**The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics.**
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.

nexusstc/Keplerian Ellipses: The Physics of the Gravitational Two-Body Problem/40cadee2baaa6a1f2e70c288a0b02ad5.pdf

lgli/Keplerian Ellipses.pdf

lgrsnf/Keplerian Ellipses.pdf

zlib/Physics/Theory of Relativity and Gravitation/Reed, Bruce Cameron/Keplerian Ellipses: The Physics of the Gravitational Two-Body Problem_19020795.pdf

Bruce Cameron Reed

Morgan & Claypool Publishers

IOP Concise Physics

Morgan & Claypool Publishers, San Rafael [California] [40 Oak Drive, San Rafael, CA, 94903, USA], 2019

United States, United States of America

producers:
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PRELIMS.pdf 1
Preface 10
Acknowledgments 14
Author biography 15
Bruce Cameron Reed 15
CH001.pdf 1
Chapter 1 Spherical coordinates—a review 16
1.1 Fundamental definitions 16
1.2 Spherical coordinate unit vectors 16
1.3 Time-derivatives of spherical coordinate unit vectors 18
1.4 Some useful integrals 19
CH002.pdf 1
Chapter 2 Dynamical quantities in spherical coordinates 20
2.1 Position, velocity, acceleration, angular momentum, torque, and energy 20
2.2 Uniform circular motion: a specific case of the acceleration formula 22
CH003.pdf 1
Chapter 3 Central forces 23
3.1 The reduced mass 23
3.2 Central force dynamics: the potential 25
3.3 Why an inverse-square law? 28
3.4 Central force dynamics: conservation of angular momentum 30
3.5 Central force dynamics: integrals of the motion 32
3.6 Central force dynamics: acceleration in terms of the azimuthal angle 33
CH004.pdf 1
Chapter 4 The ellipse 36
4.1 The ellipse in Cartesian and polar coordinates 36
4.2 Area of an ellipse 39
4.3 Area as a vector cross-product, and Kepler’s second law 39
4.4 How did Kepler plot the orbits? 41
CH005.pdf 1
Chapter 5 Elliptical orbits and the inverse-square law: geometry meets physics 43
5.1 Proof by assuming an elliptical orbit: angular momentum 43
5.2 Velocity, the vis-viva equation, and energy 45
5.3 Proof of elliptical orbits by direct integration 46
5.4 Kepler’s third law 49
5.5 The time–angle equation 50
5.6 Example: an Earth-orbiting spy satellite 52
CH006.pdf 1
Chapter 6 Kepler’s equation: anomalies true, eccentric, and mean 55
CH007.pdf 1
Chapter 7 Some sundry results 60
7.1 Average distance of a planet from the Sun 60
7.2 Determining initial launch conditions 62
7.3 A brief lesson in unit conversions 64
7.4 Orientation of Earth’s orbit 65
7.5 Some final words 69
BIBLIO.pdf 1
Outline placeholder 0
References 70

The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. 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 the 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

2022-01-26