Theory of tides

The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's Ocean) under the gravitational loading of another astronomical body or bodies (especially the Moon).

In 1609 Johannes Kepler correctly suggested that the gravitation of the Moon causes the tides, basing his argument upon ancient observations and correlations. The influence of the Moon on tides was mentioned in Ptolemy's Tetrabiblos as having derived from ancient observation.

In 1616, Galileo Galilei wrote Discourse on the Tides (Discorso sul flusso e il reflusso del mare), in a letter to Cardinal Orsini. In this discourse, he tried to explain the occurrence of the tides as the result of the Earth's rotation and revolution around the Sun. Galileo believed that the oceans moved like water in a large basin: as the basin moves, so does the water. Therefore, as the Earth revolves, the force of the Earth's rotation causes the oceans to "alternately accelerate and retardate". His view on the oscillation and "alternately accelerated and retardated" motion of the Earth's rotation is a "dynamic process" that deviated from the previous dogma, which proposed "a process of expansion and contraction of seawater." However, Galileo's theory was erroneous. In subsequent centuries, further analysis led to the current tidal physics. Galileo rejected Kepler's explanation of the tides.

Newton, in the Principia, provided a correct explanation for the tidal force, which can be used to explain tides on a planet covered by a uniform ocean, but which takes no account of the distribution of the continents or ocean bathymetry.

The dynamic theory of tides describes and predicts the actual real behavior of ocean tides.

While Newton explained the tides by describing the tide-generating forces and Bernoulli gave a description of the static reaction of the waters on Earth to the tidal potential, the dynamic theory of tides, developed by Pierre-Simon Laplace in 1775, describes the ocean's real reaction to tidal forces. Laplace's theory of ocean tides took into account friction, resonance and natural periods of ocean basins. It predicted the large amphidromic systems in the world's ocean basins and explains the oceanic tides that are actually observed. The equilibrium theory, based on the gravitational gradient from the Sun and Moon but ignoring the Earth's rotation, the effects of continents, and other important effects, could not explain the real ocean tides. Since measurements have confirmed the theory, many things have possible explanations now, like how the tides interact with deep sea ridges and chains of seamounts give rise to deep eddies that transport nutrients from the deep to the surface. The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters. Measurements from the CHAMP satellite closely match the models based on the TOPEX data. Accurate models of tides worldwide are essential for research since the variations due to tides must be removed from measurements when calculating gravity and changes in sea levels.

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