Editing Tidal acceleration (section)

=== Discovery history of the secular acceleration ===
[[Edmond Halley]] was the first to suggest, in 1695,<ref>E Halley (1695), [https://www.jstor.org/stable/102291?seq=1#page_scan_tab_contents "Some Account of the Ancient State of the City of Palmyra, with Short Remarks upon the Inscriptions Found there"], ''Phil. Trans.'', vol.19 (1695–1697), pages 160–175; esp. at pages 174–175. (see also transcription using a modern font [https://books.google.com/books?id=b-Q_AAAAYAAJ&pg=PA65 here])</ref> 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 Earth's rate of rotation: see also [[Ephemeris time#History of ephemeris time (1952 standard)|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:<ref>Richard Dunthorne (1749), [http://rstl.royalsocietypublishing.org/content/46/492/162.full.pdf "A Letter from the Rev. Mr. Richard Dunthorne to the Reverend Mr. Richard Mason F. R. S. and Keeper of the Wood-Wardian Museum at Cambridge, concerning the Acceleration of the Moon"], ''Philosophical Transactions'', Vol. 46 (1749–1750) #492, pp.162–172;  also given in Philosophical Transactions (abridgements) (1809), [https://archive.org/stream/philosophicaltra09royarich#page/669/mode/2up vol.9 (for 1744–49), p669–675] as "On the Acceleration of the Moon, by the Rev. Richard Dunthorne".</ref> 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,<ref>J de Lalande (1786): [http://gallica.bnf.fr/ark:/12148/bpt6k3585j/f484.double "Sur les equations seculaires du soleil et de la lune"], Memoires de l'Academie Royale des Sciences, pp.390–397, at page 395.</ref> and to compare with values from about 10″ to nearly 13″ being derived about a century later.<ref>J D North (2008), "Cosmos: an illustrated history of astronomy and cosmology", (University of Chicago Press, 2008), chapter 14, at [https://books.google.com/books?id=qq8Luhs7rTUC&pg=PA454 page 454].</ref><ref>See also P Puiseux (1879), [http://archive.numdam.org/article/ASENS_1879_2_8__361_0.pdf "Sur l'acceleration seculaire du mouvement de la Lune"], Annales Scientifiques de l'Ecole Normale Superieure, 2nd series vol.8 (1879), pp.361–444, at pages 361–365.</ref>

[[Pierre-Simon Laplace]] produced in 1786 a theoretical analysis giving a basis on which the Moon's mean motion should accelerate in response to [[perturbation (astronomy)|perturbational]] changes in the eccentricity of the orbit of 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.<ref>{{cite book|last=Britton|first=John|date=1992|title=Models and Precision: The Quality of Ptolemy's Observations and Parameters|url=https://archive.org/details/modelsprecisionq00brit|publisher=Garland Publishing Inc.|page=[https://archive.org/details/modelsprecisionq00brit/page/157 157]|isbn=978-0815302155  }}</ref>

However, in 1854, [[John Couch Adams]] caused the question to be re-opened by finding an error in Laplace's computations: it turned out that only about half of the Moon's apparent acceleration could be accounted for on Laplace's basis by the change in Earth's orbital eccentricity.<ref>{{cite journal|doi = 10.1098/rstl.1853.0017|last1 = Adams|first1 = J C|date = 1853|title = On the Secular Variation of the Moon's Mean Motion|journal = Phil. Trans. R. Soc. Lond.|volume = 143|pages = 397–406| s2cid=186213591 |doi-access =  }}</ref> Adams' finding provoked a sharp astronomical controversy that lasted some years, but the correctness of his result, agreed upon by other mathematical astronomers including [[Charles-Eugene Delaunay|C. E. Delaunay]], was eventually accepted.<ref>D. E. Cartwright (2001), [https://archive.org/details/tidesscientifich0000cart/page/144 "Tides: a scientific history"], (Cambridge University Press 2001), chapter 10, section: "Lunar acceleration, Earth retardation and tidal friction" at pages 144–146.</ref> 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 [[Venus]]) was also in error, was found on re-examination to be almost negligible, and practically had to disappear from the theory.  A part of the answer was suggested independently in the 1860s by Delaunay and by [[William Ferrel]]: tidal retardation of Earth's rotation rate was lengthening the unit of time and causing a lunar acceleration that was only apparent.<ref>{{cite journal|last1= Khalid|first1=  M.|last2=Sultana|first2= M.|last3= Zaidi|first3 =F.|date= 2014|title= Delta: Polynomial Approximation of Time Period 1620–2013|journal= Journal of Astrophysics|volume= 2014|pages=  1–4|doi= 10.1155/2014/480964|doi-access= free}}</ref>

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 [[Emmanuel Liais]]).  First there is a real retardation of the Moon's angular rate of orbital motion, due to tidal exchange of [[angular momentum]] between Earth and Moon.  This increases the Moon's angular momentum around Earth (and moves the Moon to a higher orbit with a lower [[orbital speed]]). Secondly, there is an apparent increase in the Moon's angular rate of orbital motion (when measured in terms of mean solar time). This arises from Earth's loss of angular momentum and the consequent increase in [[length of day]].<ref>F R Stephenson (2002), [http://articles.adsabs.harvard.edu/full/2003A%26G....44b..22S "Harold Jeffreys Lecture 2002: Historical eclipses and Earth's rotation"], in ''[[Astronomy & Geophysics]]'', vol.44 (2002), pp. 2.22–2.27.</ref>