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In the case of Earth, the principal sources of tidal force are the Sun and Moon, which continuously change location relative to each other and thus cause nutation in Earth's axis. The largest component of Earth's nutation has a period of 18.6 years, the same as that of the precession of the Moon's orbital nodes. [1]
The maximum radius of this ellipse is the constant of nutation, approximately 9.2 arcseconds. Smaller effects also contribute to nutation. These are caused by the monthly motion of the Moon around the Earth and its orbital eccentricity, and similar terms caused by the annual motion of the Earth around the Sun.
Somewhat confusingly, the direction of the Earth's rotation axis relative to the stars also varies with different periods, and these motions—caused by the tidal forces of the Moon and Sun—are also called nutations, except for the slowest, which are precessions of the equinoxes.
This motion is called Euler's free nutation. For a rigid Earth which is an oblate spheroid to a good approximation, the figure axis F would be its geometric axis defined by the geographic north and south pole, and identical with the axis of its polar moment of inertia. The Euler period of free nutation is
Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion. Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies.
Periodic motions of the Moon and of Earth in its orbit cause much smaller (9.2 arcseconds) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as nutation, which add a periodic component to Earth's obliquity. [22] [23] The true or instantaneous obliquity includes this nutation. [24]
The gravitational attraction of the Sun and Moon on the Earth's equatorial bulge cause the rotational axis of the Earth to precess in space similar to the action of a top. This is called precession. Nutation is the smaller amplitude shorter-period (< 18.6 years) wobble that is superposed on the precessional motion of the Celestial pole. It is ...
Precessional movement of Earth. Earth rotates (white arrows) once a day around its rotational axis (red); this axis itself rotates slowly (white circle), completing a rotation in approximately 26,000 years [1] In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational ...