# Earth rotation

Illustration of the earth's rotation
The movement of the earth's surface in relation to the starry sky due to the earth's rotation

The earth's rotation is the rotation of the earth around its own axis . The axis of rotation is called the earth axis . The earth is rotating to the east, which can be easily verified by orienting yourself with a compass at sunrise. Seen from the North Star , the earth rotates counterclockwise.

The rotation vector of the earth points exactly to the north of the earth according to the right-hand screw rule, and thus almost exactly to the pole star. All points on the earth's surface, with the exception of its two poles, move in the (local) east direction. For an observer who lies with his head to the north on the ground and looks at the stars at the zenith, an earth-fixed mast tip (visible within a minute compared to a very close star) also moves to the east, but this in the sky by looking from below is on the left, as seen from inside the earth.

The average duration of one revolution in relation to the cosmic background assumed to be at rest - the mean sidereal day - is 23  h 56  min 4.10  s . This corresponds to the nominal mean angular velocity determined by the IERS of 7.292115 × 10 −5 rad / s or, if this angular velocity is multiplied by the equatorial radius 6378.137 km , a peripheral velocity of 465.1 m / s . Nowadays , extragalactic radio sources observed by means of radio interferometry serve as reference points for the precise measurement of the period of rotation . Until a few decades ago, however, there were no static reference points available that would have met higher demands. The stars accessible for observation were only suitable to a limited extent because of their proper motion .

In astronomical practice, the rotation is therefore usually related to the vernal equinox , the position of which can always be calculated in relation to the stars and planets. The period of time that the earth needs to return to the same position with respect to the vernal equinox after one revolution is a sidereal day and is only 23 h 56 min 4.091 s. The precession of the earth is the reason why a sidereal day is about 8 milliseconds longer than a sidereal day .

If you divide the sidereal day into 24 hours * (hours of sidereal time ), then the sidereal time is a direct measure of the angle of rotation of the earth. Knowing the sidereal time can therefore determine the current view of the sky. In particular, the vernal equinox culminates for the observer concerned at 24 o'clock * .

Note the inconsistent designation: Despite its name, sidereal day does not refer to the stars, but to the vernal equinox. The sidereal day relates to the stars . The English names (defined by the IERS ) are, for example, exactly the opposite: the sidereal day is called sidereal day , while the sidereal day is called stellar day .

## sunny day

Sidereal day (from 1 to 2) and solar day (from 1 to 3)

The sunny day is the period from one solar high point to the next and serves as the basis for everyday time measurement. It lasts an average of 24 hours and is thus slightly longer than a sidereal day. The difference between the length of the sidereal day and the length of the solar day results from the annual movement of the earth around the sun. After a complete rotation, the earth has moved almost one degree of arc on its orbit (360 degrees in approx. 365 days). The earth must continue to rotate around this same angle until the sun can be seen in the sky in the same direction as the day before. This takes about 4 minutes on average.

However, since the earth's elliptical orbit is traversed at variable speeds over the course of the year and because the ecliptic is inclined to the celestial equator, not all sunny days of a year are the same length. A distinction is therefore made between the true sunny day as the period between two highest solar levels and the mean sunny day of the same length , whose length corresponds to the length of the true sunny days averaged over a year. The mean sunny day was divided into 24 hours by definition. Therefore clocks run according to a mean sun, unlike sundials , which naturally take the actual sun as their basis. The time difference between mean solar time and true solar time is called the equation of time .

## Axis of rotation

Due to the earth's moment of inertia , the direction of its axis of rotation is constant in space (almost, see below). To the north, the earth's axis currently points to a point in the sky that is just under one degree next to a star in the constellation Little Bear . For an earthly observer in the northern hemisphere, the sky seems to rotate around this point once a day. Therefore, the point is called celestial north pole and the star Polaris . To the south, the earth's axis does not currently point to a prominent star.

The axis of rotation is inclined by almost 23.5 ° to the normal of the plane of the earth's orbit ( skew of the ecliptic ). During the annual orbit of the earth around the sun, the northern hemisphere on one half of the orbit and the southern hemisphere on the other half are more or less inclined towards the sun. In this hemisphere it is summer because of the stronger solar radiation ; the other seasons arise accordingly.

## Temporal variability

### Physical basics

Due to its angular momentum , the earth rotates. The angular momentum is the product of the rotational speed of the earth (expressed as angular speed ) and its moment of inertia .

Since the angular momentum is a conserved quantity , it can only be changed by the action of an external torque . As a vector , the angular momentum has both a magnitude and a direction; Constancy of the angular momentum therefore means that both the speed of rotation and the position of the axis of rotation in space remain constant.

The torques acting on the earth are very small, so that their angular momentum and thus also their rotational speed and the alignment of their axis of rotation remain essentially constant. However, changes over time can be determined with precise measurement or observation of long periods of time.

The turning speed changes

• if the total angular momentum changes due to the action of an external torque,
• if the total angular momentum, which remains constant, is redistributed in different ways to subsystems ( atmosphere / mantle / core ) (the observations only cover the movement of the subsystem "mantle with earth crust"),
• if the earth's moment of inertia changes as a result of deformation (e.g. post-glacial land uplift ) or mass redistribution (e.g. melting of glaciers), so that a different rotational speed results despite constant total angular momentum ( pirouette effect ).

The position of the axis of rotation in space changes when external torques act ( precession ). Since the earth's axis of symmetry does not exactly coincide with its axis of rotation, the earth's body executes small oscillations around the axis of rotation, so that its points of penetration through the earth's surface fluctuate within a range of a few meters ( pole movement ).

### Variability of the rotation time

#### Short-term fluctuations

Day lengths 1962 to 2015

Precise measurements show that the duration of a revolution and thus the length of the day is not strictly constant. The picture on the right shows the day lengths since 1962. The figure shows the deviation of the measured day length from a nominal reference day derived from the international system of units with a length of exactly 86,400  SI seconds . After an initial increase, the trend has been declining since the early 1970s. Such fluctuations , which can span several decades to centuries, are presumably based on mass shifts in the liquid outer core of the earth.

These fluctuations are superimposed by fluctuations lasting around a decade. They are probably caused by an exchange of angular momentum between the earth's core and the earth's mantle . Long-term shifts in the distribution of water and ice on the earth's surface are also likely to play a role.

An annual fluctuation with an amplitude of around 2 ms is particularly noticeable. It can be traced back to changes in the position and strength of the larger jet streams . Fluctuations on a time scale of decades are caused by the exchange of angular momentum between the earth's surface and the atmosphere (e.g. winds that blow against larger mountain ranges such as the Andes or the Rocky Mountains ). The latter connection is now so well known that meteorological models of the atmosphere can be used to predict these fluctuations (keyword: Atmospheric Angular Momentum , AAM).

Tidal deformations of the earth and oceans cause fortnightly, monthly, half-yearly and yearly proportions of the fluctuations. They are completely predictable and are therefore often removed from the observation data in order to make the other effects more clearly apparent. They must be added again using the relevant calculation models before they can be used.

Occasionally, individual events such as B. Mass relocations due to strong earthquakes visible in the data. The graphic clearly shows the effects of a particularly pronounced El Niño in the winter of 1982/83. The 2004 seaquake in the Indian Ocean accelerated the earth's rotation so that the day length was shortened by 8  μs . The earth's rotation experienced a further acceleration on March 11, 2011 after the earthquake in the Pacific Ocean off the Japanese coast : The earth now rotates a little faster, "a day is now 1.8 μs shorter than before".

Relocations of biomass also play a certain role. The claim that the earth rotates more slowly in (northern) summer than in winter because the leaves on the trees increase the moment of inertia ( pirouette effect ) and that there are more trees in the northern hemisphere than in the southern hemisphere is not tenable. As the graphic shows, the length of the day is shortest in northern summer , so the earth rotates particularly quickly . The certainly existing influence of the foliage is thus completely masked by larger opposing effects. One of the overlapping effects is the redistribution of water masses in the form of snow to the altitude of the mountains.

With all these fluctuations, it should be remembered that even relatively small influences can add up to noticeable effects if the duration of action is long enough. In the case of longer-term fluctuations, lower torques or changes in the moment of inertia are therefore necessary than in the case of shorter-term fluctuations.

The difference between UT1 (proportional to the earth's rotation) and UTC (derived from atomic clocks, with leap seconds) from early 1973 to mid-2015

The current day lengths are mostly longer than the reference day length of 86400 SI seconds. This is because the SI second was ultimately derived from the length of the day, which existed during the middle of the 19th century, through several intermediate steps. Due to the long-term increase in day length explained below, days are generally a little longer today than they were then. The excess length of the day over the nominal 86400 s must regularly by a leap second to be compensated. For example, if the length of the day is 2 ms longer than the setpoint value, the earth's rotation is delayed by 2 ms every day compared to a constant atomic clock . After 500 days the difference would have accumulated to one second: The 500th rotation would not end until one second after midnight (atomic time) of the 500th day.

A leap second is inserted at irregular intervals, at full or half calendar years, in order to keep the difference small. This time scale, which is based on the one hand on the SI second defined by atomic clocks and therefore strictly uniform , but on the other hand is adapted to the irregular rotation of the earth by inserting (or possibly omitting) leap seconds, is Coordinated Universal Time ( UTC ). With every positive leap second, it moves further away from the strictly uniform International Atomic Time ( TAI ) , which is used only for scientific and technical purposes .

In the example mentioned, a leap second would be necessary every year and a half. This was indeed the case during the 1980s. As can be seen from the day length graph, since the mid-1990s the day length has again clearly approached the historical value, so that no leap second was required between 1999 and 2006.

#### Long term changes

Influence of the tides on the rotation of the earth and the lunar orbit: The earth's rotation, which is around 28 times faster than the orbit of the moon, shifts the tide mountains by friction to the east by the lead angle

The tidal friction exerts a braking torque on the earth, so that the day length increases slowly but continuously. In the modern series of measurements, this effect is almost completely hidden by the fluctuations described above. But because it is secular and therefore sums up squarely over longer periods of time, it can be clearly proven with the help of traditional ancient and medieval astronomical observations and also numerically determined for the past.

Since, until the introduction of atomic clocks, the time scale used by the observer was always compared to the course of the sun and thus ultimately to the rotation of the earth, it was subject to the same fluctuations and long-term drifts as the earth's rotation. On the other hand, modern physical models of planetary motion are based on a strictly uniform course of time, as can now be realized with atomic clocks, regardless of the rotation of the earth. Specifically, the so-called terrestrial time TT is used for this. If one now calculates the planetary movements back in order to determine the point in time of the observed event in the evenly running TT, and comparing this point in time with the traditional unevenly running local time of the observer, one finds a discrepancy that grows continuously the further one goes into the Past. For Babylonian reports around the year −700, for example, the traditional local time differs by about five to six hours from the time that one would expect assuming a constant earth rotation. A correction ΔT must therefore always be added to the local time taken from the reports in order to obtain the associated time in terrestrial time and to be able to compare the report with the back calculation.

The evaluation of numerous observations from the past 2700 years shows that the day length increased by an average of around 17 μs per year during this period. This is in good agreement with the obtained regardless finding that the day length on the one hand due to tidal friction by about 23 microseconds per year increases (on the conservation of angular momentum derived from the observed influence of tidal friction to the movement of the moon), while by the post-glacial land uplift caused The thinning of the earth due to the associated pirouette effect shortens the length of the day by about 6.0 μs per year (since the earth's volume cannot change, the uplifting of areas near the polar leads to a shrinkage of the equatorial bulge - an ellipsoid of revolution with less flattening has a lower moment of inertia ).

For prehistoric times, the speed of the earth's rotation can be read off daily growth rings of fossil marine organisms with calcareous skeletons. If the daily increase is modulated by the monthly change of nippy and spring tide or by the annual change of seasons (as can also be observed in relatives of such organisms living today), then by counting the rings, at least in principle, the number of days in the Determine month or year. Corresponding studies indicate, for example, that 400 million years ago the year had about 400 days; assuming the same annual duration, a day only lasted about 21.9 hours. For the time 310 million years ago, however, a day duration of 20 hours could be determined.

Mathematical models for the early earth that was just emerging, around 4 billion years ago, suggest an original day length of just 14 hours. Other scientists assume a rotation period of six to seven hours for this phase of the earth's history.

### Variability of the axis of rotation

#### Precession and nutation

Because of its flattening , the earth has a 20 km thick equatorial bulge, which is inclined to the orbit plane due to the inclination of the earth's axis. The gravitational forces exerted by the sun , the moon and the other planets try to pull it into the plane of the orbit , but according to the gyroscopic law of precession , the earth's axis deviates perpendicularly to this torque. It maintains its 67 ° inclination in relation to the plane of the orbit, but swings around once every 26,000 years on a cone surface.

Because the intersection of the equatorial plane and the ecliptic serves as the origin of the celestial coordinates, they change secularly over time.

Another correction is nutation , the swinging around the axis of rotation, with a period of approximately 19 years.

#### Pole movement

The distance covered by the earth's instantaneous axis of rotation in the years 2001 to 2005 at the North Pole

About 150 years ago, astronomers discovered that the Earth's geographic north and south poles are not completely immutable. Such shifts occur due to the superposition of several phenomena. On the one hand, the continents move relative to one another under the influence of plate tectonics . From the point of view of a measuring location on a continent, the location of the poles is gradually changing.

The Earth's axis of symmetry does not exactly coincide with the axis of rotation. The rotation is still stable, however, because it takes place around the axis with the greatest moment of inertia due to the flattening of the earth. Otherwise the deviation would build up and cause the earth to tumble. Because of the stable situation, the deviation remains limited and the symmetry axis of the earth performs a precession-like movement around the axis of rotation about once a year. The point at which the current axis of rotation pierces the surface of the earth draws an irregular spiral with a maximum diameter of about 20 m. This oscillation is made up of two components: an oscillation forced by periodic displacements of water and air masses with an annual period and a free oscillation with a period of about 14 months ( Chandler period ). The superposition of the two means that the amplitude of the total oscillation fluctuates between approx. 2 m and approx. 8 m every six years. On average, the pole drifts slowly towards 80 ° west.

Paleographic studies suggest that there have also been large polar movements in the past. Some movements greater than 50 ° in circumference took place around 800 million years ago.

## Earth rotation parameters

For numerous applications in astronomy , space travel , surveying (especially astrogeodesy ), etc., precise knowledge of the current orientation of the earth in space is necessary. If the accuracy requirements are in a range in which the short-term and long-term fluctuations explained above become noticeable, then these must be taken into account. For this purpose, the so-called earth rotation parameters are regularly measured and published. They include

• the world time correction dUT1 , which specifies the difference between the time scale UT1 , which is coupled to the variable rotation of the earth, and the coordinated world time UTC, which is derived from the uniform atomic time . UT1 is proportional to the earth's rotation and therefore a measure of the earth's current angle of rotation. The difference dUT1 = UT1 - UTC reflects the irregularity of the earth's rotation. If the difference threatens to become greater than 0.9 s, a leap second is inserted in UTC to compensate for the difference again.
• the polar coordinates x and y. They describe the position of the momentary axis of rotation of the earth's body (more precisely: the Celestial Ephemeris Pole) in relation to a certain fixed point on the earth's surface (the IERS reference pole ). The x-axis runs in the direction of the prime meridian (more precisely: the IERS reference meridian ) and the y-axis in the direction of 90 ° west. Milli-arcseconds are usually used as the unit of measurement (the distance between the two points on the earth's surface can also be expressed in meters).
• the celestial pole fluctuations and , which describe the observed deviations of the celestial pole from certain mathematical models for precession and nutation. is the deviation in ecliptical length, is the deviation in ecliptic skew.${\ displaystyle \ mathrm {d} \ psi}$${\ displaystyle \ mathrm {d} \ epsilon}$${\ displaystyle \ mathrm {d} \ psi}$${\ displaystyle \ mathrm {d} \ epsilon}$

The observations required for this, which are regularly carried out worldwide, are coordinated, evaluated and published by the International Earth Rotation and Reference Systems Service (IERS).

The data obtained in this way are themselves of scientific interest. They contain information about the structure and physical properties of the earth, changes in shape of the earth's globe, changes in the exact position of the earth's center of gravity and geophysical processes occurring in the earth's interior.

The relevant observations have been made since the end of the nineteenth century through position measurements on stars or observations of star coverings by the moon. The parameters could be determined every five days. Since the 1970s and 1980s, VLBI measurements and GPS observations as well as laser distance measurements to suitable satellites and the moon have been added, and hourly or even somewhat more frequent readings have been recorded. Recently, the fluctuations can also be tracked continuously with the help of ring lasers . The angles of rotation and direction required to determine the Earth's rotation parameters can nowadays be measured with an accuracy of about half a milli-arcsecond. Several research groups are working on this topic in Central Europe, including in Hanover ( Jürgen Müller ) and Vienna ( Harald Schuh ).

The speed at which the earth's surface moves in an easterly direction at the level of the equator is around 1670 km / h and decreases in the direction of the two poles due to the decreasing circumference of the parallels .

## Emergence

According to popular belief , the solar system emerged from a cloud of gas and dust that condensed due to its own gravity.

If two gas or dust particles move relative to each other, each has an angular momentum with respect to the other, unless they move exactly towards each other. The existence of an angular momentum is therefore not tied to a circular motion; A straight or otherwise arbitrarily moved particle also carries an angular momentum with respect to a reference point, provided that its movement has a sideways component when viewed from this reference point, i.e. is not directed directly towards the reference point. For example, consider a billiard ball that does not hit a second ball completely centrally. Both spheres will rotate around their vertical axes after the collision; the angular momentum contained in these rotations was taken from the angular momentum that the linearly moving ball had with respect to the second ball before the collision. If the balls were to stick together when they hit, the resulting object would rotate. For the same reason, the lumps formed in a cloud of gas and dust also rotate, as it is very unlikely that all of their components have collided with one another in the exact center. Even after the lumps have grown to larger planetesimals , each impact of a planetesimal on a protoplanet changes its rotation depending on the impact point and angle. The answer to the question “Where did the angular momentum come from?” Is thus: from the disordered movement of the particles, which in addition to their linear momentum associated with the movement also always carry an angular momentum and whose angular momentum has not all canceled each other out when they clustered together to form planets . The more compact the resulting body is, the faster it rotates (even if the angular momentum remains constant) due to the pirouette effect .

The direction of rotation of the earth is identical to the direction of rotation on its orbit around the sun, as with almost all other planets. Only Venus rotates in the opposite direction, and the axis of rotation of Uranus is almost in its orbital plane.

## proof

The rotation of the earth manifests itself through Coriolis and centrifugal forces on the earth's surface. This can be seen, among other things, in the direction of rotation of cloud eddies in low pressure areas .

The rotation of the earth causes a centrifugal force that increases as the equator approaches . At the equator it is directed against the force of gravity , which is why the weight of an object there is less than at the poles . Together with the flattening of the earth , which is also caused by centrifugal force, the difference is 0.53%.

The following physical experiments can be used to demonstrate the rotation of the earth in the laboratory:

 Start of experiment: stick at rest End of experiment: rod rotates
• Swiveling ideal rod (see pictures on the right, does not work on the equator)
According to Hans Bucka, this proof is achieved with a swiveling rod suspended in a rotatable holder. A homogeneous rod is mounted on the longitudinal axis close to its center with a horizontal axis of rotation with little friction and is initially in a horizontal position and at rest in relation to the earth's surface. Nevertheless, it has an angular momentum that is due to the rotation of the earth. By means of a suitable mechanism (for example a thread that burns through, which is stretched between the holder and the somewhat longer end of the rod), the rod is brought into a vertical position due to the slight excess weight of one side , whereby its moment of inertia is reduced by several orders of magnitude . Since the angular momentum does not change because of the conservation of angular momentum , the rod begins to rotate in the direction of rotation of the earth, which can be made visible, for example, with a light pointer , the mirror of which is attached to the rotation axis of the bracket.

## literature

Wiktionary: Earth rotation  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

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2. Chile quake shifted the earth's axis. In: Spiegel.de . Spiegel-Verlag , March 2, 2010, accessed October 20, 2020 .
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5. Why the days are getting longer. Spectrum of Science, 10/2007, pp. 36-45, .
6. ^ FR Stephenson: Historical Eclipses and Earth's Rotation. Cambridge University Press, Cambridge (UK) 1997, p. 37.
7. Stephenson, p. 516.
8. ^ G. Pannella: Paleontological Evidence on the Earth's Rotational History since Early Precambrian. Astrophysics and Space Science 16 (1972) 212-237, bibcode : 1972Ap & SS..16..212P .
9. William and Fank Awbrey: As the World Turns. Can Creationists Keep Time? Thwaites, 1982. pp. 18-22 (after this video ).
10. Harald Lesch: How did the moon come about? Contribution to the program alpha-Centauri , accessed on October 20, 2020.
11. Markus Becker: Imbalance in the globe. In: Spiegel.de. September 1, 2006, accessed October 20, 2020 .
12. ^ Adam C. Maloof et al .: Combined paleomagnetic, isotopic, and stratigraphic evidence for true polar wander from the Neoproterozoic Akademikerbreen Group, Svalbard, Norway. Geological Society of America Bulletin 188, 2006, pp. 1099-2014, doi : 10.1130 / B25892.1 ( online, ( October 15, 2008 memento from the Internet Archive ), accessed October 20, 2020).
13. Emmanuelle Arnaud et al. (Ed.): The Geological Record of Neoproterozoic Glaciations. Geological Society, London 2011, ISBN 978-1-86239-334-9 , limited preview in Google Book Search.
14. Hans Bucka: Two simple lecture attempts to prove the rotation of the earth. Zeitschrift für Physik A, Vol. 126, pp. 98-105 (1949), Vol. 128, pp. 104-107 (1950).