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Concept# Apsidal precession

Summary

In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points farthest (apoapsis) and closest (periapsis) from its primary body (therefore it can be also called after any of the apsides). The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements of an orbit. Apsidal precession is considered positive when the orbit's axis rotates in the same direction as the orbital motion. An apsidal period is the time interval required for an orbit to precess through 360°, which takes Earth's orbit about 112,000 years, completing a cycle and returning to the same orientation.
The ancient Greek astronomer Hipparchus noted the apsidal precession of the Moon's orbit (as the revolution of the Moon's apogee with a period of approximately 8.85 years); it is corrected for in the Antikythera Mechanism (circa 80 BCE) (with the supposed value of 8.88 years per full cycle, correct to within 0.34% of current measurements). The precession of the solar apsides (as a motion distinct from the precession of the equinoxes), was first quantified in the second century by Ptolemy of Alexandria. He also calculated the effect of precession on movement of the heavenly bodies. The apsidal precessions of the Earth and other planets are the result of a plethora of phenomena, of which a part remained difficult to account for until the 20th century when the last unidentified part of Mercury's precession was precisely explained.
A variety of factors can lead to periastron precession such as general relativity, stellar quadrupole moments, mutual star–planet tidal deformations, and perturbations from other planets.
ωtotal = ωGeneral Relativity + ωquadrupole + ωtide + ωperturbations
For Mercury, the perihelion precession rate due to general relativistic effects is 43′′ (arcseconds) per century.

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