What Is The Equation of time?

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• published: 22 Mar 2015
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The equation of time describes the discrepancy between two kinds of solar time. These are apparent solar time, which directly tracks the motion of the sun, and mean solar time, which tracks a fictitious "mean" sun with noons 24 hours apart. Apparent (or true) solar time can be obtained by measurement of the current position (hour angle) of the Sun, or 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 average to 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. 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 12 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. 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 is constant only for a planet with zero axial tilt and zero orbital eccentricity. 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 the time of its solar year orbital period. Sign of the equation of time There is no universally accepted definition of the sign of the equation of time. Some publications show it as positive when a sundial is ahead of a clock, as shown in the upper graph above; others when the clock is ahead of the sundial, as shown in the lower graph. 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 sign 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. In this article, and others in English Wikipedia, a positive value of the equation of time implies that a sundial is ahead of a clock. History The phrase "equation of time" is derived from the mediaeval Latin, Aequatio Dierum = Equation of Days. The word 'Equatio' was widely used in early astronomy to tabulate the difference between an observed value and the mean value (as in the equation of centre, the equation of the equinoxes, the equation of the epicycle). Prior to the mid-17th century, when pendulum-controlled mechanical clocks were invented, sundials were the only reliable timepieces, and were generally considered to tell the right time. 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.)