Binary stars : the two-body problem Three-body systems -- The restricted three-body problem -- Managing the program 'Planet with a satellite' -- Satellites of a planet that orbits a star -- Exact particular solutions to the three-body problem -- A space flight over the back side of the Moon -- Lunar perturbations of a satellite's orbit -- A space voyage to a distant planet and back -- Comets : interplanetary vagabonds -- A double star with a planet Many-body systems in celestial mechanics -- Planetary system : a many-body problem -- A model of the Solar System -- Hypothetical planetary systems and heavenly catastrophes -- Multiple stars -- Exact particular solutions to the many-body problem The simulated phenomena Phenomena and concepts in celestial mechanics : an introductory approach -- Newton's law of universal gravitation -- Potential energy of a body in the Newtonian gravitational field -- Circular velocity and escape velocity -- Geometric properties of Keplerian orbits -- Initial conditions and parameters of Keplerian orbits -- A satellite in the atmosphere -- Trajectories of a landing module -- A space probe -- Space rendezvous -- Kepler's laws and the solar system -- An approximate approach to the restricted three-body problem Theoretical background -- Angular momentum and areal velocity -- Dynamical derivation of Kepler's first law -- Kepler's third law -- A hodograph of the velocity vector for Keplerian motion -- Another derivation of Kepler's first law -- A family of orbits with equal energies and a common initial point -- Relative orbital motion -- The gravitational field of a distorted planet -- The two-body problem -- Exact particular solutions to the three-body problem -- The non-restricted three-body problem -- The sphere of gravitational action -- The oceanic tides Glossary. Preface -- Author biography -- Introduction : getting started -- List of the simulation programs -- How to operate the simulation programs -- Keplerian motions in celestial mechanics -- Numerical and analytical methods Review of the simulations -- Kepler's laws -- Kepler's first law -- Kepler's second law -- Kepler's third law -- The approximate nature of Kepler's laws Hodograph of the velocity vector for Keplerian motion -- Hodograph of the velocity for closed orbits -- Hodograph of the velocity for open orbits Orbits of satellites and trajectories of missiles -- Families of Keplerian orbits -- Evolution of an orbit in the atmosphere Active maneuvers in space orbits -- How to operate the program -- Space flights and orbital maneuvers -- Relative motion of bodies in space orbits -- Space probes and relative motion -- Rendezvous in space and interplanetary flights Precession of an equatorial orbit
This book, together with the accompanying software, is written for a wide range of graduate and undergraduate students studying various courses in physics and astronomy. The primary aim of the book is the understanding of the foundations of classical and modern physics, while their application to celestial mechanics is used to illustrate these concepts. The simulation programs create vivid and lasting impressions of the investigated phenomena, and provide students and their instructors with a powerful tool to explore basic concepts that are difficult to study and teach in an abstract conventional manner.
Professional and scholarly.
Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader.
Eugene Butikov is a Professor of Physics at St Petersburg State University in Russia, where he teaches general physics, optics, quantum theory of solids and theory of oscillations. His research work is associated with solid statesolid-state physics (quantum theory of electronic paramagnetic resonance, theory of Josephson effects in weak superconductivity) and theory of nonlinear oscillations. He has written several textbooks and handbooks on physics that are widely used in Russia, and is a co-author of the Concise Handbook of Mathematics and Physics, CRC Press, 1997. He devotes a lot of time and effort to developing interactive educational software for university-level physics students to investigate mathematical models of physical systems.