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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The post-Newtonian approximation

The post-Newtonian approximation

(p.527) 12 The post-Newtonian approximation
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

Keywords:   post-Newtonian corrections, two-body problem, general relativity, 1PN corrections, gravitational field, equations of motion, actual motion, post-Keplerian geodesics

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