Editing Equation of time (section)

== Major components ==

=== Eccentricity of the Earth's orbit ===
[[File:Zeitgleichung.png|thumb|upright=1.35|Equation of time (red solid line) and its two main components plotted separately, the part due to the obliquity of the ecliptic (mauve dashed line) and the part due to the Sun's varying apparent speed along the ecliptic due to eccentricity of the Earth's orbit (dark blue dash & dot line)]]

The Earth revolves around the Sun. As seen from Earth, the Sun appears to revolve once around the Earth through the background stars in one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth's axis, then the Sun would [[culmination|culminate]] every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse not centered on the Sun, and its speed varies between 30.287 and 29.291&nbsp;km/s, according to [[Kepler's laws of planetary motion]], and its angular speed also varies, and thus the Sun appears to move faster (relative to the background stars) at [[perihelion]] (currently around 3&nbsp;January) and slower at [[aphelion]] a half year later.<ref name=rmg>{{cite web|title=The Equation of Time|url=http://www.rmg.co.uk/explore/astronomy-and-time/time-facts/the-equation-of-time|website=[[Royal Museums Greenwich]]|archive-url=https://web.archive.org/web/20150910174438/http://www.rmg.co.uk/explore/astronomy-and-time/time-facts/the-equation-of-time|access-date=29 January 2021|archive-date=10 September 2015}}</ref><ref>{{cite web|title=Eccentricity|url=https://analemma.com/eccentricity.html|website=Analemma|access-date=29 January 2021}}</ref><ref name=moonkmft>{{cite web|title=The Equation of Time: Why Sundial time Differs From Clock Time Depending on Time of Year|url=http://moonkmft.co.uk/EquationOfTime.html|website=moonkmft |access-date=29 January 2021 |first=Kieran |last=Taylor |date=4 November 2018}}</ref>

At these extreme points, this effect varies the apparent solar day by 7.9&nbsp;s/day from its mean. Consequently, the smaller daily differences on other days in speed are cumulative until these points, reflecting how the planet accelerates and decelerates compared to the mean.

As a result, the eccentricity of the Earth's orbit contributes a periodic variation which is (in the first-order approximation) a [[sine wave]] with:

* amplitude: 7.66&nbsp;minutes
* [[periodic function|period]]: one year
* zero points: perihelion (at the beginning of January) and aphelion (beginning of July)
* extreme values: early April (negative) and early October (positive)

This component of the EoT is represented by aforementioned factor ''a'':
: <math>a = -7.659\sin(6.240\, 040\, 77 + 0.017\, 201\, 97(365(y-2000) + d))</math>

=== Obliquity of the ecliptic ===
[[Image:Middaysun.gif|thumb|upright|right|Sun and planets at local apparent noon (Ecliptic in red, Sun and Mercury in yellow, Venus in white, Mars in red, Jupiter in yellow with red spot, Saturn in white with rings).]]

Even if the Earth's orbit were circular, the perceived motion of the Sun along our [[celestial equator]] would still not be uniform.<ref name="jenkins" /> This is a consequence of the tilt of the Earth's rotational axis with respect to the [[orbital plane (astronomy)|plane of its orbit]], or equivalently, the tilt of the [[ecliptic]] (the path the Sun appears to take in the [[celestial sphere]]) with respect to the [[celestial equator]]. The projection of this motion onto our [[celestial equator]], along which "clock time" is measured, is a maximum at the [[solstice]]s, when the yearly movement of the Sun is parallel to the equator (causing amplification of perceived speed) and yields mainly a change in [[right ascension]]. It is a minimum at the [[equinox]]es, when the Sun's apparent motion is more sloped and yields more change in [[declination]], leaving less for the component in [[right ascension]], which is the only component that affects the duration of the solar day. A practical illustration of obliquity is that the daily shift of the shadow cast by the Sun in a sundial even on the equator is smaller close to the solstices and greater close to the equinoxes.  If this effect operated alone, then days would be up to 24&nbsp;hours and 20.3&nbsp;seconds long (measured solar noon to solar noon) near the solstices, and as much as 20.3&nbsp;seconds shorter than 24&nbsp;hours near the equinoxes.<ref name=rmg/><ref>{{cite web|title=Obliquity|url=https://analemma.com/obliquity.html|website=Analemma|access-date=29 January 2021}}</ref><ref name=moonkmft/>

In the figure on the right, we can see the monthly variation of the apparent slope of the plane of the ecliptic at solar midday as seen from Earth. This variation is due to the apparent [[precession]] of the rotating Earth through the year, as seen from the Sun at solar midday.

In terms of the equation of time, the inclination of the ecliptic results in the contribution of a sine wave variation with:

* amplitude: 9.87 minutes
* period: 1/2 year
* zero points: equinoxes and solstices
* extreme values: beginning of February and August (negative) and beginning of May and November (positive).

This component of the EoT is represented by the aforementioned factor "b":

<math>b = 
9.863\sin \left( 2 (6.240\, 040\, 77 + 0.017\, 201\, 97 (365(y-2000)+ d)) + 3.5932 \right)</math>