page_title: Tests of general relativity
section_title: Perihelion precession of Mercury
hierarchical_section_title: Tests of general relativity / Classical tests / Perihelion precession of Mercury
caption_attribution_description: Deutsch: Apsiden- oder Periheldrehung.
context_page_description: Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.
  In the 1970s, scientists began to make additional tests, starting with Irwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the sun.
context_section_description: Under Newtonian physics, a two-body system consisting of a lone object orbiting a spherical mass would trace out an ellipse with the center of mass of the system at a focus. The point of closest approach, called the periapsis (or, because the central body in the Solar System is the Sun, perihelion), is fixed. A number of effects in the Solar System cause the perihelia of planets to precess (rotate) around the Sun. The principal cause is the presence of other planets which perturb one another's orbit. Another (much less significant) effect is solar oblateness.
  Mercury deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in celestial mechanics, by Urbain Le Verrier. His reanalysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848 showed that the actual rate of the precession disagreed from that predicted from Newton's theory by 38″ (arcseconds) per tropical century (later re-estimated at 43″ by  Simon Newcomb in 1882). A number of ad hoc and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems.
  In general relativity, this remaining precession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime. Einstein showed that general relativity agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity.
  Although earlier measurements of planetary orbits were made using conventional telescopes, more accurate measurements are now made with radar. The total observed precession of Mercury is 574.10″±0.65 per century relative to the inertial ICRF. This precession can be attributed to the following causes:
  The correction by 42.980±0.001″/cy is 3/2 multiple of classical prediction with PPN parameters . Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation.
  In general relativity the perihelion shift σ, expressed in radians per revolution, is approximately given by:
  where L is the semi-major axis, T is the orbital period, c is the speed of light, and e is the orbital eccentricity (see: Two-body problem in general relativity).
  The other planets experience perihelion shifts as well, but, since they are farther from the Sun and have longer periods, their shifts are lower, and could not be observed accurately until long after Mercury's. For example, the perihelion shift of Earth's orbit due to general relativity is theoretically 3.83868" per century and experimentally 3.8387±0.0004"/cy, Venus's is 8.62473"/cy and 8.6247±0.0005″/cy and Mars' is 1.351±0.001"/cy. Both values have now been measured, with results in good agreement with theory. The periapsis shift has also now been measured for binary pulsar systems, with PSR 1913+16 amounting to 4.2° per year. These observations are consistent with general relativity. It is also possible to measure periapsis shift in binary star systems which do not contain ultra-dense stars, but it is more difficult to model the classical effects precisely – for example, the alignment of the stars' spin to their orbital plane needs to be known and is hard to measure directly. A few systems, such as DI Herculis, have been measured as test cases for general relativity.
caption: The perihelion precession of Mercury
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