Editing Tidal acceleration (section)

=== Effects of Moon's gravity ===
[[Image:Tidal braking.svg|thumb|A diagram of the [[Earth–Moon system]] showing how the tidal bulge is pushed ahead by [[Earth]]'s rotation. This offset bulge exerts a net torque on the [[Moon]], boosting it while slowing Earth's rotation.]]

The plane of the Moon's [[orbit]] around Earth lies close to the plane of Earth's orbit around the Sun (the [[ecliptic]]), rather than in the plane of the Earth's rotation (the [[equator]]) as is usually the case with planetary satellites.  The mass of the Moon is sufficiently large, and it is sufficiently close, to raise [[tide]]s in the matter of Earth.  Foremost among such matter, the [[water]] of the [[ocean]]s bulges out both towards and away from the Moon.  If the material of the Earth responded immediately, there would be a bulge directly toward and away from the Moon. In the [[solid Earth tide]]s, there is a delayed response due to the dissipation of tidal energy. The case for the oceans is more complicated, but there is also a delay associated with the dissipation of energy since the Earth rotates at a faster rate than the Moon's orbital angular velocity. This [[lunitidal interval]] in the responses causes the tidal bulge to be carried forward. Consequently, the line through the two bulges is tilted with respect to the Earth-Moon direction exerting [[torque]] between the Earth and the Moon. This torque boosts the Moon in its orbit and slows the rotation of Earth.

As a result of this process, the mean solar day, which has to be 86,400 equal seconds, is actually getting longer when measured in [[SI]] [[second]]s with stable [[atomic clock]]s. (The SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.<ref>:(1) In {{cite journal|last1 = McCarthy|first1 = D D|last2 = Hackman|first2 = C|last3 = Nelson|first3 = R A|year = 2008|title = The Physical Basis of the Leap Second|url = https://apps.dtic.mil/sti/pdfs/ADA489427.pdf|archive-url = https://web.archive.org/web/20170922113409/http://www.dtic.mil/get-tr-doc/pdf?AD=ADA489427|url-status = live|archive-date = September 22, 2017|journal = Astronomical Journal|volume = 136|issue = 5|pages = 1906–1908|doi=10.1088/0004-6256/136/5/1906|bibcode=2008AJ....136.1906M|doi-access = free }} it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770±20 cycles), see [http://www.leapsecond.com/history/1968-Metrologia-v4-n4-Essen.pdf "Time Scales", by L. Essen], in Metrologia, vol.4 (1968), pp.161–165, on p.162. As is well known, the 9192631770 figure was chosen for the [[second|SI second]].  L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".</ref>) The small difference accumulates over time, which leads to an increasing difference between our clock time ([[Universal Time]]) on the one hand, and [[International Atomic Time]] and [[ephemeris time]] on the other hand: see [[ΔT (timekeeping)|ΔT]]. This led to the introduction of the [[leap second]] in 1972 <ref>{{cite web|title=What's a Leap Second|url=http://www.timeanddate.com/time/leapseconds.html|website=Timeanddate.com}}</ref> 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.<ref>{{cite journal|first1=Walter|last1 = Munk|year = 1997|title =  Once again: once again—tidal friction|journal = Progress in Oceanography|volume = 40|issue = 1–4|pages = 7–35|doi=10.1016/S0079-6611(97)00021-9|bibcode=1997PrOce..40....7M}}</ref>

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 [[Pluto]]–[[Charon (moon)|Charon]] system. However, the slowdown of Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects make this irrelevant: about 1 to 1.5 billion years from now, the continual increase of the Sun's [[radiation]] will likely cause Earth's oceans to vaporize,<ref>Puneet Kollipara (22 January 2014), [https://www.science.org/content/article/earth-wont-die-soon-thought "Earth Won't Die as Soon as Thought"], '''Science'''.</ref> 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 [[red giant]] and likely destroy both Earth and the Moon.<ref>{{cite book|last1 = Murray|first1 = C.D.|first2 = Stanley F.|last2 = Dermott|title = Solar System Dynamics|date = 1999|publisher = Cambridge University Press|isbn = 978-0-521-57295-8|page = 184 }}</ref><ref>{{cite book|last = Dickinson|first = Terence|author-link = Terence Dickinson|title = From the Big Bang to Planet X|date = 1993|publisher = [[Camden House]]|location = Camden East, Ontario|isbn = 978-0-921820-71-0|pages = 79–81 }}
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Tidal acceleration is one of the few examples in the dynamics of the [[Solar System]] of a so-called '''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 [[gravity|gravitational]] perturbations between major or minor [[planet]]s only cause periodic variations in their orbits, that is, parameters oscillate between maximum and minimum values.  The tidal effect gives rise to a quadratic term in the equations, which leads to unbounded growth.  In the mathematical theories of the planetary orbits that form the basis of [[ephemerides]], quadratic and higher order secular terms do occur, but these are mostly [[Taylor series|Taylor expansions]] of very long time periodic terms. The reason that tidal effects are different is that unlike distant gravitational perturbations, friction is an essential part of tidal acceleration, and leads to permanent loss of [[energy]] from the dynamic system in the form of [[heat]]. In other words, we do not have a [[Hamiltonian system]] here.{{Citation needed|date = November 2015}}