Editing General relativity (section)

==== Precession of apsides ====
[[File:Relativistic precession.svg|thumb|upright=1.05|Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star. The influence of other planets is ignored.]]
{{Main|Apsidal precession}}

In general relativity, the [[apsis|apsides]] of any orbit (the point of the orbiting body's closest approach to the system's [[center of mass]]) will [[apsidal precession|precess]]; the orbit is not an [[ellipse]], but akin to an ellipse that rotates on its focus, resulting in a [[rose (mathematics)|rose curve]]-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a [[test particle]]. For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by [[Urbain Le Verrier]] in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.<ref>{{Harvnb|Schutz|2003|pp=48–49}}, {{Harvnb|Pais|1982|pp=253–254}}</ref>

The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass)<ref>{{Harvnb|Rindler|2001|loc=sec. 11.9}}</ref> or the much more general [[post-Newtonian formalism]].<ref>{{Harvnb|Will|1993|pp=177–181}}</ref> It is due to the influence of gravity on the geometry of space and to the contribution of [[self-energy]] to a body's gravity (encoded in the [[nonlinearity]] of Einstein's equations).<ref>In consequence, in the parameterized post-Newtonian formalism (PPN), measurements of this effect determine a linear combination of the terms β and γ, cf. {{Harvnb|Will|2006|loc=sec. 3.5}} and {{Harvnb|Will|1993|loc=sec. 7.3}}</ref> Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),<ref>The most precise measurements are [[VLBI]] measurements of planetary positions; see {{Harvnb|Will|1993|loc=ch. 5}}, {{Harvnb|Will|2006|loc=sec. 3.5}}, {{Harvnb|Anderson|Campbell|Jurgens|Lau|1992}}; for an overview, {{Harvnb|Ohanian|Ruffini|1994|pp=406–407}}</ref> as well as in binary pulsar systems, where it is larger by five [[order of magnitude|orders of magnitude]].<ref>{{Harvnb|Kramer|Stairs|Manchester|McLaughlin|2006}}</ref>

In general relativity the perihelion shift <math>\sigma</math>, expressed in radians per revolution, is approximately given by:{{sfn|Dediu|Magdalena|Martín-Vide|2015|p=[https://books.google.com/books?id=XmwiCwAAQBAJ&pg=PA141 141]}}

:<math>\sigma=\frac {24\pi^3L^2} {T^2c^2(1-e^2)} \ ,</math>

where:
*<math>L</math> is the [[semi-major axis]]
*<math>T</math> is the [[orbital period]]
*<math>c</math> is the speed of light in vacuum
*<math>e</math> is the [[orbital eccentricity]]