Solar times are measures of the apparent position of the
SunThe Sun is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 99.86% of the Solar System's mass....
on the
celestial sphereIn astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...
. They are not actually the physical
timeTime is a component of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects...
, but rather
hour angleIn astronomy, the hour angle is one of the coordinates used in the equatorial coordinate system for describing the position of a point on the celestial sphere....
s, that is,
angleIn geometry and trigonometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle...
s expressed in time units. They are also
local times in the sense that they depend on the
longitudeLongitude , identified by the Greek letter lambda , is the geographic coordinate most commonly used in cartography and global navigation for east-west measurement...
of the observer.
Apparent solar time
Apparent solar time or
true solar time is the hour angle of the Sun. It is based on the
apparent solar day, which is the interval between two successive returns of the Sun to the local
meridianThis article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere...
. Note that the solar day starts at
noonNoon is the hour of 12:00 in an observer's local time zone, or more loosely, a time near the middle of the day when workers in many countries take a meal break...
, so apparent solar time 00:00 means noon and 12:00 means
midnightMidnight is, literally, "the middle of the night". In most systems it is when one day ends and the next begins: when the date changes. Originally midnight was halfway between sunset and dawn, varying according to the seasons....
. Solar time can be measured by a
sundial{| align="right" | |}A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a flat surface marked with lines indicating the hours of the day...
.
The length of a solar day varies throughout the year for two reasons. First, Earth's
orbitIn physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star....
is an
ellipseIn mathematics, an ellipse is the bounded case of a conic section, the geometric shape that results from cutting a circular conical or cylindrical surface with an oblique plane...
, not a
circleA circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre. The common distance of the points of a circle from its center is called its radius....
, so the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see
Kepler's laws of planetary motionIn astronomy, Kepler's three laws of planetary motion are:#The orbit of every planet is an ellipse with the sun at a focus.#A line joining a planet and the sun sweeps out equal areas during equal intervals of time....
). Second, due to Earth's
axial tiltIn astronomy, axial tilt is the angle between an object's rotational axis and a line perpendicular to its orbital plane. The angle is measured between the line perpendicular to object's orbital plane and object's rotational axis passing through north pole at which the planet appears to rotate...
, the Sun moves along a
great circleA great circle of a sphere is a circle that runs along the surface of that sphere so as to cut it into two equal halves, as distinct from a small circle. The great circle therefore has both the same circumference and the same center as the sphere...
(the
eclipticThe ecliptic is the apparent path that the Sun traces out in the sky during the year, appearing to move eastwards on an imaginary spherical surface, the celestial sphere, relative to the fixed stars. More accurately, it is the intersection of the celestial sphere with the ecliptic plane, which is...
) that is tilted to Earth's
celestial equatorThe celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space...
. When the Sun crosses the equator at both
equinoxAn equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the Sun being vertically above a point on the Equator...
es, the Sun is moving at an angle to the equator, so the projection of this tilted motion onto the equator is slower than its
mean motionMean motion, , is a measure of how fast a satellite progresses around its orbit. Unless the orbit is circular, the mean motion is only an average value, and does not represent the instantaneous angular rate....
; when the Sun is farthest from the equator at both
solsticeA solstice is an astronomical event that happens twice each year, when the tilt of the Earth's axis is most inclined toward or away from the Sun, causing the Sun's apparent position in the sky to reach its northernmost or southernmost extreme...
s, the Sun moves parallel to the equator, so the projection of this parallel motion onto the equator is faster than its mean motion (see
tropical yearA tropical year is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.A tropical year can equivalently be defined as the time taken...
). Consequently, apparent solar days are shorter in March (26–27) and September (12–13) than they are in June (18–19) or December (20–21). These dates are shifted from those of the equinoxes and solstices by the fast/slow Sun at Earth's perihelion/aphelion.
Mean solar time
Mean solar time is the hour angle of the
mean Sun (see below). As the mean Sun is a mathematical construction only and cannot be physically observed, the mean solar time is computed from an artificial clock time adjusted via observations of the
diurnal rotationDiurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle, that is called the diurnal circle...
of the fixed stars to agree with average apparent solar time. Though the amount of daylight varies significantly, the length of a
mean solar day does not change on a seasonal basis. However, the length of a mean solar day increases at a rate of approximately 1.4 milliseconds each century. It was exactly 86,400 (i.e. 24 hours × 60 minutes/hour × 60
secondThe second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units base unit of time...
s/minute) SI seconds in approximately 1820. Currently, the length of a mean solar day is approximately 86400.002 SI seconds. An apparent solar day may differ from a mean solar day by as much as nearly 22 seconds shorter to nearly 29 seconds longer. Because many of these long or short days occur in succession, the difference builds up to as much as nearly 17 minutes early or a little over 14 minutes late. Since these periods are cyclical, they do not accumulate from year to year. The difference between apparent solar time and mean solar time is called the
equation of timeThe equation of time is the difference between apparent solar time and mean solar time, both taken at a given place at the same real instant of time....
. The mean solar day also starts at noon, with 00:00 meaning noon and 12:00 meaning midnight. As this is inconvenient for civilian use, the
civil timeIn modern usage, civil time refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks. Modern civil time is generally standard time at a fixed offset from Coordinated Universal Time or from GMT, possibly adjusted by daylight saving time during part of...
is defined as mean solar time minus 12 hours.
The length of the mean solar day is increasing due to the
tidal accelerationTidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the planet that it orbits. The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of...
of the Moon by Earth, and the corresponding deceleration of the Earth by the Moon.
The
mean Sun is defined as follows. First, consider a fictitious Sun that moves along the ecliptic at a constant speed and occupies the same position as the real Sun when Earth passes through the
perihelionIn celestial mechanics, an apsis, plural apsides is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system....
and also when it passes through the
aphelionIn celestial mechanics, an apsis, plural apsides is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system....
. Then, the
mean sun is a second fictive Sun that moves along the celestial equator at constant speed and passing through the vernal point simultaneously with the first fictive sun.
History
Many methods have been used to simulate mean solar time throughout history. The earliest were clepsydras or
water clockA water clock or clepsydra is any timepiece in which time is measured by the regulated flow of liquid into or out from a vessel where the amount is then measured.Water clocks, along with sundials, are likely to be the oldest time-measuring instruments, with the only exceptions being...
s, used for almost four millennia from as early as the middle of the
second millennium BCThe 2nd millennium BC marks the transition from the Middle to the Late Bronze Age.Its first half is dominated by the Middle Kingdom of Egypt and Babylonia. The alphabet develops. Indo-Iranian migration onto the Iranian plateau and onto the Indian subcontinent propagates the use of the chariot...
until the early
second millenniumBeethoven|Te Kooti|- align="left"!20th Century|Nelson Mandela
Paul Rusesabagina|Martin Luther King, Jr.
Franklin D...
. Before the middle of the
first millennium BCThe 1st millennium BC encompasses the Iron Age and sees the rise of many successive empires.The Neo-Assyrian Empire, followed by the Achaemenids. In Greece, Classical Antiquity begins with the colonization of Magna Graecia and peaks with the rise of Hellenism. The close of the millennium sees the...
, the water clocks were only adjusted to agree with the apparent solar day, thus were no better than the shadow cast by a
gnomonThe gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."It has come to be used for a variety of purposes in mathematics and other fields....
(a vertical pole), except that they could be used at night.
Nevertheless, it has long been known that the sun moves eastward relative to the fixed stars along the ecliptic. Thus since the middle of the first millennium BC, the diurnal rotation of the fixed stars has been used to determine mean solar time, against which clocks were compared to determine their error rate.
BabyloniaBabylonia was a civilization in Lower Mesopotamia , with Babylon as its capital. Babylonia emerged when Hammurabi created an empire out of the territories of the former kingdoms of Sumer and Akkad...
n astronomers knew of the
equation of timeThe equation of time is the difference between apparent solar time and mean solar time, both taken at a given place at the same real instant of time....
and were correcting for it as well as the different rotation rate of stars,
sidereal timeAstronomers use sidereal time as a way to keep track of the direction in which their telescopes need to be pointed to view any given star in the night sky...
, to obtain a mean solar time much more accurate than their water clocks. This ideal mean solar time has been used ever since then to describe the motions of the planets, Moon, and Sun.
Mechanical clocks did not achieve the accuracy of Earth's "star clock" until the beginning of the 20th century. Even though today's
atomic clockAn atomic clock is a type of clock that uses an atomic resonance frequency standard as its timekeeping element. They are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, and to control the frequency of television...
s have a much more constant rate than the Earth, its
star clockA star clock is a method of using the stars to determine the time. Some methods require no tools; others use an astrolabe and a planisphere.A clock's regulator can be adjusted so that it keeps the Mean Sidereal Time rate...
is still used to determine mean solar time. Since sometime in the late 20th century, Earth's rotation has been defined relative to an ensemble of extra-galactic radio sources and then converted to mean solar time by an adopted ratio. The difference between this calculated mean solar time and
Coordinated Universal TimeCoordinated Universal Time , ) is a time standard based on International Atomic Time with leap seconds added at irregular intervals to compensate for the Earth's slowing rotation...
(UTC) is used to determine whether a
leap secondA leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
is needed. (The UTC time scale now runs on
SI secondsThe second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units base unit of time...
, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.)
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