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
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References