# Equation of time

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.
This graph uses the opposite sign to the one above it. There is no universally followed convention for the sign of the 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 "reconcile 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 noons 24 hours apart. 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 resolve to 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]

## The concept

Clock with auxiliary dial displaying the equation of time. Piazza Dante, Naples (1853).

During a year the equation of time varies as shown on the graph; its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 12 February). The equation of time has zeros near 15 April, 13 June, 1 September and 25 December. Ignoring very slow changes in the Earth's orbit and rotation, these events are repeated at the same times every tropical year. However, due to the non-integer number of days in a year, these dates can vary by a day or so from year to year.[4][5]

The graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year. The curves reflect two astronomical effects, each causing a different non-uniformity in the apparent daily motion of the Sun relative to the stars:

• the obliquity of the ecliptic (the plane of the Earth's annual orbital motion around the Sun), which is inclined by about 23.44 degrees relative to the plane of the Earth's equator; and
• the eccentricity of the Earth's orbit around the Sun, which is about 0.0167.

The equation of time is constant only for a planet with zero axial tilt and zero orbital eccentricity. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has an extremely large axial tilt, has an equation of time that makes its days start and finish several hours earlier or later depending on where it is in its orbit.

Other Languages
azərbaycanca: Vaxt tənliyi
беларуская: Ураўненне часу
Deutsch: Zeitgleichung
한국어: 균시차
हिन्दी: काल समीकरण
lietuvių: Laiko lygtis
magyar: Időegyenlet
Nederlands: Tijdsvereffening

oʻzbekcha/ўзбекча: Vaqt tenglamasi
português: Equação do tempo
slovenčina: Časová rovnica
slovenščina: Časovna enačba
Türkçe: Zaman denklemi