Editing Equation of time (section)

{{Short description|Apparent solar time minus mean solar time}}
{{Use dmy dates|date=December 2024}}
[[File:Equation of time.svg|thumb|right|upright=1.35|The equation of time: above the axis a sundial will appear fast relative to a clock showing local mean time, and below the axis a sundial will appear slow]]
[[File:Tijdvereffening-equation of time-en.jpg|thumb|right|upright=1.35|This graph shows how many minutes the clock is ahead (+) or behind (−) the apparent sun. See the section "[[#Notation|Notation]]" below.]]

The '''equation of time''' describes the discrepancy between two kinds of [[solar time]]. The two times that differ are the [[apparent solar time]], which directly tracks the [[diurnal motion]] of the [[Sun]], and [[mean solar time]], which tracks a theoretical [[mean]] Sun with uniform motion along the [[celestial equator]]. Apparent solar time can be obtained by measurement of the current position ([[Hour angle#Solar hour angle|hour angle]]) of the Sun, as indicated (with limited accuracy) by a [[sundial]]. ''Mean'' solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.<ref name="Maskelyne67">{{cite book |last1=Maskelyne |first1=Nevil |author-link=Nevil Maskelyne |title=The Nautical Almanac and Astronomical Ephemeris |date=1767 |url=https://archive.org/details/the-nautical-almanac-and-astronomical-ep |publisher=[[Board of Longitude|Commissioners of Longitude]] |location=London}}</ref>

The equation of time is the east or west component of the [[analemma]], a curve representing the angular offset of the Sun from its mean position on the [[celestial sphere]] as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical [[observatory|observatories]], were widely listed in [[almanac]]s and [[ephemeris|ephemerides]].<ref name="Milham"/>{{r|BCL|p=14}}

The equation of time can be approximated by a sum of two [[sine wave]]s:

: <math>\Delta t_{ey} =  -7.659\sin(D) + 9.863\sin \left(2D + 3.5932 \right)</math> [minutes]

where: <math>D = 6.240\, 040\, 77 + 0.017\, 201\, 97(365.25(y-2000) + d)</math>

where <math>d</math> represents the number of days since 1 January of the current year, <math>y</math>.