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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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Tests in the solar system

Tests in the solar system

(p.513) 11 Tests in the solar system
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter describes observable relativistic effects in the solar system. In the solar system we can, as a first approximation, neglect the gravitational field of all the stars except the Sun. In Newtonian theory, the planet trajectories are then Keplerian ellipses. Relativistic effects are weak because the dimensionless ratio characterizing them is everywhere less than GM/c² R≃ 2 × 10–6, and so they can be added linearly to the Newtonian perturbations due to the other planets, the non-spherical shape of celestial bodies, and so on. The chapter first describes the gravitational field of the Sun using a Schwarzschild spacetime, before moving on to look at the geodesic equation. It also discusses the bending of light, the Shapiro effect, the perihelion, post-Keplerian geodesics, and spin in a gravitational field.

Keywords:   solar system, relativistic effects, gravitational field of the Sun, Sun, Schwarzschild spacetime, bending of light, Shapiro effect, perihelion, post-Keplerian geodesics, spin

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