Nutation

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

Nutation is the short-period small oscillation superimposed on the precessional motion of the Earth's rotation axis. Unlike the long-term slow variation of precession, nutation periods range from a few days to 18.6 years, with a maximum amplitude of approximately 9.2 arcseconds (the nutation constant). Nutation results from the gravitational action of the Moon and the Sun on the Earth's equatorial bulge.

Core Elements

Physical Cause

Nutation is primarily caused by the motion of the lunar orbital plane (the lunar orbital plane). The line of intersection of the lunar orbital plane and the ecliptic rotates with a period of approximately 18.6 years, causing periodic changes in the gravitational torque exerted by the Moon on the Earth's equatorial bulge. This results in periodic oscillation of the Earth's rotation axis on the precessional cone.

Principal Components

Nutation can be decomposed into two components:

Component	Definition	Typical Value
Obliquity nutation $\Delta\varepsilon$	Variation in the obliquity of the ecliptic	Maximum approximately +/- 9.2 arcsec
Longitude nutation $\Delta\psi$	Periodic displacement of the vernal equinox along the ecliptic	Maximum approximately +/- 17.2 arcsec

Nutation Series

Nutation can be described by a series (nutation series) containing multiple periodic components:

\Delta\psi = \sum_{i} (A_i + B_i t) \sin(\text{argument}_i)

\Delta\varepsilon = \sum_{i} (C_i + D_i t) \cos(\text{argument}_i)

where the argument is obtained from a linear combination of fundamental parameters such as the longitude of the lunar ascending node and the mean anomaly of the Sun. The IAU 2000A nutation model contains 678 periodic components.

Distinction from Precession

Characteristic	Precession	Nutation
Period	Approximately 25,800 years	A few days to 18.6 years
Amplitude	Approximately 50 arcsec/year	Maximum approximately 9.2 arcsec
Trajectory	Smooth cone	Oscillation on the cone surface
Cause	Average effect of solar and lunar gravitation	Periodic variations in solar and lunar gravitation

Application Value

Nutation is a fundamental correction for establishing high-precision celestial reference frames. For precise orbit determination of cislunar missions and deep-space probe navigation, the accuracy of nutation correction directly affects position and velocity determination. The choice of nutation model (e.g., IAU 1980, IAU 2000A) depends on the precision requirements of the mission.

References

郑伟, 安雪滢, 周祥, 何睿智. 空天飞行力学[M]. 国防科技大学, 2026.
任萱, 肖峰. 人造地球卫星轨道力学[M]. 国防科技大学出版社.
IAU SOFA. IAU 2000A Nutation Model[S].