Rotation (green), Precession (blue) and Nutation in obliquity (red) of the Earth

Nutation is a slight irregular motion (etymologically a "nodding") in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet.

Nutation is also the name of one of the Euler rotations, the Euler rotation that measures the change in angle due to the "nodding" mentioned above.

Of a planet

The nutation of a planet happens because the tidal forces which cause the precession of the equinoxes vary over time so that the speed of precession is not constant. It was discovered in 1728 by the English astronomer James Bradley, but was not explained until 20 years later.

Because the dynamics of the planets are so well known, nutation can be calculated within seconds of arc over periods of many decades. There is another disturbance of the Earth's rotation called polar motion that can be estimated only a few months ahead, because it is influenced by rapidly and unpredictably varying things such as ocean currents, wind systems, and motions in the Earth's core.

Values of nutation are usually divided into components parallel and perpendicular to the ecliptic. The component which works along the ecliptic is known as the nutation in longitude. The component perpendicular to the ecliptic is known as the nutation in obliquity. Celestial coordinate systems are based on an "equator" and "equinox," which means a great circle in the sky that is the projection of the Earth's equator outwards, and a line, the Vernal equinox intersecting that circle, which determines the starting point for measurement of right ascension. These items are affected both by precession of the equinoxes and nutation, and thus depend on the theories applied to precession and nutation, and on the date used as a reference date for the coordinate system. In simpler terms, nutation (and precession) values are important in observation from Earth for calculating the apparent positions of astronomical objects.

Of the Earth

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. However, there are other significant periodical terms which must be calculated depending on the desired accuracy of the result. A mathematical description (set of equations) that represents nutation is called a "theory of nutation" (see, e.g. http://www.iers.org/iers/earth/resolutions/UAI_b3.html). In the theory, parameters are adjusted in a more or less ad hoc method to obtain the best fit to data. As can be seen from the IERS publication just cited, nowadays simple rigid-body mechanics do not give the best theory; one has to account for deformations of the solid Earth.

Values

The principal term of nutation is due to the regression of the moon's nodal line and has the same period of 6798 days (18.6 years). It reaches 17″ in longitude and 9″ in obliquity. All other terms are much smaller. The next largest, with a period of 183 days (0.5 year) has amplitudes 1.3″ and 0.6″ respectively. Interestingly the periods of all terms larger than 0.0001″ (about as accurately as one can measure) lie between 5.5 and 6798 days and seem to avoid the range from 34.8 to 91 days. It is therefore customary to split the nutation into long-period and short-period terms. The long-period terms are calculated and mentioned in the almanacs, while the additional correction due to the short-period terms is usually taken from a table.

See also

• Euler angles

External links

• For a synopsis and comparison of recent nutation theories, see Cyril Ron, "The Tables of Differences Between the Nutation Series IAU2000, IERS1996 and IAU1980" (PDF), at iers.org.

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