Keplerian ellipses : the physics of the gravitational two-body problem /

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....

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Reed, Bruce Cameron (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2019]
Colección:IOP (Series). Release 6.
IOP concise physics.
Temas:
Two-body problem.
Elliptical orbits.
Celestial mechanics.
Kepler's laws.
Astrophysics.
SCIENCE / Physics / Astrophysics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Spherical coordinates--a review
  • 1.1. Fundamental definitions
  • 1.2. Spherical coordinate unit vectors
  • 1.3. Time-derivatives of spherical coordinate unit vectors
  • 1.4. Some useful integrals
  • 2. Dynamical quantities in spherical 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 reduced mass
  • 3.2. Central force dynamics : the potential
  • 3.3. Why an inverse-square law?
  • 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
  • 4. The ellipse
  • 4.1. The ellipse in Cartesian and polar 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?
  • 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
  • 6. Kepler's equation : anomalies true, eccentric, and mean
  • 7. Some sundry results
  • 7.1. Average distance of a planet from the Sun
  • 7.2. Determining initial launch conditions
  • 7.3. A brief lesson in unit conversions
  • 7.4. Orientation of Earth's orbit
  • 7.5. Some final words.

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