Solar time is a calculation of the passage of

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...

based on the

position of the Sun The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on th ...

in the sky. The fundamental unit of solar time is the

day A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two so ...

, based on the synodic rotation period. Two types of solar time are apparent solar time (

sundial A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a fl ...

time) and

mean solar time Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial t ...

(clock time).

Introduction

A tall pole vertically fixed in the ground casts a shadow on any sunny day. At one moment during the day, the shadow will point exactly north or south (or disappear when and if the Sun moves directly overhead). That instant is local apparent noon, or 12:00 local apparent time. About 24 hours later the shadow will again point north–south, the Sun seeming to have covered a 360-degree arc around Earth's axis. When the Sun has covered exactly 15 degrees (1/24 of a circle, both angles being measured in a plane perpendicular to Earth's axis), local apparent time is 13:00 exactly; after 15 more degrees it will be 14:00 exactly. The problem is that in September the Sun takes less time (as measured by an accurate clock) to make an apparent revolution than it does in December; 24 "hours" of solar time can be 21 seconds less or 29 seconds more than 24 hours of clock time. This change is quantified by the equation of time, and is due to the eccentricity of Earth's orbit (as in, Earth's orbit is not perfectly circular, meaning that the EarthSun distance varies throughout the year), and the fact that Earth's axis is not perpendicular to the plane of its orbit (the so-called obliquity of the ecliptic). The effect of this is that a clock running at a constant ratee.g. completing the same number of pendulum swings in each hourcannot follow the actual Sun; instead it follows an imaginary "mean Sun" that moves along the celestial equator at a constant rate that matches the real Sun's average rate over the year. This is "mean solar time", which is still not perfectly constant from one century to the next but is close enough for most purposes. , a mean solar day is about 86,400.002 SI seconds. The two kinds of solar time ( apparent solar time and

) are among the three kinds of time reckoning that were employed by astronomers until the 1950s. (The third kind of traditional time reckoning is

sidereal time Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...

, which is based on the apparent motions of

star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...

s other than the Sun.) By the 1950s it had become clear that Earth's rotation rate was not constant, so astronomers developed ephemeris time, a time-scale based on the positions of solar system bodies in their orbits.

Apparent solar time

The apparent sun is the true sun as seen by an observer on Earth. Apparent solar time or true solar time is based on the apparent motion of the actual Sun. It is based on the apparent solar day, the interval between two successive returns of the Sun to the local

meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

. Apparent solar time can be crudely measured by a

. The equivalent on Mars is termed Mars local true solar time (LTST). The length of a solar day varies through the year, and the accumulated effect produces seasonal deviations of up to 16 minutes from the mean. The effect has two main causes. First, due to the eccentricity of

Earth's orbit Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi) in a counterclockwise direction as viewed from above the Northern Hemisphere. One complete orbit takes days (1 sidereal year), during which time Eart ...

, Earth moves faster when it is nearest the Sun (

perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any e ...

) and slower when it is farthest from the Sun (

aphelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any e ...

) (see

Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular or ...

). Second, due to Earth's

axial tilt In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orb ...

(known as the ''obliquity of the

ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agai ...

''), the Sun's annual motion is along a

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...

(the

) that is tilted to Earth's

celestial equator The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projec ...

. When the Sun crosses the equator at both

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears zenith, directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" ...

es, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its

average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...

for the year; when the Sun is farthest from the equator at both

solstice A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many count ...

s, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see

tropical year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time ...

). In June and December when the sun is farthest from the celestial equator, a given shift along the ecliptic corresponds to a large shift at the equator. Therefore, apparent solar days are shorter in March and September than in June or December. These lengths will change slightly in a few years and significantly in thousands of years.

Mean solar time

Mean solar time is the hour angle of the mean Sun plus 12 hours. This 12 hour offset comes from the decision to make each day start at midnight for civil purposes, whereas the hour angle or the mean sun is measured from the local meridian. , this is realized with the UT1 time scale, constructed mathematically from very-long-baseline interferometry observations of the

diurnal motion Diurnal motion (, ) is an astronomical term referring to the apparent motion of celestial objects (e.g. the Sun and stars) around Earth, or more precisely around the two celestial poles, over the course of one day. It is caused by Earth's r ...

s of radio sources located in other galaxies, and other observations. The duration of daylight varies during the year but the length of a mean solar day is nearly constant, unlike that of an apparent solar day. An apparent solar day can be 20 seconds shorter or 30 seconds longer than a mean solar day. Long or short days occur in succession, so the difference builds up until mean time is ahead of apparent time by about 14 minutes near February 6, and behind apparent time by about 16 minutes near November 3. The equation of time is this difference, which is cyclical and does not accumulate from year to year. Mean time follows the mean sun. Jean Meeus describes the mean sun as follows: The length of the mean solar day is slowly increasing due to the

tidal acceleration Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away f ...

of the Moon by Earth and the corresponding slowing of Earth's rotation by the Moon.

History

The sun has always been visible in the sky, and its position forms the basis of apparent solar time, the timekeeping method used in antiquity. An Egyptian

obelisk An obelisk (; from grc, ὀβελίσκος ; diminutive of ''obelos'', " spit, nail, pointed pillar") is a tall, four-sided, narrow tapering monument which ends in a pyramid-like shape or pyramidion at the top. Originally constructed by An ...

constructed c. 3500 BC, a

gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. History A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the o ...

in China dated 2300 BC, and an Egyptian

dated 1500 BC are some of the earliest methods for measuring the sun's position.

Babylonia Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state ...

n astronomers knew that the hours of daylight varied throughout the year. A tablet from 649 BC shows that they used a 2:1 ratio for the longest day to the shortest day, and estimated the variation using a linear zigzag function. It is not clear if they knew of the variation in the length of the solar day and the corresponding equation of time.

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of import ...

clearly distinguishes the mean solar day and apparent solar day in his ''

Almagest The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it cano ...

'' (2nd century), and he tabulated the equation of time in his ''Handy Tables''. Apparent solar time grew less useful as commerce increased and mechanical clocks improved. Mean solar time was introduced in almanacs in England in 1834 and in France in 1835. Because the sun was difficult to observe directly due to its large size in the sky, mean solar time was determined as a fixed ratio of time as observed by the stars, which used point-like observations. A specific standard for measuring "mean solar time" from midnight came to be called Universal Time. Conceptually

Universal Time Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle wi ...

is the rotation of the Earth with respect to the sun and hence is mean solar time. However, UT1, the version in common use since 1955, uses a slightly different definition of rotation that corrects for the motion of Earth's poles as it rotates. The difference between this corrected mean solar time and

Coordinated Universal Time Coordinated Universal Time or UTC is the primary time standard by which the world regulates clocks and time. It is within about one second of mean solar time (such as UT1) at 0° longitude (at the IERS Reference Meridian as the currently ...

(UTC) determines whether a

leap second A leap second is a one- second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise observ ...

is needed. (Since 1972 the UTC time scale has run on SI seconds, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.:(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770 ± 20 cycles), se
"Time Scales", by L. Essen
, in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the

SI second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each ...

. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".)

Notes

References

External links

Sunrise and Sunset and maximum Sun altitude, all year long, anywhere
Apparent solar time in a digital display. {{The Sun Time scales Day Time in astronomy