U.S. Naval Observatory Earth Orientation Department

What is Earth Orientation?

The term "Earth orientation" refers to the direction in space of axes which have been defined on the Earth. It is usually measured using five quantities: two angles which identify the direction of the Earth's rotation axis within the Earth, an angle describing the rotational motion of the Earth, and two angles which characterize the direction of the Earth's rotation axis in space. With these coordinates, the orientation of the Earth in space is fully described. The Rapid Service/Prediction Center of the International Earth Rotation Service (IERS), located at the U.S. Naval Observatory (USNO), monitors the Earth's orientation and disseminates this information to many organizations on a continuous basis.


The angles which characterize the direction of the rotational pole within the Earth are called the polar coordinates, x and y. Variation in these coordinates is called polar motion. The polar coordinates measure the position of the Earth's instantaneous pole of rotation in a reference frame which is defined by the adopted locations of terrestrial observatories. The coordinate x is measured along the 0o (Greenwich) meridian while the coordinate y is measured along the 90o W meridian. These two coordinates determine the directions on a plane onto which the polar motion is projected.

Polar motion consists largely of two motions, an annual elliptical component and a Chandler circular component with a period of about 435 days. These two motions describe most of the spiral motion of the pole as seen from the Earth (Figure 1 below).

Polar Motion


The Earth rotation coordinate measures the angle through which the Earth has turned in a given period of time. This angle expressed as the difference between a time scale measured by the rotation of the Earth, UT1, and a uniform time scale, UTC, refers to the angular difference between the direction of the 0o meridian on the Earth and the direction to a point defined in space astronomically.

Historically some form of time based on the rotation of the Earth has always been the basis for civil time, the definition and the measurement procedures depending on available technology and precision requirements. In modern practice, UT1 is defined using a fiducial direction defined mathematically in the celestial reference system. This direction is referred to as the Mean Sun.

UTC, standing for Coordinated Universal Time, designates the atomic time scale which approximates the rotational time of the Earth. From the time of its inception, its rate and/or epoch have been adjusted to keep it near UT1. The current practice is to adjust UTC in epoch by integral seconds (leap seconds) to keep the difference between UT1 and UTC less than 0.9 seconds. UTC as defined by the International Radio Consultative Committee (CCIR) Recommendation 460-4, differs from TAI (Temps Atomique International) by an integral number of seconds. TAI is an atomic time scale determined by the Bureau International des Poids et Mesures (BIPM). Its unit is exactly one Système Internationale (SI) second at mean sea level.

Analyses of astronomical observations reveal different types of variations in the speed of rotation. The ancient observational data form the basis for estimates of the secular deceleration in the speed of rotation. The more recent information, having been obtained with higher accuracy and more regularity, has shown the changes in the acceleration causing irregular variations in the length of the day (LOD). These data have also been used to detect the periodic variations in the length of the day. Figure 2 (below) shows the difference between the rotationally determined length of day (corrected for the effects of known tidal variations, LODS) and 24 hours of UTC time, otherwise known as the excess length of day (in milliseconds).



The gravitational attraction of the Sun and Moon on the non-spherical Earth cause the rotational axis of the Earth to precess in space similar to the action of a top. In addition to this precessional motion the axis undergoes a small "nodding" motion called nutation. Both of these motions can be described theoretically to a high degree of accuracy. This mathematical description depends on assumed values of physical constants describing the shape and internal structure of the Earth. Observations indicate that small residual corrections are required to the currently adopted International Astronomical Union (IAU) model. These corrections are given in longitude (dpsi) and obliquity (deps), where longitude refers to the angle measured eastward along the ecliptic from the intersection of the two planes and obliquity is the angle between the plane of the Earth's orbit (ecliptic) and the equatorial plane.


There are various factors which cause the orientation of the Earth to change with time. Polar motion is caused, in part, by large scale movements of water and changes in the atmospheric angular momentum. For example, the yearly melting of snow and ice in northern Spring contributes to the annual term of polar motion. It is also thought that large earthquakes and the embayment of water by dams and reservoirs might affect polar motion, but this has yet to be quantitatively demonstrated.

The secular variation of the rotational speed seen by the apparently linear increase in the length of the day is due chiefly to tidal friction. The Moon raises tides in the ocean diminishing the speed of rotation. This effect causes a slowing of the Earth's rotational speed resulting in a lengthening of the day by about 0.0015 to 0.0020 seconds per day per century.

The irregular changes in speed appear to be the result of random accelerations, but may be correlated with physical processes occurring on or within the Earth. These cause the length of the day to vary by as much as 0.001 to 0.002 seconds. Irregular changes consist of "decade fluctuations" with characteristic periods of five to fifteen years as well as variations which occur at shorter time scales. The decade fluctuations are related apparently to processes occurring deep within the Earth. The higher frequency variations with periods less than two years are now known to be related largely to the changes in the total angular momentum of the atmosphere.

Periodic variations are associated with periodically repeatable physical processes affecting the Earth. Tides raised in the solid Earth by the Moon and the Sun produce variations in the length of the day with a total amplitude on the order of 0.001 seconds and with individual periods of 18.6 years, 1 year, 1/2 year, 27.55 days, 13.66 days and others. A standard model including 62 periodic components, can be employed to correct the observations for tidal effects.

The rotational speed of the Earth remains essentially unpredictable in nature due to incompletely understood variations. Because of this, astronomical observations continue to be made regularly with increasing accuracy, and the resulting data are the subject of continuing research in the field.


In order to observe Earth orientation, observations must be made from the Earth of objects located in space. Objects that are used include stars, artificial satellites, the Moon, and distant radio sources called quasars. These provide useful reference directions with which to measure the Earth's orientation.

To determine the Earth's orientation very accurate observations of these objects must be made. Stars have been observed photographically for decades to determine the motion of the pole and the rotation of the Earth. Recently, more accurate methods have been devised including the use of lasers and radio telescopes. Laser bursts can be bounced off of artificial satellites or the Moon. This provides information on exactly where the satellite is at a particular time which, in turn, can be used to determine the Earth's orientation in space.

Radio telescopes can also be utilized in a technique called Very Long Baseline Interferometry (VLBI). By having several radio telescopes observing the same quasar at the same time and recording the information that is seen at each telescope, the Earth's orientation can be determined. USNO operates a VLBI network for this purpose, in close cooperation with other groups in the U.S. and abroad. The recorded information then needs to be processed further before the final results can be determined. The reduction procedure involves the use of a highly specialized computer called a correlator. Currently, there are three such correlators in the United States, one located at USNO, one in Boston (Haystack Observatory), and one located in Socorro, NM. Once the data from a VLBI observing session has been correlated, it can be processed further to produce information on Earth orientation and other useful quantities.

Astronomical observations are made routinely by a number of observatories located around the world for this purpose. The IERS is the international organization responsible for the coordination of observations of polar motion and nutation as well as astronomical time. The IERS organization consists of various product centers to provide specific services to users, such as rapid service/predictions of Earth orientation, data related to the motions of geophysical fluids (e.g., atmosphere and oceans), and the celestial and terrestrial reference frames. Observations are contributed to the IERS by individual observing techniques, which in turn receive results from numerous observatories, laboratories, and analysis centers around the world. The IERS Rapid Service/Prediction Center then combines these data into a series of x, y, UT1-UTC, and celestial pole offsets. This information is recomputed at least daily and disseminated by e-mail, anonymous ftp, and the World Wide Web. Additional related information can be obtained upon request.


Anyone who must relate changing aspects of reference systems on Earth to a system in space requires information on the Earth's orientation. Users include navigators, geodesists, and those involved in timekeeping. For navigators using celestial navigation, failure to account for the changing UT1, in particular, could result in significant positional errors.

Other users are those concerned with navigation in space. Precise positions of satellites located hundreds to tens of thousands of kilometers away in space must take into account the Earth's variable rotation. Without this information, the positions of the satellites cannot be accurately related to points on the Earth's surface, which is necessary for many space-based applications. Increasing use of artificial satellites for world-wide navigation and communication makes this area an important concern.

Suggested Reading

Lambeck, K., 1980, The Earth's Variable Rotation: Geophysical Causes and Consequences, Cambridge University Press, London.

Munk W. H. and MacDonald, G. J. F., 1960, The Rotation of the Earth, Cambridge University Press, London.

[IERS] [IERS Rapid Service/Prediction Center] [IERS Bulletin A] [USNO EO Dept.]

Last modified: 24 July 2001 Approved by EO Dept. Head, USNO