Methods of Celestial Mechanics

Volume I: Physical, Mathematical, and Numerical Principles

  • Gerhard Beutler

Part of the Astronomy and Astrophysics Library book series (AAL)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Physical, Mathematical, and Numerical Principles

  3. Back Matter
    Pages 441-464

About this book


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.


Celestial Mechanics Computational Astronomy Planetary System Satellite Orbits astronomy

Authors and affiliations

  • Gerhard Beutler
    • 1
  1. 1.Astronomisches InstitutUniversität BernBernSwitzerland

Bibliographic information