Keplerian ellipses :a student guide to the physics of the gravitational two-body problem /

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"Version: 202303"--Title page verso.Includes bibliographical references.1. Polar coordinates--a review -- 1.1. Fundamental definitions -- 1.2. Polar coordinate unit vectors -- 1.3. Time derivatives of polar coordinate unit vectors -- 1.4. Some useful integrals and expansions2. Dynamical quantities in polar coordinates -- 2.1. Position, velocity, acceleration, angular momentum, torque, and energy -- 2.2. Uniform circular motion : a specific case of the acceleration formula3. Central forces -- 3.1. The center of mass and the reduced mass -- 3.2. Central force dynamics : the potential -- 3.3. Why an inverse-square law? The sesquialterate proportion -- 3.4. Central force dynamics : conservation of angular momentum -- 3.5. Central force dynamics : integrals of the motion -- 3.6. Central force dynamics : acceleration in terms of the azimuthal angle -- 3.7. Newton's shell-point equivalency theorem4. The ellipse -- 4.1. The ellipse in polar and Cartesian coordinates -- 4.2. Area of an ellipse -- 4.3. Area as a vector cross-product, and Kepler's second law -- 4.4. How did Kepler plot the orbits? -- 4.5. The optical theorem for ellipses5. Elliptical orbits and the inverse-square law : geometry meets physics -- 5.1. Proof by assuming an elliptical orbit : angular momentum -- 5.2. Velocity, the vis-viva equation, and energy -- 5.3. Proof of elliptical orbits by direct integration -- 5.4. Kepler's third law -- 5.5. The time-angle equation -- 5.6. Example : an Earth-orbiting spy satellite -- 5.7. The Laplace-Runge-Lenz vector -- 5.8. Kepler's third law for non-inverse-square central forces -- 5.9. The effective potential -- 5.10. A taste of perturbation theory -- 5.11. Escape velocity6. Kepler's equation : anomalies true, eccentric, and mean -- 7. Transfer and rendezvous orbits -- 7.1. The Hohmann ellipse transfer orbit -- 7.2. The Lambert problem -- 7.3. The ham sandwich throw8. Some sundry results -- 8.1. Average distance of a planet from the Sun -- 8.2. Time-average orbital speed -- 8.3. Determining initial launch conditions -- 8.4. The l2 Lagrange point and the James Webb Space Telescope -- 8.5. An approximate treatment of Mercury's perihelion advance -- 8.6. A brief lesson in unit conversion -- 8.7. Orientation of Earth's orbit -- 8.8. Motion of the Sun -- 8.9. Gravitational scattering -- 8.10. Some final wordsAppendix A. Spherical coordinates -- Appendix B. Circular-orbit perturbation theory for non-inverse-square central forces -- Appendix C. Further reading -- Appendix D. Summary of useful formulae -- Appendix E. Glossary of symbols.Kepler's three laws of planetary motion were a stunning development in human intellectual history. This second edition is a concise, self-contained treatment of Kepler/Newton planetary orbits at the level of an advanced undergraduate physics student. New to this edition are elements such as a detailed derivation of Newton's shell-point equivalency theorem, a revised derivation of the polar equation for an ellipse, Kepler's third law for non-inverse-square central potentials, a chapter on transfer and rendezvous orbits, and an expanded treatment of methods of calculating the average distance between the Sun and a planet. The approach is student-friendly, featuring brief sections, clear notation and diagrams, and mathematics that undergraduates will be comfortable with, accompanied by numerous exercises.Undergraduate physics/astronomy students; higher-level students who need a compact refresher.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Bruce Cameron Reed is the Charles A. Dana Professor of Physics Emeritus at Alma College, Michigan, with a 35-year career of undergraduate-level teaching in Canada and the United States. He has published around 140 regular journal papers, 60 semi-popular articles, review papers, and book reviews, plus eight texts on the Manhattan Project, quantum mechanics, and Keplerian orbits. In 2009, he was elected a Fellow of the American Physical Society. He has served as Editor of American Physical Society's "Physics & Society" newsletter for four years (2009-13), and is currently an Associate Editor with American Journal of Physics.Title from PDF title page (viewed on March 31, 2023).

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Publisher

: .,

Collation

1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9780750356084

Classification

521.1/1

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-

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-

Edition

Second edition.

Subject(s)

SCIENCE / Space Science / Astronomy.
Theoretical & mathematical astronomy.
Two-body problem.
Elliptical orbits.
Celestial mechanics.
Kepler\'s laws.

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Bruce Cameron Reed.

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