Earth tide

Body tide components

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. 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.

Tidal constituents

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

See also Theory of tides#Tidal constituents.

Ocean tidal loading

Ocean tidal loading is the deformation of the underlying crust in response to periodic variations of water mass associated with the ocean tide, and is typically one order of magnitude smaller than the body tide deformation. 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

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

The semidiurnal M₂ 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. The semi-diurnal Earth tides are nearly in phase with the Moon with a lag in the earth's principal semidiurnal lunar tide of 0.204°±0.047°, corresponding to a time lag of approximately 25 seconds. This implies that the solid tide dissipates at least 110 GW (150,000,000 hp) of tidal power, or about 5% of what the ocean tides dissipate.

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. 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 particle-beam energy.

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." It plays a key role in long-term dynamics of planetary systems. For example, body tides dissipate energy, slowing the spin of satellites until they lock into a spin-orbit resonance. Thus the Moon that it is captured into the 1:1 resonance, always showing the Earth one side while Mercury is trapped in a 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.