18. Polar motion

The Earth rotates around an axis, an imaginary straight line that all points not on the line move around in circles. The axis passes through the Earth’s North Pole and the South Pole. So the positions of the two Poles are defined by the position of the rotation axis.

Earth rotation and poles

The Earth’s North and South Poles are defined as the points where the axis of rotation passes through the surface of the planet. (Earth photo is a public domain image from NASA.)

Interestingly, the Earth’s rotation axis is not fixed – it moves slightly. This means that the Earth’s poles move.

The positions of the Earth’s poles can be determined by looking at the motions of the stars. As we’ve already seen, if you observe the positions of stars throughout a night, you will see that they rotate in the sky about a central point. The point on the Earth’s surface directly underneath the centre of rotation of the stars is one of the poles of the Earth.

Star trails in the northern hemisphere

Star trails above Little Hawk Lake in Canada. The northern hemisphere stars rotate around the North Celestial Pole (the point directly above the Earth’s North Pole). The bright spot in the centre is Polaris, the pole star. The circles are somewhat distorted in the upper corners of the photo because of the wide angle lens used. (Creative Commons Attribution 2.0 image by Dave Doe.)

Through the 19th century, astronomers were improving the precision of astronomical observations to the point where the movement of the Earth’s rotational poles needed to be accounted for in the positions of celestial objects. The motion of the poles was also beginning to affect navigation, because as the poles move, so does the grid system of latitude and longitude that ships rely on to reach their destinations and avoid navigational hazards. In 1899 the International Geodetic Association established a branch known as the International Latitude Service.

The fledgling International Latitude Service established a network of six observatories, all located close to latitude 39° 08’ north, spread around the world. The initial observatories were located in Gaithersburg, Maryland, USA; Cincinatti, Ohio, USA; Ukiah, California, USA; Mizusawa, Japan; Charjui, Turkestan; and Carloforte, Italy. The station in Charjui closed due to economic problems caused by war, but a new station opened in Kitab, Uzbekistan after World War I. Each observatory engaged in a program of observing the positions of 144 selected reference stars, and the data from each station were cross referenced to provide accurate measurements of the location of the North Pole.

International Latitude Service station in Ukiah

International Latitude Service station in Ukiah, California. (Public domain image from Wikimedia Commons.)

In 1962, the International Time Bureau founded the International Polar Motion Service, which incorporated the International Latitude Service observations and additional astronomical observations to provide a reference of higher accuracy, suitable for both navigation and defining time relative to Earth’s rotation. Finally in 1987, the the International Astronomical Union and the International Union of Geodesy and Geophysics established the International Earth Rotation Service (IERS), which took over from the International Polar Motion Service. The IERS is the current authority responsible for timekeeping and Earth-based coordinate systems, including the definitions of time units, the introduction of leap seconds to keep clocks in synch with the Earth’s rotation, and definitions of latitude and longitude, as well as measurements of the motion of the Earth’s poles, which are necessary for accurate use of navigation systems such as GPS and Galileo.

The motion of Earth’s poles can be broken down into three components:

1. An annual elliptical wobble. Over the period of a year, the Earth’s poles move around in an ellipse, with the long axis of the ellipse about 6 metres in length. In March, the North Pole is about 6 metres from where it is in September (though see below). This motion is generally agreed by scientists to be caused by the annual shift in air pressure between winter and summer over the northern and southern hemispheres. In particular there is an imbalance between the Northern Atlantic ocean and Asia, with higher air pressure over the ocean in the northern winter, but higher air pressure over the Asian continent in summer. This change in the mass distribution of the atmosphere is enough to cause the observed wobble.

Annual wobble of North Pole

Annual elliptical wobble of the Earth’s North Pole. Deviation is given in milliarcseconds of axial tilt; 100 milliarcseconds corresponds to a bit over 3 metres at ground level. (Figure adapted from [1].)

2. Superimposed on the annual elliptical wobble is another, circular, wobble, with a period of around 433 days. This is called the Chandler wobble, named after its discoverer, American astronomer Seth Carlo Chandler, who found it in 1891. The Chandler wobble occurs because the Earth is not a perfect sphere. The Earth is slightly elliptical, with the radius at the equator about 20 kilometres larger than the polar radius. When elliptical objects spin, they experience a slight wobble in the rotation known as free nutation. This is the sort of wobble seen in a spinning rugby ball or American football in flight (where the effect is exaggerated by the ball’s exaggerated elliptical shape). This wobble would die away over time, but is driven by changes in the mass distribution of cold and warm water in the oceans and high and low pressure systems in the atmosphere. The Chandler wobble has a diameter of about 9 metres at the poles.

The combined effect of the annual wobble and the Chandler wobble is that the North and South Poles move in a spiralling pattern, sometimes circling with a diameter up to 15 metres, then reducing down to about 3 metres, before increasing again. This beat pattern occurs over a period of about 7 years.

Annual _ Chandler wobble of North Pole

Graph showing the movement of the North Pole over a period of 4500 days (12.3 years), with time on the vertical axis and the spiralling motion mapped in the x and y axes. The motion tickmarks are 0.1 arcsecond in rotation angle of the axis apart, corresponding to about 3 metres of motion along the ground at the Pole. (Public domain image from Wikimedia Commons.)

3. The third and final motion of the Earth’s poles is a systematic drift, of about 200 millimetres per year. Since 1900, the central point of the spiral wobbles of the North Pole has drifted by about 20 metres. This drift is caused by changes in the mass distribution of Earth due to shifts in its structure: movement of molten rock in the mantle, isostatic rebound of crust following the last glacial period, and more recently the melting of the Greenland ice sheet. The melting of the Greenland ice sheet in the last few decades has shifted the direction of polar drift dramatically; one of the serious indications of secondary changes to the Earth caused by human-induced climate change. Changes in Earth’s mass distribution alter its rotational moment of inertia, and the rotational axis adjusts to conserve angular momentum.

Motion of North Pole since 1900

Plot of motion of the North Pole since 1900. The actual position of the Pole from 2008 to 2014 is shown with blue crosses, showing the annual and Chandler wobbles. The mean position (i.e. the centre of the wobbles) is shown for 1900 to 2014 as the green line. The pole has mostly drifted towards the 80° west meridian, but has changed direction dramatically since 2000. (Figure reproduced from [2].)

Each of the three components of Earth’s polar motion are: (a) observable with 19th century technology, (b) accurately measurable using current technology, and (c) understandable and quantitatively explainable using the fact that the Earth is a rotating spheroid and our knowledge of its structure.

If the Earth were flat, it would not be possible to reconcile the changes in position of the North and South Poles with the known shifts in mass distribution of the Earth. The Chandler wobble would not even have any reason to exist at close to its observed period unless the Earth was an almost spherical ellipsoid.

References:

[1] Höpfner, J. “Polar motion at seasonal frequencies”. Journal of Geodynamics, 22, p. 51-61, 1996. https://doi.org/10.1016/0264-3707(96)00012-9

[2] Dick, W., Thaller, D. IERS Annual Report 2013. International Earth Rotation Service, 2014. https://www.iers.org/IERS/EN/Publications/AnnualReports/AnnualReport2013.html

5 thoughts on “18. Polar motion”

  1. Surely the observation of the sky in general would be a proof. Your illustration of stellar rotation about the North Celestial Pole would apply to the entire Earth, since there are no hemispheres on a flat Earth. In reality, people in your home country see stars rotating about the South Celestial Pole, which could only exist on a flat Earth if you could cross over to the bottom.

      1. I have a later post planned specifically about observations of stars at different latitudes.

  2. Instead of ‘American football’, you can say ‘gridiron football’, to include the Canadian football (a different shape). I assume that you're omitting the Australian football out of national modesty.

    1. Ah, I didn’t know Canadian football used a different shape again!

      As for the Australian one, that never even occurred to me. I live in a rugby playing state, and I know virtually nothing about Australian rules football.

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