Nutation
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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.
The nutation of a planet is due to the fact that 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.
In the case of
Earth, the principal sources of tidal force are the
Sun and
Moon, which continually 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. [
1]). Generally, the theory is really a theory, in the sense that it applies physical laws and astronomical measurements; however, there may be parameters which are adjusted in a more or less
ad hoc way 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.
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 accurate as one can measure), which lie between 5.5 and 6798 days 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, whilst the additional correction due to the short-period terms is usually taken from a table.
