# Tidal acceleration

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Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon), and the primary planet that it orbits (e.g. the Earth). The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking of first the smaller, and later the larger body. The Earth-Moon system is the best studied case.

The similar process of tidal deceleration occurs for satellites that have an orbital period that is shorter than the primary's rotation period, or that orbit in a retrograde direction.

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### Discovery history of the secular acceleration

Edmond Halley was the first to suggest, in 1695,[1] that the mean motion of the Moon was apparently getting faster, by comparison with ancient eclipse observations, but he gave no data. (It was not yet known in Halley's time that what is actually occurring includes a slowing-down of the Earth's rate of rotation: see also Ephemeris time - History. When measured as a function of mean solar time rather than uniform time, the effect appears as a positive acceleration.) In 1749 Richard Dunthorne confirmed Halley's suspicion after re-examining ancient records, and produced the first quantitative estimate for the size of this apparent effect:[2] a centurial rate of +10" (arcseconds) in lunar longitude (a surprisingly good result for its time, not far different from values assessed later, e.g. in 1786 by de Lalande,[3] and to compare with values from about 10" to nearly 13" being derived about century later.)[4][5]

Pierre-Simon Laplace produced in 1786 a theoretical analysis giving a basis on which the Moon's mean motion should accelerate in response to perturbational changes in the eccentricity of the orbit of the Earth around the Sun. Laplace's initial computation accounted for the whole effect, thus seeming to tie up the theory neatly with both modern and ancient observations.