Polar motion

As polar motion or Polschwankung (English Polar Motion) denote astronomers and geoscientists a slow, oscillating displacement of the Earth's axis within the earth system. Although it accounts for only a few millionth of the Earth's radius, but for today's Earth science - especially Geodesy and Geophysics - as well as for astronomy and its fundamental system of great importance.

That north and south poles of the earth are not completely immutable, individual astronomers have suspected for some 150 years ago. We now know that the North Pole is moving in an approximately annual spiral vibration amplitude of a few meters above the soil surface and also around 10-12 meters per century approximately in direction 80 ° west drifts (the latter is referred to as polar wandering ). The periodic slight wobble ( colloquially " eggs ") of the Earth's axis has its origin in the fact that the rotation axis and the principal axis of inertia not quite coincide, and the Earth's body is slightly elastic. Therefore, the earth body reacts slightly to seasonal or mass tectonic shifts. The polar motion must be taken into account for accurate earth and the space coordinate and reference systems (see ICRS and ITRF ).

As a reference point for the geographic north and south poles, one has the set from 1900 to 1905 averaged intersection of the rotation axis with the Earth's surface and CIO ( Conventional International Origin ) called. The polar motion is not to be confused with the variable orientation of the rotation axis in space (see celestial pole ). The gravitational forces of the moon, the sun and the other planets exert torques on the Earth's body, which lead to a precession of Earth's axis in 26,000 years. On the other hand hang the magnetic poles of the Earth not directly related to the position of the earth's axis; their shift is much faster.

Understanding

The axis of rotation of the earth - as the axis of rotation of each stable gyroscope - the tendency to retain its direction in space exactly (see also inertial system ). So you has during the annual orbit around the sun is always in nearly the same direction - currently for so-called polar star in the constellation Ursa Minor - although their years of railway to slants.

If the earth were perfectly rigid and not subject to external forces, its axis of rotation would have over millions of years in exactly the same direction. Because the momentum of the Earth's rotation puts the huge energy of 6.1022 kWh. In fact, the attraction forces cause planets in the system (in particular the gravitation of the Moon and Sun ) is a small, regular tipping, because the earth is slightly different from the spherical shape. These so-called precession and a related effect, nutation have, although not directly related to the polar motion, but are often confused with it.

The polar motion treated in the present article is the result of the fact that the earth

( Factors 3 and 4 ) indicate the inner and outer shape changes of the earth, that varies with the distribution of mass and the axis of the largest moment of inertia: the Earth's axis responds with a slight wobble, so that the geographical latitudes and longitudes of stations can no longer be considered immutable. The previously well-defined relationship between the earth-fixed coordinate system and the sky (extended axis of the earth = celestial pole ) becomes more complicated if one wants to take into account the present-day demands and high measurement accuracy.

Historical

Although the polar motion makes only a few meters, the effect was already suspected in 1860 and confirmed in 1885 by the Bonn astronomers Karl Friedrich Küstner by precise measurements of the " latitude " ( astronomical latitude). For longer measurement series, the presumed changes in the Earth's axis as small periodic width variations were filtered out of about ± 0.3 ". Only at the end of the 19th century, the astro- geodetic measurements with passages instruments and zenith telescopes had reached this level of precision.

Periods and interpretation of the polar motion

The most accurate empirical studies of polar motion have been made in addition to Küstner from Vienna geodesics Richard Schumann and the American astronomer Seth Carlo Chandler. The latter discovered here in 1891 Chandler period is about 435 days. In contrast, Leonhard Euler had derived a theoretical value of about 305 days for a rigid Earth. The theoretical basis for this is the following:

The symmetry axis of the earth does not fall exactly together with their rotational axis which runs through the center of the earth. Therefore, " staggers " body of the earth a little with respect to its own axis of rotation, which is reflected in changes in the geographical coordinates of a stationary observer. Such tumbling is stable only if the rotation ( approximately) takes place about the body axis with the largest or the smallest moment of inertia. If this is not the case, the tumbling takes to long term and the rotating body appears around until one of the two said body axes ( approximately) coincides with the axis of rotation. Since the symmetry axis of the Earth is the axis with the largest moment of inertia due to the Earth flattening occurs such instability does not occur. Therefore, the difference between symmetry and rotational axis remains limited and the axis of symmetry performs about once a year präzessionsähnliche movement about the axis of rotation.

The behavior of the "Earth - gyro " and his gentle tumbling can be calculated using the methods of scientific mechanics exactly, if one assumes a rigid solid with the dimensions of the earth for him. Is the Earth's body (especially the plastic interior of the Earth ), however slightly - what the geology of folded rocks based white for a long time - to extend the period of this wobbling because the disruptive forces can no longer fix " grippy ".

The total oscillation consists of a free and a forced component. The free vibration has an amplitude of about 6 m and a period 415-433 days ( Chandlersche period). The variation of the period is related to seasonal effects together ( leaf fall and vegetation, glaciation, plate tectonics, etc.) that go back to ground displacements at the surface or inside the earth. From the difference between Chandler and Euler period, the rigidity of the earth can be calculated, which is, however, considerably more difficult by their stratification in the Earth's crust and mantle. But can the deformability of the Earth determine by other methods, eg by the earth tides.

The forced oscillation has about half as large amplitude and an annual period. It is stimulated by seasonal shifts of water and air masses. The superposition of two different long-lasting oscillations causes the amplitude of the total vibration will vary approximately six years rhythm of between about 2 m and 8 m.

This spiral motion superimposed small oscillations with periods of a few hours to a few decades. Spontaneous small displacements are sometimes determine the amount to a few centimeters - triggered about the tsunamis of 26 December 2004 in Sumatra that triggered the massive tsunami in the Indian Ocean.

The center of oscillation drifts at a speed of about 10 m per century in the direction of 80 ° West. This movement is due to large-scale tectonic processes.

International Latitude Service, IPMS and IERS

To investigate these effects in more detail, 1899, the International Latitude Service was founded. It consisted of five observatories on different continents, but all were at 39.8 ° north latitude. Through nightly measurement of astronomical width to obtain a continuous curve of the polar motion, the small ( inevitable ) contradictions in the data opposing continents were minimized by balancing calculation.

A few years after the start of the space astronomical measurements were supplemented by methods of satellite geodesy, and will soon also be improved. For the International Polar Motion Service was founded (abbreviation IPMS). He went on in the 1990s in the IERS Earth Rotation, the results of which now are based on data from five to six different measuring methods.

See special articles: fundamental astronomy.

Theory

Seasonal wave

Today, there is general agreement that the seasonal component is a forced oscillation, which is by atmospheric dynamics materialize substantially. This is due to a standing antisymmetric atmospheric tidal wave of meridional wave number m = 1 and the period of one year, the cos to sin?, A pressure amplitude is proportional to a first approximation has ( with the pole distance θ ). In the winter in the northern hemisphere an anticyclone over the North Atlantic and a low pressure system over Siberia with temperature differences of up to 50 ° exists. In summer it is vice versa. This means a Massenimbalance ( imbalance) on the Earth's surface that has a rotational motion of the figure axis of the earth against its axis of rotation result.

From the Euler's equations to find the position of the polar motion. The position of the vector m of the seasonal component of the polar motion describes an ellipse (Fig. 3), the major and minor axes in the ratio

Stand ( with νC = 0.83 the Chandler resonance frequency, or a Chandler - resonant period of? c = 441 sidereal days = 1.20 sidereal years ). The result in Figure 3 is in good agreement with the observations. The amplitude of the atmospheric pressure wave generated by this sweeping is po = 2.2 hPa with a maximum at? O = -170 ° longitude.

It is difficult to determine the influence of the ocean. Its effect has been estimated to be 5-10%.

Chandler wobble

During the year component remains fairly constant from year to year, the observed Chandler period fluctuates considerably over the years. This variation is represented by the empirical formula

Fairly well described. The amount of m increases with the reciprocal frequency. One explanation for the Chandler - wobble is excited by quasi-periodic atmospheric dynamics. In fact, it has been read from a coupled atmosphere - ocean model, a quasi -14- month period, and it is a regional 14 -month signal in the ocean - surface temperature have been observed.

For a theoretical treatment of Euler's equations, the (normalized ) frequency ν must be replaced by a complex frequency ν iνD where the imaginary term vd Dissipationseffekte simulated on the basis of the elastic earth's body. As in Figure 3, the solution of a prograde and retrograde circular polarized wave is composed. For frequencies ν <0.9, the retrograde wave can be neglected, and it remains the circularly polarized wave prograde, the vector m moves in a circle counterclockwise. The calculated amount of m is

This is a resonance curve, the flanks by

Can be approximated. The maximum amplitude of m at ν = νC is

In the area of ​​validity of the empirical formula Eq. (2) is in good agreement with Eq. (4). From the observations of the past 100 years shows that so far no major value was found as mmax ~ 230 mas ( Milliarcsekunden ). This gives a lower bound for? D = 1/νD ≥ 100 years. The corresponding pressure amplitude of the atmospheric wave is po ~ 0.2 hPa This number is small, in fact, and points to the resonance effect in the vicinity of the resonance frequency Chandlerschen.

Pole coordinates

Regularly determined by the addition to the IERS earth rotation parameters describing instantaneous rotational velocity of the earth and the current orientation of the rotary axis of the chamber and the current orientation of the earth with respect to the axis of rotation.

The pole coordinates and specify the location of the instantaneous axis of rotation (more precisely, of the Celestial Ephemeris Pole) with respect to a certain fixed point on the Earth's surface ( the IERS Referenzpols ) to. The x - axis in the direction of the prime meridian (more precisely, of the IERS Reference Meridian ) and the y- axis in the direction 90 ° west. The unit of measurement milliarcseconds are mostly used ( the distance between the two points on the earth's surface can also be expressed in meters).

As part of the polar motion, the situation of a stationary observer, with respect to the axis of rotation changes. Does this observer an astronomical determining its geographical coordinates by, he shall receive according to the current position of the axis of rotation slightly different results. Is his middle astronomical length and its average width, and has the instantaneous axis of rotation and the pole coordinates, so be the detected deviations from its mean coordinates in a first approximation

Geophysical implications

If we imagine the Earth as a precise, rigid sphere and completely symmetrical rotating, the Earth's axis would be immutable and north and south poles remain on the ball in the same position. In fact, the Earth has

• A flattening, thereby attacking from the outside forces are no longer symmetrical;
• A certain elasticity and consequent oscillations ( see, eg, earthquakes)
• And plasticity ( ductility in longer periods), visible, eg of geological folds in the mountain building or continental drift,
• As well as seasonal changes (atmosphere, ocean currents, vegetation, etc.)

This takes the true axis of the earth very complicated, but mostly periodic motions. The shift of mass on and in the earth, and the resilience of the earth can be partly theoretically appropriate physical models, partly calculated empirically and refine a little every year.

In 2003, the Descartes Prize Prof. Véronique Dehant of the Observatoire Royal de Belgique and a Europe-wide group of about 30 researchers was awarded that developed under her guidance an extended theory of the Earth's rotation and nutation.

Applications and reductions

The exact knowledge of the position of Earth's axis is in addition to the research required for several purposes practice. These include satellite navigation, the geoid determination, the reduction of geodetic precision measurements (see vertical deflection ) and the aerospace industry. If one did not take into account the current pole position, would be error in the position of more than 10 meters in the result. For example, a 100 km network of a large land surveying differences would suffer from cm to dm, or a Mars rocket would miss their target by several 1000 km.