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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Equation of time | 2/9 | https://en.wikipedia.org/wiki/Equation_of_time | reference | science, encyclopedia | 2026-05-05T11:12:39.793727+00:00 | kb-cron |
=== Early astronomy === The irregular daily movement of the Sun was known to the Babylonians. Book III of Ptolemy's Almagest (2nd century) is primarily concerned with the Sun's anomaly, and he tabulated the equation of time in his Handy Tables. Ptolemy discusses the correction needed to convert the meridian crossing of the Sun to mean solar time and takes into consideration the nonuniform motion of the Sun along the ecliptic and the meridian correction for the Sun's ecliptic longitude. He states the maximum correction is 8+1⁄3 time-degrees or 5⁄9 of an hour (Book III, chapter 9). However he did not consider the effect to be relevant for most calculations since it was negligible for the slow-moving luminaries and only applied it for the fastest-moving luminary, the Moon. Based on Ptolemy's discussion in the Almagest, values for the equation of time (Arabic taʿdīl al-ayyām bi layālayhā) were standard for the tables (zij) in the works of medieval Islamic astronomy.
=== Early modern period ===
A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767: "Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time." He went on to say that, at sea, the apparent time found from observation of the Sun must be corrected by the equation of time, if the observer requires the mean time. The right time was originally considered to be that which was shown by a sundial. When good mechanical clocks were introduced, they agreed with sundials only near four dates each year, so the equation of time was used to "correct" their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this "correction". Later, as clocks became the dominant good timepieces, uncorrected clock time, i.e., "mean time", became the accepted standard. The readings of sundials, when they were used, were then, and often still are, corrected with the equation of time, used in the reverse direction from previously, to obtain clock time. Many sundials, therefore, have tables or graphs of the equation of time engraved on them to allow the user to make this correction. The equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, there were several common land-based ways to set clocks. A sundial was read and corrected with the table or graph of the equation of time. If a transit instrument was available or accuracy was important, the sun's transit across the meridian (the moment the sun appears to be due south or north of the observer, known as its culmination) was noted; the clock was then set to noon and offset by the number of minutes given by the equation of time for that date. A third method did not use the equation of time; instead, it used stellar observations to give sidereal time, exploiting the relationship between sidereal time and mean solar time. The more accurate methods were also precursors to finding the observer's longitude in relation to a prime meridian, such as in geodesy on land and celestial navigation on the sea. The first tables to give the equation of time in an essentially correct way were published in 1665 by Christiaan Huygens. Huygens, following the tradition of Ptolemy and medieval astronomers in general, set his values for the equation of time so as to make all values positive throughout the year. This meant that any clock being set to mean time by Huygens's tables was consistently about 15 minutes slow compared to today's mean time. Another set of tables was published in 1672–73 by John Flamsteed, who later became the first Astronomer Royal of the new Royal Greenwich Observatory. These appear to have been the first essentially correct tables that gave today's meaning of Mean Time (previously, as noted above, the sign of the equation was always positive and it was set at zero when the apparent time of sunrise was earliest relative to the clock time of sunrise). Flamsteed adopted the convention of tabulating and naming the correction in the sense that it was to be applied to the apparent time to give mean time. The equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion, was not generally adopted until after Flamsteed's tables of 1672–73, published with the posthumous edition of the works of Jeremiah Horrocks. Robert Hooke (1635–1703), who mathematically analyzed the universal joint, was the first to note that the geometry and mathematical description of the (non-secular) equation of time and the universal joint were identical, and proposed the use of a universal joint in the construction of a "mechanical sundial".
=== 18th and early 19th centuries === The corrections in Flamsteed's tables of 1672–1673 and 1680 gave mean time computed essentially correctly and without need for further offset. But the numerical values in tables of the equation of time have somewhat changed since then, owing to three factors:
General improvements in accuracy that came from refinements in astronomical measurement techniques, Slow intrinsic changes in the equation of time, occurring as a result of small long-term changes in the Earth's obliquity and eccentricity (affecting, for instance, the distance and dates of perihelion), and The inclusion of small sources of additional variation in the apparent motion of the Sun, unknown in the 17th century but discovered from the 18th century onwards, including the effects of the Moon (See barycentre), Venus and Jupiter.