Why Mother Earth Wobbles

The 17th century English physicist Isaac Newton theorized that the diurnal rotation of Earth should cause it to be ellipsoidal in shape—slightly flattened at the north and south poles and bulged about the equator, as compared to a sphere. Meridian arc measurements at widely different latitudes proved Newton correct. This subtle departure from sphericity is important because the “extra” ring of mass about the equator results in a preferred axis of rotation—the axis of figure, which is perpendicular to the equator, and passes through the north and south poles. Gravitational attractions of other bodies in the solar system acting on the equatorial bulge still result in periodic changes in the orientation of Earth and its axis of rotation in space (precession and nutation), but they can be computed centuries in advance.1

In the 18th century Swiss mathematician Leonhard Euler suggested that if Earth were somehow made to rotate about an axis slightly different from the axis of figure, that Earth would wobble slightly about the new axis of rotation, with a period of about 10 months. This wobble would result in a periodic variation in latitude of every point on Earth.

For more than a century the leading astronomers of Europe searched for variation of latitude. All attempts failed outright, or led to confusing and seemingly inconsistent results. In 1891 the International Geodetic Association (IGA), reacting to a claim by German Astronomer Karl Friedrich Kustner of having detected variation of latitude at the Berlin Observatory, launched an international observing program to confirm his results. The IGA organized simultaneous observations in Germany and Hawaii, on opposite sides of the globe. If the latitude of one increased the latitude of the other should decrease.

Seth Carlo Chandler, an amateur American astronomer, did not wait for the results of the IGA observing program. Using his own observations and others obtained from observatories around the world, Chandler not only verified the variation of latitude but proved that there were two components, an annual motion caused by the seasonal relocation of mass on Earth each year, and a second having a 14 month period. Both terms were tiny, only one or two tenths of a second of arc, and they alternately added to or cancelled one another—explaining why they had been so difficult to detect.

Another American astronomer, Simon Newcomb, quickly identified the 14 month component as the motion predicted by Euler, explaining that the period was increased from 10 to 14 months because of the elasticity of Earth. Newcomb even used the period found by Chandler to estimate the elasticity of Earth, finding Earth to be slightly more rigid than steel.

In 1899 the IGA established the International Latitude Service (ILS), which consisted of several dedicated observatories located along a common parallel of latitude. The stations were equipped with identical zenith telescopes and observed identical sets of stars each night, following a method developed by yet another American, Captain John Talcott, of the U.S. Army Corps of Engineers.

In 1962 the ILS was reorganized into the International Polar Motion Service (IPMS), with the addition of many new observatories scattered at different latitudes and equipped with several different types of instruments. The IPMS monitored variation of latitude and variations in Earth rotation (length of day). By 1980 space age observing methods, particularly very long baseline interferometry (VLBI), satellite laser ranging (SLR) and the Global Positioning System (GPS), were able to track changes in the orientation of Earth in space orders of magnitude better than the classical optical instruments used at the IPMS stations. The IMPS was closed (including the original ILS observations at Gaithersburg MD and Ukiah, CA), and its duties were transferred to the International Earth Rotation Service (IERS).

A night at the Gaithersburg Latitude Observatory - How the observations are made and collected using the Zenith Telescope.

1 Earth is tilted 23.5 degrees relative to its plane of orbit about the Sun, and the orbit of the Moon is tilted by 28.6 degrees relative to the equatorial plane of Earth. The asymmetrical and ever changing gravitational attractions of the Sun, Moon, and planets on this equatorial bulge, results in torques which cause Earth, and its axis of rotation, to wobble (precess) in a manner similar to that of a toy top or gyroscope, and to perform a very complex pattern of nods (nutation). The precession causes the axis of rotation to sweep out a 23.5 degree radius circle among the stars (on the celestial sphere) every 25,800 years, and nutation causes excursions from a smooth circle comprised of hundreds of periodic motions ranging in period and amplitude from 18.6 years and 17 seconds of arc, to a fraction of a day and milli-seconds of arc. In principal, all of these oscillations could be accurately computed if the mass and orbits of all the bodies in the solar system were known.