Earth tide

Earth tide

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Earth tide is the sub-meter motion of the Earth of about 12 hours or longer caused by Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 and Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

, also called body tide which is the largest contribution globally. The largest body tide contribution is from the semidiurnal constituents, but there are also significant diurnal constituents. There also semi-annual and fortnightly contributions due to the axial tilt
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...

The use of the word tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

is by analogy, and although the forcing is quite similar, the responses are quite different.

Tidal forcing

The larger of the periodic gravitational forcings is from the Moon but that of the Sun is also important.
The images here show lunar tidal forcing 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 center of the red areas are centered 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 center of the red area is 30° N, 90° W and 30° S, 90° E, and the center of the bluish band follows the great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

 equidistant from those points. At 30° latitude a strong peak occurs once per lunar day, giving significant diurnal forcing at that latitude. Along the equator two equally sized peaks (and depressions) are equally sized, giving semi-diurnal forcing there.

Body tide

The Earth tide encompasses the entire body of the Earth and is unhindered by the thin crust
Crust (geology)
In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...

 and land masses of the surface, on scales that make the rigidity of rock irrelevant. Ocean tides are a consequence of 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 in opposition, 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 classical theory of Earth tides first became established in 1905,
primarily to explain nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

s, but are also used in Earth rotation predictions. The semi-diurnal tide (one maximum every 12 or so hours) is primarily lunar (only S2 is purely solar) and gives rise to sectorial deformations which rise and fall at the same time along the same longitude.
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.
Tesseral variation have one cycle per latitude, one bulge and one depression; the bulge are opposed (antipodal), that is to say the western part of the northern hemisphere and the eastern part of the southern hemisphere, for example, and similarly the depressions are opposed, the western part of the northern hemisphere and the western part of the southern hemisphere, in this case.
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
Vertical direction
In astronomy, geography, geometry and related sciences and contexts, a direction passing by a given point is said to be vertical if it is locally aligned with the gradient of the gravity field, i.e., with the direction of the gravitational force at that point...

 east-west and north-south variations are often tabulated in milliarc seconds for astronomical use. The vertical displacement is frequent tabulated in μgal
Gal (unit)
The gal, sometimes called galileo, is a unit of acceleration used extensively in the science of gravimetry. The gal is defined as 1 centimeter per second squared ....

, since the gradient of gravity is location dependent so that the distance conversion is only approximately 3 μgal per cm

Other Earth tide contributors

In coastal areas because the ocean tide is quite out of step with the earth tide, at high ocean tide there is an excess (or at low tide a deficit) of water about what would be the gravitational equilibrium level and the adjacent ground falls (or rises) in response to the resulting differences in weight. 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.

Tidal constituents

Principal body tide constituents. The amplitudes may vary from those listed within several per cent.


Tidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)
M2 12.421 hr 384.83 53.84
S2 (solar semi-diurnal) 12.000 hr 179.05 25.05
N2 12.658 hr 73.69 10.31
K2 11.967 hr 48.72 6.82


Tidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)
K1 23.934 hr 191.78 32.01
O1 25.819 hr 158.11 22.05
P1 24.066 hr 70.88 10.36
φ1 23.804 hr 3.44 0.43
ψ1 23.869 hr 2.72 0.21
S1 (solar diurnal) 24.000 hr 1.65 0.25

Long term

Tidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)
Mf 13.661 days 40.36 5.59
Mm (moon monthly) 27.555 days 21.33 2.96
Ssa (solar semi-annual) 0.50000 yr 18.79 2.60
Lunar node 18.613 yr 16.92 2.34
Sa (solar annual) 1.0000 yr 2.97 0.41

Earth tide effects

Volcanologists use the regular, predictable Earth tide movements to calibrate and test sensitive volcano deformation monitoring instruments. The tides may also trigger volcanic events.

Seismologists have determined that microseismic events are correlated to tidal variations in Central Asia (north of the Himalayas).

The semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator which is important in GPS calibration and VLBI measurements. Also to make precise astronomical angular measurements requires knowledge of the Earth's rate of rotation and nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

, both of which are influenced by earth tides. Terrestrial tides also need to be taken in account in the case of some particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...


For instance, at the CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

 or SLAC, the very large particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s 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 particle beam energy.
Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth's magnetic field
Earth's magnetic field
Earth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...