Editing Equation of time (section)

== Concept ==
[[File:L' equazione del tempo. Foro Carolino in piazza Dante, Napoli.jpg|thumb|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&nbsp;[[minute|min]]&nbsp;33&nbsp;[[second|s]] (around 3&nbsp;November), or behind (slow) by as much as 14&nbsp;min&nbsp;6&nbsp;s (around 11&nbsp;February). The equation of time has zeros near 15&nbsp;April, 13&nbsp;June, 1&nbsp;September, and 25&nbsp;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-integral number of days in a year, these dates can vary by a day or so from year to year. As an example of the inexactness of the dates, according to the U.S. Naval Observatory's ''Multiyear Interactive Computer Almanac'' the equation of time was zero at 02:00 [[UT1]] on 16&nbsp;April 2011.{{r|Heilbron|p=277}}

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 [[Axial tilt|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 [[Orbital eccentricity|eccentricity]] of the [[Earth's orbit]] around the Sun, which is about 0.0167.

The equation of time vanishes only for a planet with zero axial tilt and zero orbital eccentricity.<ref name="jenkins">{{cite journal |doi=10.1088/0143-0807/34/3/633 |title=The Sun's position in the sky |journal=European Journal of Physics |volume=34 |issue=3 |pages=633–652 |year=2013 |last= Jenkins |first= Alejandro |arxiv=1208.1043 |bibcode=2013EJPh...34..633J|s2cid=119282288 | author-link= Alejandro Jenkins}}</ref> Two examples of planets with large equations of time are Mars and Uranus. On [[Mars]] the difference between sundial time and clock time can be as much as 50&nbsp;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.