Math 2.0

Astronomy and astrophysics Definition

Equation of time

Builds on Hour angleEcliptic coordinate systemKepler orbit

Definition

Fix an observer on the Earth. The apparent solar time is the hour angle of the true Sun plus 12h12^{\mathrm h}. The mean Sun is a fictitious point that moves along the celestial equator at a constant rate. Its period equals the mean period of the true Sun. The mean solar time is the hour angle of the mean Sun plus 12h12^{\mathrm h}. The equation of time is the apparent solar time minus the mean solar time, as a function of the date.

Remarks

Equivalently, it is the hour angle of the true Sun minus the hour angle of the mean Sun. Some texts use the opposite sign. Two effects add up. The Earth's orbit is a Kepler orbit of small eccentricity, so the true Sun moves along the ecliptic faster near perihelion in early January. The ecliptic is tilted against the equator, so even uniform motion along the ecliptic gives non-uniform motion in right ascension. Example: in early November the equation of time is about +16+16 minutes, so a sundial is ahead of mean time. Non-example: the difference between local mean time and the time of a time zone is not part of the equation of time; it depends only on longitude.

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Ecliptic coordinate system, concept, no evidence levelEcliptic coordinate s…conceptHour angle, concept, no evidence levelHour angleconceptKepler orbit, concept, no evidence levelKepler orbitconceptEquation of time, definition, no evidence levelEquation of timedefinition
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  1. Ecliptic coordinate system concept
  2. Hour angle concept
  3. Kepler orbit concept
  4. Equation of time definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Equation_of_time
About this page
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URIm2://7ZSCC8Y0GP
Kinddefinition
WritingW0 stub
MSC85A04, 70F15
DefinesEquation of time
UsesHour angle, Ecliptic coordinate system, Kepler orbit
Changed3 November 2026

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