Perihelion precession
In celestial mechanics, perihelion precession, apsidal precession or orbital precession is the precession (rotation) of the orbit of a celestial body. More precisely, it is the gradual rotation of the line joining the apsides of an orbit, which are the points of closest and farthest approach. Perihelion is the closest point to the Sun. The apsidal precession is the first derivative of the argument of periapsis, one of the six primary orbital elements of an orbit.
The ancient Greek astronomer Hipparchos noted the apsidal precession of the Moon's orbit; it is corrected for in the Antikythera Mechanism (circa 80 BCE) with the rather exact value of 8.88 years per full cycle, correct within 0.34%. The precession of the solar apsides was discovered in the eleventh century by al-Zarqālī. The lunar apsidal precession was not accounted for in Claudius Ptolemy's Almagest, and as a group these precessions, the result of a plethora of phenomena, remained difficult to account for until the 20th century when the last unidentified part of Mercury's precession was precisely predicted in Albert Einstein's general theory of relativity.
There are a variety of factors which can lead to periastron precession, such as general relativity, stellar quadrupole moments, mutual star–planet tidal deformations, and perturbations from other planets.
For Mercury, the perihelion precession rate due to general relativistic effects is 43″ per century. By comparison, the precession due to perturbations from the other planets in the Solar System is 532″ per century, whereas the oblateness of the Sun (quadrupole moment) causes a negligible contribution of 0.025″ per century.
From classical mechanics, if stars and planets are considered to be purely spherical masses, then they will obey a simple 1/r2 force law and hence execute closed elliptical orbits. Non-spherical mass effects are caused by the application of external potential(s): the centrifugal potential of spinning bodies causes rotational flattening and the tidal potential of a nearby mass raises tidal bulges. Rotational and tidal bulges create gravitational quadrupole fields (1/r3) that lead to orbital precession
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