Chandler wobble
Encyclopedia
The Chandler wobble is a small motion in the Earth
's axis of rotation
relative to the Earth's surface, which was discovered by American
astronomer
Seth Carlo Chandler
in 1891. It amounts to 9 metres (29.5 ft) on the Earth's surface and has a period of 433 days. This wobble 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 spinning object that is not a sphere; this is called a free nutation
. Somewhat confusingly, the direction of the
Earth's spin axis relative to the stars also varies with different periods, and these motions (caused by the tidal attraction of the Moon and Sun) are also called nutation
s, except for the slowest, which is the precession of the equinoxes
.
The existence of a free nutation of the Earth 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 1755 as part of his studies of the dynamics of rotating bodies. Based on the known flattening
of the Earth he predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none were 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 c. 6 mm, the pole tide, which is the only tide not caused by extraterrestrial bodies. Despite the small amplitude, the gravitational effect of the pole tide is easily detected by the superconducting gravimeter
(see e.g. Fig. 2.3 in Virtanen 2006).
To measure the wobble, the International Latitude Observatories
were established in 1899. (The wobble is also called the variation of latitude.) 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though they were eventually superseded by other methods of measurement.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. While it has to be maintained by changes in the mass distribution
or angular momentum
of the Earth's outer core
, atmosphere
, oceans, or crust (from earthquake
s), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.
Richard Gross (2001) of the Jet Propulsion Laboratory
, California, used computer simulations to discover the source of the Chandler Wobble. Gross found that two thirds of the 'wobble' was caused by fluctuating pressure on the sea bottom due to temperature
and salinity
changes and wind
-driven changes in the circulation of the oceans. The remaining third is due to atmospheric fluctuations
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
's axis of rotation
Earth rotation
Earth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates towards the east. As viewed from the North Star Polaris, the Earth turns counter-clockwise.- Rotation period :...
relative to the Earth's surface, which was discovered by American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
Seth Carlo Chandler
Seth Carlo Chandler
Seth Carlo Chandler, Jr. was an American astronomer.He was born in Boston, Massachusetts. During his last year in high school he performed mathematical computations for Benjamin Peirce, of the Harvard College Observatory.After graduating, he became the assistant of Benjamin A. Gould...
in 1891. It amounts to 9 metres (29.5 ft) on the Earth's surface and has a period of 433 days. This wobble combines with another wobble with a period of one year so that the total polar motion
Polar motion
Polar motion of the earth is the movement of Earth's rotational axis across its surface. This is measured with respect to a reference frame in which the solid Earth is fixed...
varies with a period of about 7 years.
The Chandler wobble is an example of the kind of motion that can occur for a spinning object that is not a sphere; this is called a free nutation
Free nutation
Free nutation is a kind of motion that can occur for a spinning object that is not a sphere....
. Somewhat confusingly, the direction of the
Earth's spin axis relative to the stars also varies with different periods, and these motions (caused by the tidal attraction of the Moon and Sun) are also called nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...
s, except for the slowest, which is the precession of the equinoxes
Precession of the equinoxes
In astronomy, axial precession is a gravity-induced, slow and continuous change in the orientation of an astronomical body's rotational axis. In particular, it refers to the gradual shift in the orientation of Earth's axis of rotation, which, like a wobbling top, traces out a pair of cones joined...
.
The existence of a free nutation of the Earth was predicted by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by
Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
in 1755 as part of his studies of the dynamics of rotating bodies. Based on the known flattening
Flattening
The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator...
of the Earth he predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none were 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
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
) 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
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....
with an amplitude of c. 6 mm, the pole tide, which is the only tide not caused by extraterrestrial bodies. Despite the small amplitude, the gravitational effect of the pole tide is easily detected by the superconducting gravimeter
Gravimeter
A gravimeter or gravitometer is an instrument used in gravimetry for measuring the local gravitational field of the Earth. A gravimeter is a type of accelerometer, specialized for measuring the constant downward acceleration of gravity, which varies by about 0.5% over the surface of the Earth...
(see e.g. Fig. 2.3 in Virtanen 2006).
To measure the wobble, the International Latitude Observatories
International Latitude Observatory
The International Latitude Observatories were a system of six observatories located near the parallel of 39° 08' north latitude. They were used to measure the variation in latitude that occurs as a result of the "wobble" of the Earth on its polar axis.The original six observatories were located...
were established in 1899. (The wobble is also called the variation of latitude.) 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
Polar motion
Polar motion of the earth is the movement of Earth's rotational axis across its surface. This is measured with respect to a reference frame in which the solid Earth is fixed...
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. While it has to be maintained by changes in the mass distribution
Mass distribution
Mass distribution is a term used in physics and mechanics and describes the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on earth their mass distribution is almost homogeneous.-Astronomy:...
or angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
of the Earth's outer core
Structure of the Earth
The interior structure of the Earth, similar to the outer, is layered. These layers can be defined by either their chemical or their rheological properties. The Earth has an outer silicate solid crust, a highly viscous mantle, a liquid outer core that is much less viscous than the mantle, and a...
, atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
, oceans, or crust (from earthquake
Earthquake
An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...
s), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.
Richard Gross (2001) of the Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...
, California, used computer simulations to discover the source of the Chandler Wobble. Gross found that two thirds of the 'wobble' was caused by fluctuating pressure on the sea bottom due to temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and salinity
Salinity
Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...
changes and wind
Wind
Wind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...
-driven changes in the circulation of the oceans. The remaining third is due to atmospheric fluctuations