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reed b keplerian ellipses physics two body problem 2019

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Textbook in PDF format This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of 'central force' orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law, and how the geometry of ellipses relates to physical quantities, such as energy and momentum. Exercises are provided, and derivations are set up in such a way that readers can gain analytic practice by filling in the missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own. Preface Acknowledgments Author biography Bruce Cameron Reed Spherical coordinates—a review Fundamental definitions Spherical coordinate unit vectors Time-derivatives of spherical coordinate unit vectors Some useful integrals Dynamical quantities in spherical coordinates Position, velocity, acceleration, angular momentum, torque, and energy Uniform circular motion: a specific case of the acceleration formula Central forces The reduced mass Central force dynamics: the potential Why an inverse-square law? Central force dynamics: conservation of angular momentum Central force dynamics: integrals of the motion Central force dynamics: acceleration in terms of the azimuthal angle The ellipse The ellipse in Cartesian and polar coordinates Area of an ellipse Area as a vector cross-product, and Kepler’s second law How did Kepler plot the orbits? Elliptical orbits and the inverse-square law: geometry meets physics Proof by assuming an elliptical orbit: angular momentum Velocity, the vis-viva equation, and energy Proof of elliptical orbits by direct integration Kepler’s third law The time–angle equation Example: an Earth-orbiting spy satellite Kepler’s equation: anomalies true, eccentric, and mean Some sundry results Average distance of a planet from the Sun Determining initial launch conditions A brief lesson in unit conversions Orientation of Earth’s orbit Some final words Outline placeholder References

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Reed B. Keplerian Ellipses. The Physics...Two-Body Problem 2019.pdf 3.5 MB

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reed b keplerian ellipses physics two body problem 2019

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