6.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Equation of time | 1/9 | https://en.wikipedia.org/wiki/Equation_of_time | reference | science, encyclopedia | 2026-05-05T11:12:39.793727+00:00 | kb-cron |
The equation of time describes the discrepancy between two kinds of solar time. The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero. The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. The equation of time can be approximated by a sum of two sine waves:
Δ
t
e
y
=
−
7.659
sin
(
D
)
+
9.863
sin
(
2
D
+
3.5932
)
{\displaystyle \Delta t_{ey}=-7.659\sin(D)+9.863\sin \left(2D+3.5932\right)}
[minutes] where:
D
=
6.240
040
77
+
0.017
201
97
(
365.25
(
y
−
2000
)
+
d
)
{\displaystyle D=6.240\,040\,77+0.017\,201\,97(365.25(y-2000)+d)}
where
d
{\displaystyle d}
represents the number of days since 1 January of the current year,
y
{\displaystyle y}
.
== Concept ==
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 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 11 February). The equation of time has zeros near 15 April, 13 June, 1 September, and 25 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 April 2011. 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 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 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. 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 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.
== Notation ==
The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative. The equation of time is shown in the upper graph above for a period of slightly more than a year. The lower graph (which covers exactly one calendar year) has the same absolute values but the sign is reversed as it shows how far the clock is ahead of the sun. Publications may use either format: in the English-speaking world, the former usage is the more common, but is not always followed. Anyone who makes use of a published table or graph should first check its sign usage. Often, there is a note or caption which explains it. Otherwise, the usage can be determined by knowing that, during the first three months of each year, the clock is ahead of the sundial. The mnemonic "NYSS" (pronounced "nice"), for "new year, sundial slow", can be useful. Some published tables avoid the ambiguity by not using signs, but by showing phrases such as "sundial fast" or "sundial slow" instead.
== History == The phrase "equation of time" is derived from the medieval Latin aequātiō diērum, meaning "equation of days" or "difference of days". The word equation is used in the medieval sense of "reconciliation of a difference". The word aequātiō (and Middle English equation) was used in medieval astronomy to tabulate the difference between an observed value and the expected value (as in the equation of the centre, the equation of the equinoxes, the equation of the epicycle). Gerald J. Toomer uses the medieval term "equation", from the Latin aequātiō (equalization or adjustment), for Ptolemy's difference between the mean solar time and the apparent solar time. Johannes Kepler's definition of the equation is "the difference between the number of degrees and minutes of the mean anomaly and the degrees and minutes of the corrected anomaly." The difference between apparent solar time and mean time was recognized by astronomers since antiquity, but prior to the invention of accurate mechanical clocks in the mid-17th century, sundials were the only reliable timepieces, and apparent solar time was the generally accepted standard. Mean time did not supplant apparent time in national almanacs and ephemerides until the early 19th century.