Editing Equation of time (section)

=== 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>