put on clear first-principles discussions of the interpretations of calculations and expressions

• Student-friendly, with numerous worked examples, clear notation, and exercises

• Sets a solid foundation for more advanced studies of phenomena such as orbital perturbations, precession, and unbound orbits