Earth tide


Earth 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 forcing causing earth tides and ocean tides is the same, the responses are quite different.

Tide raising force

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. This pattern remains fixed with the red area directed toward the Moon. Red indicates upward pull, blue downward. If, for example the Moon is directly over 90° W, 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 , 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 impart semi-diurnal force.

Body tide

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 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 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 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 about once every 12 hours and one full cycle of maximum height about once every 14 days.
The semi-diurnal tide is primarily lunar 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. The tesseral variation has one cycle per latitude, one bulge and one depression; the bulges are opposed, 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, 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.

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 of water about what would be the gravitational equilibrium level, and therefore the adjacent ground falls 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 tide constituents. The amplitudes may vary from those listed within several per cent.

Semi-diurnal

Diurnal

Long term

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.
The semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator which is important in Global Positioning System, very-long-baseline interferometry, and satellite laser ranging measurements. Also, to make precise astronomical angular measurements requires accurate knowledge of the Earth's rate of rotation, which is influenced by Earth tides. Terrestrial tides also need to be taken in account in the case of some particle physics experiments.
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.
Body tides in planets and moons, as well as in binary stars and binary asteroids, play 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. Owing to the body tides in it, Mercury is trapped in the 3:2 spin-orbit resonance with the Sun.
For the same reason, it is believed that many of the exoplanets are captured in higher spin-orbit resonances with their host stars.