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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 cycle, 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.
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.Paul Melchior, "Earth Tides", Surveys in Geophysics, 1, pp. 275–303, March, 1974. 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 harmonics 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 arc seconds 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.
See also Theory of tides#Tidal constituents.
| Semi-diurnal | ||||
| Species | Tidal constituent | Period | Amplitude (mm) | |
| vertical | horiz. | |||
| Principal lunar semidiurnal | M2 | 12.421 h | 384.83 | 53.84 |
| Principal solar semidiurnal | S2 | 12 h | 179.05 | 25.05 |
| Larger lunar elliptic semidiurnal | N2 | 12.658 h | 73.69 | 10.31 |
| Lunisolar semidiurnal | K2 | 11.967 h | 48.72 | 6.82 |
| Diurnal | ||||
| Species | Tidal constituent | Period | Amplitude (mm) | |
| vertical | horiz. | |||
| Lunar diurnal | K1 | 23.934 h | 191.78 | 32.01 |
| Lunar diurnal | O1 | 25.819 h | 158.11 | 22.05 |
| Solar diurnal | P1 | 24.066 h | 70.88 | 10.36 |
| φ1 | 23.804 h | 3.44 | 0.43 | |
| ψ1 | 23.869 h | 2.72 | 0.21 | |
| Solar diurnal | S1 | 24 h | 1.65 | 0.25 |
| Long Term | ||||
| Species | Tidal constituent | Period | Amplitude (mm) | |
| vertical | horiz. | |||
| Lunisolar fortnightly | Mf | 13.661 d | 40.36 | 5.59 |
| Lunar monthly | Mm | 27.555 d | 21.33 | 2.96 |
| Solar semiannual | Ssa | 0.5 yr | 18.79 | 2.60 |
| Lunar node | 18.613 yr | 16.92 | 2.34 | |
| Solar annual | Sa | 1 yr | 2.97 | 0.41 |
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.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., , Sec. 7.1.1, "Effects of the solid Earth tides" [2]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" [3] 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. Accelerator on the move, but scientists compensate for tidal effects , Stanford online. 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.Wenninger, J. (1999, March). Observation of radial ring deformations using closed orbits at LEP. In Proceedings of the 1999 Particle Accelerator Conference (Cat. No. 99CH36366) (Vol. 5, pp. 3014-3016). IEEE. Among the effects that need to be taken into account are circumference deformation for circular accelerators and particle-beam energy.
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