Chandler Wobble
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Chandler Wobble

The Chandler wobble or variation of latitude is a small deviation in the Earth's axis of rotation relative to the solid earth,[1] which was discovered by American astronomer Seth Carlo Chandler in 1891. It amounts to change of about 9 metres (30 ft) in the point at which the axis intersects the Earth's surface and has a period of 433 days.[2][3] This wobble, which is a nutation, combines with another wobble with a period of one year, so that the total polar motion varies with a period of about 7 years.

The Chandler wobble is an example of the kind of motion that can occur for a freely rotating object that is not a sphere; this is called a free nutation. 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.

## Predictions

The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies. Based on the known ellipticity of the Earth, Euler predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none was found. Chandler's contribution was to look for motions at any possible period; once the Chandler wobble was observed, the difference between its period and the one predicted by Euler was explained by Simon Newcomb as being caused by the non-rigidity of the Earth. The full explanation for the period also involves the fluid nature of the Earth's core and oceans--the wobble, in fact, produces a very small ocean tide with an amplitude of approximately 6 mm ( in), called a "pole tide", which is the only tide not caused by an extraterrestrial body. Despite the small amplitude, the gravitational effect of the pole tide is easily detected by the superconducting gravimeter.[4]

Because the earth is not a rigid body, the Chandler wobble should die down with a time constant of about 68 years.[5] Various theories have been proposed to explain why it still exists even though the earth has been around for much longer than 68 years (see below).

## Attempts at measurement

The International Latitude Observatories were established in 1899 to measure the wobble. These provided data on the Chandler and annual wobble for most of the 20th century, though they were eventually superseded by other methods of measurement. Monitoring of the polar motion is now done by the International Earth Rotation Service.

The wobble's amplitude has varied since its discovery, reaching its largest size in 1910 and fluctuating noticeably from one decade to another. In 2009, Malkin & Miller's analysis of International Earth Rotation and Reference Systems Service (IERS) Pole coordinates time series data from January 1946 to January 2009 showed three phase reversals of the wobble, in 1850, 1920, and 2005.[2]

## Hypotheses

Since the Chandler wobble should die down in a matter of decades or centuries, there must be influences that continually re-excite it. While it must be due to changes in the mass distribution or angular momentum of the Earth's outer core, atmosphere, oceans, or crust (from earthquakes), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.

An investigation was done in 2001 by Richard Gross at the Jet Propulsion Laboratory managed by the California Institute of Technology. He used angular momentum models of the atmosphere and the oceans in computer simulations to show that from 1985 to 1996, the Chandler wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean-bottom pressure fluctuations. Gross found that two-thirds of the "wobble" was caused by fluctuating pressure on the seabed, which, in turn, is caused by changes in the circulation of the oceans caused by variations in temperature, salinity, and wind. The remaining third is due to atmospheric fluctuations.[5]

## References

1. ^ e.g. Mueller, I.I. (1969). Spherical and Practical Astronomy as Applied to Geodesy. Frederick Ungar Publishing, NY, pp. 80.
2. ^ a b Zinovy Malkin and Natalia Miller (2009). "Chandler wobble: two more large phase jumps revealed". Earth, Planets and Space. 62 (12): 943-947. arXiv:0908.3732. Bibcode:2010EP&S...62..943M. doi:10.5047/eps.2010.11.002.
3. ^ "Earth's Chandler Wobble Changed Dramatically in 2005". TechnologyReview.com. MIT Technology Review. 2009. Retrieved 2013.
4. ^ See, e.g., Fig. 2.3. Virtanen, H. (2006). Studies of Earth Dynamics with the Superconducting Gravimeter (PDF) (Academic Dissertation at the University of Helsinki). Geodetiska Institutet. Archived from the original (PDF) on June 5, 2011. Retrieved 2009.
5. ^ a b Gross, Richard S. (2000). "The Excitation of the Chandler Wobble". Geophysical Research Letters. 27 (15): 2329-2332. Bibcode:2000GeoRL..27.2329G. doi:10.1029/2000gl011450. Retrieved 2011.

• Carter, B. and M. S. Carter, 2003, "Latitude, How American Astronomers Solved the Mystery of Variation," Naval Institute Press, Annapolis.
• Gross, Richard S (2000). "The Excitation of the Chandler Wobble". Geophysical Research Letters. 27 (15): 2329-2332. Bibcode:2000GeoRL..27.2329G. doi:10.1029/2000gl011450.
• Lambeck, Kurt, 1980, The Earth's Variable Rotation: Geophysical Causes and Consequences (Cambridge Monographs on Mechanics), Cambridge University Press, London.
• Munk, W. H. and MacDonald, G. J. F., 1960, The Rotation of the Earth, Cambridge University Press, London.
• Moritz, H. and I.I. Mueller, 1987, Earth Rotation: Theory and Observation, Continuum International Publishing Group, London.