Earth tide

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Earth tide (also known as solid-Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer. The largest body tide constituents are semi-diurnal, but there are also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational force causing earth tides and ocean tides is the same, the responses are quite different.

Contents

Tide raising force

Tideforcenw.jpg
Tideforcese.jpg
Lunar tidal force: these images depict the Moon directly over 30° N (or 30° S) viewed from above the Northern Hemisphere, showing both sides of the planet. Red up, blue down.

The larger of the periodic gravitational forces is from the Moon but that of the Sun is also important. The images here show lunar tidal force when the Moon appears directly over 30° N (or 30° S). This pattern remains fixed with the red area directed toward (or directly away from) the Moon. Red indicates upward pull, blue downward. If, for example the Moon is directly over 90° W (or 90° E), the red areas are centred on the western northern hemisphere, on upper right. Red up, blue down. If for example the Moon is directly over 90° W (90° E), the centre of the red area is 30° N, 90° W and 30° S, 90° E, and the centre of the bluish band follows the great circle equidistant from those points. At 30° latitude a strong peak occurs once per lunar day, giving a significant diurnal force at that latitude. Along the equator two equally sized peaks (and depressions) impart semi-diurnal force.

Body tide components

Sectorialvert.jpg
Vertical displacements of sectorial movement.
Red up, blue down.
Sectorialeastwest.jpg
East-west displacements of sectorial movement.
Red east, blue west.
Sectorialnorthsouth.jpg
North-south displacements of sectorial movement.
Red north, blue south.
Tesseralvert.jpg
Vertical displacements of tesseral movement.
Red up, blue down.
Tesseraleastwest.jpg
East-West displacements of tesseral movement.
Red east, blue west.
Tesseralnorthsouth.jpg
North-South displacements of tesseral movement.
Red north, blue south.

The Earth tide encompasses the entire body of the Earth and is unhindered by the thin crust and land masses of the surface, on scales that make the rigidity of rock irrelevant. Ocean tides are a consequence of tangent forces (see: equilibrium tide) and the resonance of the same driving forces with water movement periods in ocean basins accumulated over many days, so that their amplitude and timing are quite different and vary over short distances of just a few hundred kilometres. The oscillation periods of the Earth as a whole are not near the astronomical periods, so its flexing is due to the forces of the moment.

The tide components with a period near twelve hours have a lunar amplitude (Earth bulge/depression distances) that are a little more than twice the height of the solar amplitudes, as tabulated below. At new and full moon, the Sun and the Moon are aligned, and the lunar and the solar tidal maxima and minima (bulges and depressions) add together for the greatest tidal range at particular latitudes. At first- and third-quarter phases of the moon, lunar and solar tides are perpendicular, and the tidal range is at a minimum. The semi-diurnal tides go through one full cycle (a high and low tide) about once every 12 hours and one full cycle of maximum height (a spring and neap tide) about once every 14 days.

The semi-diurnal tide (one maximum every 12 or so hours) is primarily lunar (only S2 is purely solar) and gives rise to sectorial (or sectoral) deformations which rise and fall at the same time along the same longitude. [1] Sectorial variations of vertical and east-west displacements are maximum at the equator and vanish at the poles. There are two cycles along each latitude, the bulges opposite one another, and the depressions similarly opposed. The diurnal tide is lunisolar, and gives rise to tesseral deformations. The vertical and east-west movement is maximum at 45° latitude and is zero on the equator and at the poles. The tesseral variation has one cycle per latitude, one bulge and one depression; the bulges are opposed (antipodal), in other words the western part of the northern hemisphere and the eastern part of the southern hemisphere, for example. Similarly, the depressions are opposed, in this case the eastern part of the northern hemisphere and the western part of the southern hemisphere. Finally, fortnightly and semi-annual tides have zonal deformations (constant along a circle of latitude), as the Moon or Sun gravitation is directed alternately away from the northern and southern hemispheres due to tilt. There is zero vertical displacement at 35°16' latitude.

Since these displacements affect the vertical direction, the east-west and north-south variations are often tabulated in milliarcseconds for astronomical use. The vertical displacement is frequently tabulated in μGal, since the gradient of gravity is location dependent, so that the distance conversion is only approximately 3 μGal per centimetre.

Vertical displacements of zonal movement. Red up, blue down. Zonalvert.jpg
Vertical displacements of zonal movement. Red up, blue down.

Tidal constituents

Principal tidal constituents. The amplitudes may vary from those listed within several per cent. [2] [3]

See also Theory of tides#Tidal constituents.

Semi-diurnal
SpeciesTidal
constituent
PeriodAmplitude (mm)
verticalhoriz.
Principal lunar semidiurnalM212.421 h384.8353.84
Principal solar semidiurnalS212 h179.0525.05
Larger lunar elliptic semidiurnalN212.658 h73.6910.31
Lunisolar semidiurnalK211.967 h48.726.82
Diurnal
SpeciesTidal
constituent
PeriodAmplitude (mm)
verticalhoriz.
Lunar diurnalK123.934 h191.7832.01
Lunar diurnalO125.819 h158.1122.05
Solar diurnalP124.066 h70.8810.36
φ123.804 h3.440.43
ψ123.869 h2.720.21
Solar diurnalS124 h1.650.25
Long Term
SpeciesTidal
constituent
PeriodAmplitude (mm)
verticalhoriz.
Lunisolar fortnightlyMf13.661 d40.365.59
Lunar monthlyMm27.555 d21.332.96
Solar semiannualSsa0.5 yr18.792.60
Lunar node18.613 yr16.922.34
Solar annualSa1 yr2.970.41

Ocean tidal loading

In coastal areas, because the ocean tide is quite out of step with the Earth tide, at high ocean tide there is an excess of water above what would be the gravitational equilibrium level, and therefore the adjacent ground falls in response to the resulting differences in weight. At low tide there is a deficit of water and the ground rises. Displacements caused by ocean tidal loading can exceed the displacements due to the Earth body tide. Sensitive instruments far inland often have to make similar corrections. Atmospheric loading and storm events may also be measurable, though the masses in movement are less weighty.

Effects

Seismologists have determined that microseismic events are correlated to tidal variations in Central Asia (north of the Himalayas);[ citation needed ] see: tidal triggering of earthquakes. Volcanologists use the regular, predictable Earth tide movements to calibrate and test sensitive volcano deformation monitoring instruments; tides may also trigger volcanic events. [4] [5]

The semidiurnal amplitude of terrestrial tides can reach about 55 cm (22 in) at the equator which is important in geodesy using Global Positioning System, very-long-baseline interferometry, and satellite laser ranging measurements. [6] [7] Also, to make precise astronomical angular measurements requires accurate knowledge of the Earth's rate of rotation (length of day, precession, in addition to nutation), which is influenced by Earth tides (see also: pole tide).

Terrestrial tides also need to be taken in account in the case of some particle physics experiments. [8] For instance, at the CERN or the SLAC National Accelerator Laboratory, the very large particle accelerators were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are circumference deformation for circular accelerators and also particle-beam energy. [9] [ unreliable source? ] [10] [ unreliable source? ]

In other astronomical objects

Body tides also exist in other astronomical objects, such as planets and moons. In Earth's moon, body tides "vary by about ±0.1 m each month." [11] It plays a key role in long-term dynamics of planetary systems. For example, it is due to body tides in the Moon that it is captured into the 1:1 spin-orbit resonance and is always showing us one side.[ citation needed ] Body tides in Mercury make it trapped in the 3:2 spin-orbit resonance with the Sun. [12] For the same reason, it is believed that many of the exoplanets are captured in higher spin-orbit resonances with their host stars. [13]

See also

Related Research Articles

<span class="mw-page-title-main">Tidal acceleration</span> Natural phenomenon due to which tidal locking occurs

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body. The Earth–Moon system is the best-studied case.

<span class="mw-page-title-main">Tide</span> Rise and fall of the sea level under astronomical gravitational influences

Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and are also caused by the Earth and Moon orbiting one another.

<span class="mw-page-title-main">Tidal force</span> A gravitational effect also known as the differential force and the perturbing force

The tidal force or tide-generating force is a gravitational effect that stretches a body along the line towards and away from the center of mass of another body due to spatial variations in strength in gravitational field from the other body. It is responsible for the tides and related phenomena, including solid-earth tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearer side is attracted more strongly than the farther side. The difference is positive in the near side and negative in the far side, which causes a body to get stretched. Thus, the tidal force is also known as the differential force, residual force, or secondary effect of the gravitational field.

<span class="mw-page-title-main">Orbital inclination</span> Angle between a reference plane and the plane of an orbit

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

<span class="mw-page-title-main">Tidal locking</span> Situation in which an astronomical objects orbital period matches its rotational period

Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon, as well as for Eris and Dysnomia. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking.

<span class="mw-page-title-main">Equatorial bulge</span> Outward bulge around a planets equator due to its rotation

An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

<span class="mw-page-title-main">Lunar node</span> Where the orbit of the Moon intersects the Earths ecliptic

A lunar node is either of the two orbital nodes of the Moon, that is, the two points at which the orbit of the Moon intersects the ecliptic. The ascending node is where the Moon moves into the northern ecliptic hemisphere, while the descending node is where the Moon enters the southern ecliptic hemisphere.

<span class="mw-page-title-main">Libration</span> Apparent oscillation of a minor body seen from the major body it orbits

In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon perceived by Earth-bound observers and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see slightly different hemispheres of the surface at different times. It is similar in both cause and effect to the changes in the Moon's apparent size due to changes in distance. It is caused by three mechanisms detailed below, two of which cause a relatively tiny physical libration via tidal forces exerted by the Earth. Such true librations are known as well for other moons with locked rotation.

<span class="mw-page-title-main">Amphidromic point</span> Location at which there is little or no tide

An amphidromic point, also called a tidal node, is a geographical location where there is little or no difference in sea height between high tide and low tide; it has zero tidal amplitude for one harmonic constituent of the tide. The tidal range for that harmonic constituent increases with distance from this point, though not uniformly. As such, the concept of amphidromic points is crucial to understanding tidal behaviour. The term derives from the Greek words amphi ("around") and dromos ("running"), referring to the rotary tides which circulate around amphidromic points. It was first discovered by William Whewell, who extrapolated the cotidal lines from the coast of the North Sea and found that the lines must meet at some point.

<span class="mw-page-title-main">Lunar standstill</span> Moon stops moving north or south

A lunar standstill or lunistice is when the Moon reaches its furthest north or furthest south point during the course of a month. The declination at lunar standstill varies in a cycle 18.6 years long between 18.134° and 28.725°, due to lunar precession. These extremes are called the minor and major lunar standstills.

<span class="mw-page-title-main">Earth's rotation</span> Rotation of Earth around its axis

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise.

<span class="mw-page-title-main">Orbit of the Moon</span> The Moons circuit around Earth

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km from Earth's centre, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 384,400 km (238,900 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.

Tidal heating occurs through the tidal friction processes: orbital and rotational energy is dissipated as heat in either the surface ocean or interior of a planet or satellite. When an object is in an elliptical orbit, the tidal forces acting on it are stronger near periapsis than near apoapsis. Thus the deformation of the body due to tidal forces varies over the course of its orbit, generating internal friction which heats its interior. This energy gained by the object comes from its orbital energy and/or rotational energy, so over time in a two-body system, the initial elliptical orbit decays into a circular orbit and the rotational periods of the two bodies adjust towards matching the orbital period. Sustained tidal heating occurs when the elliptical orbit is prevented from circularizing due to additional gravitational forces from other bodies that keep tugging the object back into an elliptical orbit. In this more complex system, orbital and rotational energy still is being converted to thermal energy; however, now the orbit's semimajor axis would shrink rather than its eccentricity.

Atmospheric tides are global-scale periodic oscillations of the atmosphere. In many ways they are analogous to ocean tides. They can be excited by:

<span class="mw-page-title-main">Equatorial electrojet</span>

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<span class="mw-page-title-main">Long-period tides</span> Small amplitude gravitational tides

Long-period tides are gravitational tides with periods longer than one day, typically with amplitudes of a few centimeters or less. Long-period tidal constituents with relatively strong forcing include the lunar fortnightly (Mf) and lunar monthly (Ms) as well as the solar semiannual (Ssa) and solar annual (Sa) constituents.

<span class="mw-page-title-main">Planetary coordinate system</span> Coordinate system for planets

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Tides in marginal seas are tides affected by their location in semi-enclosed areas along the margins of continents and differ from tides in the open oceans. Tides are water level variations caused by the gravitational interaction between the Moon, the Sun and the Earth. The resulting tidal force is a secondary effect of gravity: it is the difference between the actual gravitational force and the centrifugal force. While the centrifugal force is constant across the Earth, the gravitational force is dependent on the distance between the two bodies and is therefore not constant across the Earth. The tidal force is thus the difference between these two forces on each location on the Earth.

References

  1. Paul Melchior, "Earth Tides", Surveys in Geophysics, 1, pp. 275–303, March, 1974.
  2. John Wahr, "Earth Tides", Global Earth Physics, A Handbook of Physical Constants, AGU Reference Shelf, 1, pp. 40–46, 1995.
  3. Michael R. House, "Orbital forcing timescales: an introduction", Geological Society, London, Special Publications; 1995; v. 85; p. 1-18. http://sp.lyellcollection.org/cgi/content/abstract/85/1/1
  4. Sottili G., Martino S., Palladino D.M., Paciello A., Bozzano F. (2007), Effects of tidal stresses on volcanic activity at Mount Etna, Italy, Geophys. Res. Lett., 34, L01311, doi : 10.1029/2006GL028190, 2007.
  5. Volcano watch, USGS.
  6. IERS Conventions (2010). Gérard Petit and Brian Luzum (eds.). (IERS Technical Note ; 36) Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2010. 179 pp., ISBN   9783898889896, Sec. 7.1.1, "Effects of the solid Earth tides"
  7. User manual for the Bernese GNSS Software, Version 5.2 (November 2015), Astronomical Institute of the University of Bern. Section 10.1.2. "Solid Earth Tides, Solid and Ocean Pole Tides, and Permanent Tides"
  8. Accelerator on the move, but scientists compensate for tidal effects Archived 2010-03-25 at the Wayback Machine , Stanford online.
  9. "circumference deformation" (PDF). Archived from the original (PDF) on 2011-03-24. Retrieved 2007-03-25.
  10. particle beam energy Archived 2011-07-20 at the Wayback Machine affects
  11. Williams, James G.; Boggs, Dale. H. (2015). "Tides on the Moon: Theory and determination of dissipation". Journal of Geophysical Research: Planets. 120 (4). American Geophysical Union (AGU): 689–724. Bibcode:2015JGRE..120..689W. doi:10.1002/2014je004755. ISSN   2169-9097. S2CID   120669399.
  12. Noyelles, B.; Frouard, J.; Makarov, V. V. & Efroimsky, M. (2014). "Spin-orbit evolution of Mercury revisited". Icarus. 241: 26–44. arXiv: 1307.0136 . Bibcode:2014Icar..241...26N. doi:10.1016/j.icarus.2014.05.045. S2CID   53690707.
  13. Makarov, V. V.; Berghea, C. & Efroimsky, M. (2012). "Dynamical Evolution and Spin–Orbit Resonances of Potentially Habitable Exoplanets: The Case of GJ 581d". The Astrophysical Journal. 761 (2): 83. arXiv: 1208.0814 . Bibcode:2012ApJ...761...83M. doi:10.1088/0004-637X/761/2/83. S2CID   926755. 83.

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