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

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 d...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Reed, Bruce Cameron (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2023]
Edición:Second edition.
Colección:IOP (Series). Release 22.
AAS-IOP astronomy. 2022 collection.
Temas:
Two-body problem.
Elliptical orbits.
Celestial mechanics.
Kepler's laws.
Theoretical & mathematical astronomy.
SCIENCE / Space Science / Astronomy.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 expansions
  • 2. 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 formula
  • 3. 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 theorem
  • 4. 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 ellipses
  • 5. 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 velocity
  • 6. 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 throw
  • 8. 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 words
  • Appendix 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.

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