## Tidal acceleration |

**Tidal acceleration** is an effect of the

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

The naming is somewhat confusing, because the speed of the satellite relative to the body it orbits is *decreased* as a result of tidal acceleration, and *increased* as a result of tidal deceleration.

- earth–moon system
- other cases of tidal acceleration
- tidal deceleration
- theory
- see also
- references
- external links

^{[1]} that the mean motion of the Moon was apparently getting faster, by comparison with ancient ^{[2]} a centurial rate of +10″ (arcseconds) in lunar longitude, which is a surprisingly accurate result for its time, not differing greatly 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 a century later.^{[4]}^{[5]}

^{[6]}

However, in 1854, ^{[7]} Adams's finding provoked a sharp astronomical controversy that lasted some years, but the correctness of his result, agreed upon by other mathematical astronomers including ^{[8]} The question depended on correct analysis of the lunar motions, and received a further complication with another discovery, around the same time, that another significant long-term perturbation that had been calculated for the Moon (supposedly due to the action of ^{[9]}

It took some time for the astronomical community to accept the reality and the scale of tidal effects. But eventually it became clear that three effects are involved, when measured in terms of mean solar time. Beside the effects of perturbational changes in Earth's orbital eccentricity, as found by Laplace and corrected by Adams, there are two tidal effects (a combination first suggested by ^{[10]}

Because the

As a result of this process, the mean solar day, which is nominally 86,400 seconds long, is actually getting longer when measured in ^{[11]}) The small difference accumulates over time, which leads to an increasing difference between our clock time (^{[12]} to compensate for differences in the bases for time standardization.

In addition to the effect of the ocean tides, there is also a tidal acceleration due to flexing of Earth's crust, but this accounts for only about 4% of the total effect when expressed in terms of heat dissipation.^{[13]}

If other effects were ignored, tidal acceleration would continue until the rotational period of Earth matched the orbital period of the Moon. At that time, the Moon would always be overhead of a single fixed place on Earth. Such a situation already exists in the ^{[14]} removing the bulk of the tidal friction and acceleration. Even without this, the slowdown to a month-long day would still not have been completed by 4.5 billion years from now when the Sun will probably evolve into a ^{[15]}^{[16]}

Tidal acceleration is one of the few examples in the dynamics of the **secular perturbation** of an orbit, i.e. a perturbation that continuously increases with time and is not periodic. Up to a high order of approximation, mutual ^{[citation needed]}

The gravitational torque between the Moon and the tidal bulge of Earth causes the Moon to be constantly promoted to a slightly higher orbit and Earth to be decelerated in its rotation. As in any physical process within an isolated system, total ^{[citation needed]} is converted to heat by frictional losses in the oceans and their interaction with the solid Earth, and only about 1/30th (+0.121 TW) is transferred to the Moon). The Moon moves farther away from Earth (+38.247±0.004 mm/y), so its ^{2}) of its rotation around Earth. The actual speed of the Moon also decreases. Although its

The rotational angular momentum of Earth decreases and consequently the length of the day increases. The *net* tide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. **Tidal friction** is required to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exchange of rotational and orbital energy between Earth and the Moon as heat. If the friction and heat dissipation were not present, the Moon's gravitational force on the tidal bulge would rapidly (within two days) bring the tide back into synchronization with the Moon, and the Moon would no longer recede. Most of the dissipation occurs in a turbulent bottom boundary layer in shallow seas such as the
European Shelf around the ^{[17]}

The dissipation of energy by tidal friction averages about 3.75 terawatts, of which 2.5 terawatts are from the principal M_{2} lunar component and the remainder from other components, both lunar and solar.^{[18]}

An *equilibrium tidal bulge* does not really exist on Earth because the continents do not allow this mathematical solution to take place. Oceanic tides actually rotate around the ocean basins as vast * gyres* around several

This mechanism has been working for 4.5 billion years, since oceans first formed on Earth. There is geological and paleontological evidence that Earth rotated faster and that the Moon was closer to Earth in the remote past. * Tidal rhythmites* are alternating layers of sand and silt laid down offshore from

The motion of the Moon can be followed with an accuracy of a few centimeters by ^{[20]}^{[21]} Measuring the return time of the pulse yields a very accurate measure of the distance. These measurements are fitted to the equations of motion. This yields numerical values for the Moon's secular deceleration, i.e. negative acceleration, in longitude and the rate of change of the semimajor axis of the Earth–Moon ellipse. From the period 1970–2012, the results are:

- −25.82±0.03 arcsecond/century
^{2}in ecliptic longitude^{[22]} - +38.08±0.04 mm/yr in the mean Earth–Moon distance
^{[22]}

This is consistent with results from

Finally, ancient observations of solar ^{[23]}

The other consequence of tidal acceleration is the deceleration of the rotation of Earth. The rotation of Earth is somewhat erratic on all time scales (from hours to centuries) due to various causes.^{[24]} The small tidal effect cannot be observed in a short period, but the cumulative effect on Earth's rotation as measured with a stable clock (^{[25]} A table of the actual length of the day in the past few centuries is also available.^{[26]}

From the observed change in the Moon's orbit, the corresponding change in the length of the day can be computed:

- +2.3 ms/century

However, from historical records over the past 2700 years the following average value is found:

- +1.70 ± 0.05 ms/century
^{[27]}^{[28]}

The corresponding cumulative value is a parabola having a coefficient of T^{2} (time in centuries squared) of:

- ΔT = +31 s/century
^{2}

Opposing the tidal deceleration of Earth is a mechanism that is in fact accelerating the rotation. Earth is not a sphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. The explanation is that during the

Other Languages

العربية: تسارع مدي

беларуская: Прыліўное паскарэнне

български: Приливно ускорение

català: Acceleració de marea

español: Aceleración de marea

euskara: Itsasaldiaren azelerazio

français: Accélération par effet de marée

한국어: 조석 가속

italiano: Accelerazione secolare della Luna

Nederlands: Seculiere versnelling van de maan

日本語: 潮汐加速

norsk: Tidevannsakselerasjon

norsk nynorsk: Tidvassakselerasjon

português: Aceleração de marés

русский: Приливное ускорение

Türkçe: Gelgitsel ivme

українська: Припливне прискорення

اردو: افزائش مدوجزری

中文: 潮汐加速