Editing Equation of time (section)

== Secular effects ==

The two above mentioned factors have different wavelengths, amplitudes and phases, so their combined contribution is an irregular wave. At [[Epoch (astronomy)|epoch]] 2000 these are the values (in minutes and seconds with [[Universal Time|UT]] dates):
{| class="wikitable"
!Point !! Value !! Date
|-
| minimum
| style="text-align:right;"|−14&nbsp;min&nbsp;15&nbsp;s
| 11 February
|-
| zero
| style="text-align:right;"|0&nbsp;min&nbsp;{{0}}0&nbsp;s
| 15 April
|-
| maximum
| style="text-align:right;"|+3&nbsp;min&nbsp;41&nbsp;s
| 14 May
|-
| zero
| style="text-align:right;"|0&nbsp;min&nbsp;{{0}}0&nbsp;s
| 13 June
|-
| minimum
| style="text-align:right;"|−6&nbsp;min&nbsp;30&nbsp;s
| 26 July
|-
| zero
| style="text-align:right;"|0&nbsp;min&nbsp;{{0}}0&nbsp;s
| 1 September
|-
| maximum
| style="text-align:right;"|+16&nbsp;min&nbsp;25&nbsp;s
| 3 November
|-
| zero
| style="text-align:right;"|0&nbsp;min&nbsp;{{0}}0&nbsp;s
| 25 December
|}{{citation needed|date=July 2012}}
{{bi|1=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&nbsp;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. At this moment both are slowly decreasing, but they increase and decrease over a timescale of hundreds of thousands of years.<ref name = Karney>{{cite web
|first=Kevin
|last=Karney
|date=December 2005
|title=Variation in the Equation of Time
|url=http://www.precisedirections.co.uk/Sundials/E-o-T_Variability.pdf
|archive-url=https://web.archive.org/web/20240818114558/http://www.precisedirections.co.uk/Sundials/E-o-T_Variability.pdf
|url-status=dead
|archive-date=2024-08-18
}}</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}}