page_title: Apsidal precession
section_title: Newton's theorem of revolving orbits
hierarchical_section_title: Apsidal precession / Newton's theorem of revolving orbits
context_page_description: In celestial mechanics, apsidal precession is the precession of the line connecting the apsides of an astronomical body's orbit. The apsides are the orbital points closest and farthest from its primary body. 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°.
context_section_description: Newton derived an early theorem which attempted to explain apsidal precession.  This theorem is historically notable, but it was never widely used and it proposed forces which have been found not to exist, making the theorem invalid.  This theorem of revolving orbits remained largely unknown and undeveloped for over three centuries until 1995.  Newton proposed that variations in the angular motion of a particle can be accounted for by the addition of a force that varies as the inverse cube of distance, without affecting the radial motion of a particle.  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.  However, his theorem did not account for the apsidal precession of the Moon without giving up the inverse-square law of Newton's law of universal gravitation.  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.
caption: 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.