Apsidal precession


In celestial mechanics, apsidal precession 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 closest (periapsis) and farthest (apoapsis) from its primary body. The apsidal precession is the first 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 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. Einstein showed that for a planet, the major semi-axis of its orbit being α, the eccentricity of the orbit e and the period of revolution T, then the apsidal precession due to relativistic effects, during one period of revolution in radians, can be calculated by this equation.

Related formulas


ϵapsidal precession (rad)
amajor semi-axis of orbit (m)
Tperiod of revolution (s)
cSpeed of light
eeccentricity of orbit (dimensionless)