Equation of time: Difference between revisions

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:E.T. = apparent − mean. Positive means: Sun runs fast and culminates earlier, or the sundial is ahead of mean time. A slight yearly variation occurs due to presence of leap years, resetting itself every 4 years.
 
The exact shape of the equation of time curve and the associated [[analemma]] slowly change over the centuries, due to [[secular variation]]s in both eccentricity and obliquity.<ref>{{cite web
|first=Kevin
|last=Karney
|title=Variation in the Equation of Time
|url=http://www.precisedirections.co.uk/Sundials/E-o-T_Variability.pdf}}
</ref> over the centuries, due to [[secular variation]]s in both eccentricity and obliquity. At this moment both are slowly decreasing, but they increase and decrease over a timescale of hundreds of thousands of years. If and when the Earth's orbital eccentricity (now about 0.0167 and slowly decreasing) reaches 0.0047, the eccentricity effect may in some circumstances overshadow the obliquity effect, leaving the equation of time curve with only one maximum and minimum per year, as is the case on Mars.<ref>[http://www.giss.nasa.gov/research/briefs/allison_02/ Telling Time on Mars]</ref>
</ref>
 
On shorter timescales (thousands of years) the shifts in the dates of equinox and perihelion will be more important. The former is caused by [[precession]], and shifts the equinox backwards compared to the stars. But it can be ignored in the current discussion as our [[Gregorian calendar]] is constructed in such a way as to keep the vernal equinox date at 20&nbsp;March (at least at sufficient accuracy for our aim here). The shift of the perihelion is forwards, about 1.7&nbsp;days every century. In 1246 the perihelion occurred on 22&nbsp;December, the day of the solstice, so the two contributing waves had common zero points and the equation of time curve was symmetrical: in ''Astronomical Algorithms'' Meeus gives February and November extrema of 15&nbsp;m&nbsp;39&nbsp;s and May and July ones of 4&nbsp;m&nbsp;58&nbsp;s. Before then the February minimum was larger than the November maximum, and the May maximum larger than the July minimum. In fact, in years before −1900 (1901&nbsp;BCE) the May maximum was larger than the November maximum. In the year −2000 (2001&nbsp;BCE) the May maximum was +12&nbsp;minutes and a couple seconds while the November maximum was just less than 10&nbsp;minutes. The secular change is evident when one compares a current graph of the equation of time (see below) with one from 2000&nbsp;years ago, e.g., one constructed from the data of Ptolemy.{{sfn|Meeus|1997}}
 
==Graphical representation==
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{{refbegin}}
* {{cite web|last=Helyar |first=A.G. |title=Sun Data |url=http://freepages.pavilion.net/users/aghelyar/sundat.htm |url-status=dead |archiveurl=https://web.archive.org/web/20040111160307/http://freepages.pavilion.net/users/aghelyar/sundat.htm |archivedate=11 January 2004 }}
* {{Cite book | ref=harv | last=Meeus| first = J | year = 1997 |title= Mathematical Astronomy Morsels|location= Richmond, Virginia| publisher= Willman-Bell}}
* {{Cite book | ref=harv | last1 = McCarthy | first1 = Dennis D. | author1-link = Dennis McCarthy (scientist) | last2 = Seidelmann | first2 = P. Kenneth | year = 2009 | publisher = Wiley VCH | location = Weinheim | title = TIME From Earth Rotation to Atomic Physics | isbn = 978-3-527-40780-4}}
{{refend}}