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Astronomy - Astrophysics and Astroparticles | Methods of Celestial Mechanics - Volume I: Physical, Mathematical, and Numerical Principles

Methods of Celestial Mechanics

Volume I: Physical, Mathematical, and Numerical Principles

In cooperation with Prof. Leos Mervart and Dr. Andreas Verdun

Beutler, Gerhard

2005, XVI, 466 p.

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  • About this textbook

  • Paperback edition of this successful graduate textbook
  • Gives a detailed introduction into the theoretical concepts of celestial mechanics as used in planetary sciences and satellite navigation
  • Addresses numerical techniques and GPS navigation
  • G. Beutler is an internationally known expert

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students in physics, mathematics and engineering as well as an excellent reference for practitioners. This  Volume I gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. After a brief review of the history of celestial mechanics, the equations of motion (Newtonian and relativistic versions) are developed for planetary systems (N-body-problem), for artificial Earth satellites, and for extended bodies (which includes the problem of Earth and lunar rotation). Perturbation theory is outlined in an elementary way from generally known mathematical principles without making use of the advanced tools of analytical mechanics. The variational equations associated with orbital motion - of fundamental importance for parameter estimation (e.g., orbit determination), numerical error propagation, and stability considerations - are introduced and their properties discussed in considerable detail. Numerical methods, especially for orbit determination  and orbit improvement, are discussed in considerable depth. The algorithms may be easily applied to objects of the planetary system and to Earth satellites and space debris.

Content Level » Graduate

Keywords » Celestial Mechanics - Computational Astronomy - Planetary System - Satellite Orbits - astronomy

Related subjects » Astrophysics and Astroparticles - Classical Continuum Physics - Computational Science & Engineering - Theoretical, Mathematical & Computational Physics

Table of contents 

Physical, Mathematical, and Numerical Principles.- Overview of the Work.- Historical Background.- The Equations of Motion.- The Two- and the Three-Body Problems.- Variational Equations.- Theory of Perturbations.- Numerical Solution of Ordinary Differential Equations: Principles and Concepts.- Orbit Determination and Parameter Estimation.

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