Apsidal precession

[3] 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);[4] 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).

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.

[10][11] From classical mechanics, if stars and planets are considered to be purely spherical masses, then they will obey a simple ⁠1/r2⁠ inverse-square law, relating force to distance and hence execute closed elliptical orbits according to Bertrand's theorem.

[15] Using a forerunner of the Taylor series, Newton generalized his theorem to all force laws provided that the deviations from circular orbits are small, which is valid for most planets in the Solar System.

Additionally, the rate of apsidal precession calculated via Newton's theorem of revolving orbits is not as accurate as it is for newer methods such as by perturbation theory.

[citation needed] An apsidal precession of the planet Mercury was noted by Urbain Le Verrier in the mid-19th century and accounted for by Einstein's general theory of relativity.

Earth's apsidal precession slowly increases its argument of periapsis; it takes about 112,000 years for the ellipse to revolve once relative to the fixed stars.

[19] Earth's polar axis, and hence the solstices and equinoxes, precess with a period of about 26,000 years in relation to the fixed stars.

Each planet orbiting the Sun follows an elliptic orbit that gradually rotates over time (apsidal precession). This figure illustrates positive apsidal precession (advance of the perihelion), with the orbital axis turning in the same direction as the planet's orbital motion. The eccentricity of this ellipse and the precession rate of the orbit are exaggerated for visualization. Most orbits in the Solar System have a much lower eccentricity and precess at a much slower rate, making them nearly circular and stationary .
The main orbital elements (or parameters). The line of apsides is shown in blue, and denoted by ω . The apsidal precession is the rate of change of ω through time, ⁠ d ω / d t ⁠ .
Animation of Moon 's orbit around Earth - Polar view
Moon · Earth
change in orbit over time
Effects of apsidal precession on the seasons with the eccentricity and ap/peri-helion in the orbit exaggerated for ease of viewing. The seasons shown are in the northern hemisphere and the seasons will be reverse in the southern hemisphere at any given time during orbit. Some climatic effects follow chiefly due to the prevalence of more oceans in the Southern Hemisphere.