Equation of time

The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconciliation of a difference". 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) 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.^[1]

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 observatories, were widely listed in almanacs and ephemerides.^[2][3]: 14

The equation of time can be approximated by a sum of two sine waves (see explanation below):

${\displaystyle D=6.240\,040\,77+0.017\,201\,97(365.25(y-2000)+d)}$

${\displaystyle \Delta t_{ey}=-7.659\sin(D)+9.863\sin \left(2D+3.5932\right)}$ [minutes]

where ${\displaystyle d}$ represents the number of days since January 1 of the current year, ${\displaystyle y}$.