Chapter

Gravitational physics of few‐body systems

H. Asada, T. Futamase and P. A. Hogan

in Equations of Motion in General Relativity

Published in print December 2010 | ISBN: 9780199584109
Published online January 2011 | e-ISBN: 9780191723421 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199584109.003.0007

Series: International Series of Monographs on Physics

Gravitational physics of few‐body systems

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A subject closely related to equations of motion is the gravitational physics of few body systems. First, the chapter reviews choreographic solutions for the N‐body problem in Newton's theory of gravity. A solution is called choreographic if each massive particle moves periodically in a single closed orbit. One such choreographic solution is a stable figure‐eight orbit for a three‐body system. The chapter describes connections between the choreographic solutions and the gravitational waves that are predicted by Einstein's theory of general relativity and thus general relativistic choreography is discussed. General relativistic effects cause, for example to binary orbits, a complicated flower‐like pattern by the periastron advance. It is not trivial whether general relativistic effects admit a choreographic solution such as the figure eight. At least at the first and second post Newtonian orders (neglecting dissipative effects starting at the second and half post Newtonian order) the tricky figure eight remarkably remains true.

Keywords: choreographic solutions; general relativistic figure eight solution; N-body problem; Newton's theory of gravity; gravitational waves

Chapter.  4547 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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