6.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Equation of time | 3/9 | https://en.wikipedia.org/wiki/Equation_of_time | reference | science, encyclopedia | 2026-05-05T11:12:39.793727+00:00 | kb-cron |
From 1767 to 1833, the British Nautical Almanac and Astronomical Ephemeris tabulated the equation of time in the sense 'add or subtract (as directed) the number of minutes and seconds stated to or from the apparent time to obtain the mean time'. Times in the Almanac were in apparent solar time, because time aboard ship was most often determined by observing the Sun. This operation would be performed in the unusual case that the mean solar time of an observation was needed. In the issues since 1834, all times have been in mean solar time, because by then the time aboard ship was increasingly often determined by marine chronometers. The instructions were consequently to add or subtract (as directed) the number of minutes stated to or from the mean time to obtain the apparent time. So now addition corresponded to the equation being positive and subtraction corresponded to it being negative. As the apparent daily movement of the Sun is one revolution per day, that is 360° every 24 hours, and the Sun itself appears as a disc of about 0.5° in the sky, simple sundials can be read to a maximum accuracy of about one minute. Since the equation of time has a range of about 33 minutes, the difference between sundial time and clock time cannot be ignored. In addition to the equation of time, one also has to apply corrections due to one's distance from the local time zone meridian and summer time, if any. The tiny increase of the mean solar day due to the slowing down of the Earth's rotation, by about 2 ms per day per century, which currently accumulates up to about 1 second every year, is not taken into account in traditional definitions of the equation of time, as it is imperceptible at the accuracy level of sundials.
== Major components ==
=== Eccentricity of the Earth's orbit ===
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 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 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 January) and slower at aphelion a half year later. At these extreme points, this effect varies the apparent solar day by 7.9 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 minutes 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:
a
=
−
7.659
sin
(
6.240
040
77
+
0.017
201
97
(
365
(
y
−
2000
)
+
d
)
)
{\displaystyle a=-7.659\sin(6.240\,040\,77+0.017\,201\,97(365(y-2000)+d))}
=== Obliquity of the ecliptic ===
Even if the Earth's orbit were circular, the perceived motion of the Sun along our celestial equator would still not be uniform. This is a consequence of the tilt of the Earth's rotational axis with respect to the 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 solstices, 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 equinoxes, 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 hours and 20.3 seconds long (measured solar noon to solar noon) near the solstices, and as much as 20.3 seconds shorter than 24 hours near the equinoxes. 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":
b
=
9.863
sin
(
2
(
6.240
040
77
+
0.017
201
97
(
365
(
y
−
2000
)
+
d
)
)
+
3.5932
)
{\displaystyle b=9.863\sin \left(2(6.240\,040\,77+0.017\,201\,97(365(y-2000)+d))+3.5932\right)}