Editing Solar time (section)

==Mean solar time <span class="anchor" id="Mean time"></span>==
{{Main|Universal Time}}
[[Image:Equation of time.svg|thumb|right|250px|The equation of time—above the x-axis a sundial will appear ''fast'' relative to a clock showing local mean time, and below the axis a sundial will appear ''slow''.]]
'''Mean solar time''' is the [[hour angle]] of the [[mean]] position of the Sun, plus 12 hours. This 12 hour offset comes from the decision to make each day start at midnight for civil purposes, whereas the hour angle or the mean sun is measured from the local meridian.<ref>{{cite book |author1-last=Hilton |author1-first= James L| author2-last=McCarthy| author2-first=Dennis D. | author2-link=Dennis McCarthy (scientist) | chapter = Precession, Nutation, Polar Motion, and Earth Rotation | editor1-last = Urban | editor1-first = Sean E. | editor2-last = Seidelmann | editor2-first = P. Kenneth | title = Explanatory Supplement to the Astronomical Almanac | edition = 3rd | date = 2013 | publisher = University Science Books | location = Mill Valley, CA | isbn=978-1-891389-85-6}}</ref> {{As of|2009}}, this is realized with the [[Universal Time|UT1]] time scale, constructed mathematically from [[very-long-baseline interferometry]] observations of the [[diurnal motion]]s of radio sources located in other galaxies, and other observations.<ref name="time-from-earth-rotation-to-atomic-physics">{{cite book|author-link1=Dennis McCarthy (scientist)|last1=McCarthy|first1=D. D.|last2=Seidelmann|first2=P. K.|date=2009|title=TIME From Earth Rotation to Atomic Physics|location=Weinheim|publisher=[[Wiley-VCH|Wiley-VCH Verlag GmbH & Co. KGa]]|isbn=978-3-527-40780-4}}</ref>{{rp|68,326}}<ref>{{cite journal|author-link1=Nicole Capitaine|last1=Capitaine|first1=N.|last2=Wallace|first2=P. T.|last3=McCarthy|first3=D. D.|date=2003|url=http://www.aanda.org/index.php?option=article&access=bibcode&bibcode=2003A%2526A...406.1135CFUL|title=Expressions to implement the IAU 2000 definition of UT1|journal=Astronomy and Astrophysics|volume=406|issue=3 |pages=1135–1149|doi=10.1051/0004-6361:20030817 |bibcode=2003A&A...406.1135C |s2cid=54008769 |doi-access=free}} (or [http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003A%26A...406.1135C&link_type=ARTICLE&db_key=AST&high= in pdf form]); and for some earlier definitions of UT1 see {{cite journal|last1=Aoki|first1=S.|last2=Guinot|first2=B.|last3=Kaplan|first3=G. H.|last4=Kinoshita|first4=H.|last5=McCarthy|first5=D. D.|last6=Seidelmann|first6=P. K.|date=1982|url=http://articles.adsabs.harvard.edu/full/1982A%26A...105..359A|title=The new definition of universal time|journal=Astronomy and Astrophysics|volume=105|issue=2 |pages=359–361|bibcode=1982A&A...105..359A }}</ref> The duration of daylight varies during the year but the length of a '''mean solar day''' is nearly constant, unlike that of an apparent solar day.<ref>For a discussion of the slight changes that affect the mean solar day, see the [[ΔT (timekeeping)|ΔT]] article.</ref> An apparent solar day can be 20 seconds shorter or 30 seconds longer than a mean solar day.<ref name=Meeus/><ref>{{cite web|url=http://www.pierpaoloricci.it/dati/giornosolarevero_eng.htm|title=The duration of the true solar day|first=Pierpaolo|last=Ricci|website=pierpaoloricci.it|archive-url=https://web.archive.org/web/20090826184737/http://www.pierpaoloricci.it/dati/giornosolarevero_eng.htm|archive-date=August 26, 2009|url-status=live}}</ref> Long or short days occur in succession, so the difference builds up until mean time is ahead of apparent time by about 14 minutes near February 6, and behind apparent time by about 16 minutes near November 3. The [[equation of time]] is this difference, which is cyclical and does not accumulate from year to year.

Mean time follows the mean sun. [[Jean Meeus]] describes the mean sun as follows:

{{blockquote|Consider a first fictitious Sun travelling along the ''ecliptic'' with a constant speed and coinciding with the true sun at the perigee and apogee (when the Earth is in perihelion and aphelion, respectively). Then consider a second fictitious Sun travelling along the ''celestial equator'' at a constant speed and coinciding with the first fictitious Sun at the equinoxes. This second fictitious sun is the ''mean Sun''.<ref>Meeus, J. (1998). ''Astronomical Algorithms.'' 2nd ed. Richmond VA: Willmann-Bell. p. 183.</ref>}}

The length of the mean solar day is slowly increasing due to the [[tidal acceleration]] of the Moon by Earth and the corresponding slowing of Earth's rotation by the Moon.