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Home , Day, Ephemeris time, Equation of time, Equinox, Sidereal year, Solar time

TROPICAL

A (also known as a solar year), for general purposes, is the length of that the takes to return to the same position in the cycle of , as seen from ; for example, the time from vernal to vernal equinox, or from to . Because of the of the , the seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. As a consequence, the tropical year is about 20 shorter than the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed (the ). Since antiquity, astronomers have progressively refined the definition of the tropical year, and currently define it as the time required for the mean Sun's tropical (longitudinal position along the relative to its position at the vernal equinox) to increase by 360 degrees (that is, to complete one full seasonal circuit). (Meeus & Savoie, 1992, p. 40) The mean tropical year on January 1, 2000 was 365.2421897 days, each lasting 86,400 SI . The Gregorian has an average year length of 365.2425 days, being designed to match the northward (March) equinox year of 365.2424 days (as of January 2000).

History

Origin The word "tropical" comes from the Greek tropikos meaning "turn". (tropic, 1992) Thus, the of Cancer and Capricorn mark the extreme north and south where the Sun can appear directly overhead, and where it appears to "turn" in its annual seasonal . Because of this connection between the tropics and the seasonal cycle of the apparent , the word "tropical" also lent its name to the "tropical year". The early Chinese, Hindus, Greeks, and others made approximate measures of the tropical year; early astronomers did so by noting the time required between the appearance of the Sun in one of the tropics to the next appearance in the same tropic. (Meeus & Savoie, 1992, p. 40)

Early value, precession discovery In the 2nd BC introduced a new definition which was still used by some authors in the 20th century, the time required for the Sun to travel from an equinox to the same equinox again. He reckoned the length of the year to be 365 solar days, 5 , 55 minutes, 12 seconds (365.24667 days). Meeus and Savoie used a modern computer model to find the correct value was 365 solar days, 5 hours 49 minutes 9 seconds (365.24247 mean solar days). Hipparchus adopted the new definition because the instrument he used, the armillae, was better able to detect the more rapid motion in at the time of the equinoxes, compared to the . (Meeus & Savoie, 1992, p. 40) Hipparchus also discovered that the equinoctial points moved along the ecliptic (plane of the Earth's orbit, or what Hipparchus would have thought of as the plane of the Sun's orbit about the Earth) in a direction opposite that of the movement of the Sun, a phenomenon that came to be named "precession of the equinoxes". He reckoned the value as 1° per century, a value that was not improved upon until about 1000 later, by Islamic astronomers. Since this discovery a distinction has been made between the tropical year and the sidereal year. (Meeus & Savoie, 1992, p. 40)

Middle Ages and the Renaissance During the Middle Ages and Renaissance a number of progressively better tables were published that allowed computation of the positions of the Sun, and relative to the . An important application of these tables was the reform of the calendar. The Alfonsine Tables, published in 1252, were based on the theories of and were revised and updated after the original publication; the most recent update in 1978 was by the French National Centre for Scientific Research. The length of the tropical year (using the equinox-based definition) was 365 solar days 5 hours 49 minutes 16 seconds (365.24255 days). It was these tables that were used in the reform process that led to the . (Meeus & Savoie, 1992, p. 41) In the 16th century Copernicus put forward a heliocentric cosmology. Erasmus Reinhold used Copernicus' theory to compute the in 1551, and found a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days). (Meeus & Savoie, 1992, p. 41) Major advances in the 17th century were made by and Isaac . In 1609 and 1619 Kepler published his three laws of planetary motion. (McCarthy & Seidelmann, 2009, p. 26) In 1627, Kepler used the observations of and Waltherus to produce the most accurate tables up to that time, the . He evaluated the mean tropical year as 365 solar days, 5 hours, 48 minutes, 45 seconds (365.24219 days). (Meeus & Savoie, 1992, p. 41) Newton's three laws of dynamics and theory of gravity were published in his Philosophiæ Naturalis Principia Mathematica in 1687. Newton's theoretical and mathematical advances influenced tables by Edmund Halley published in 1693 and 1749 (McCarthy & Seidelmann, 2009, pp. 26–28) and provided the underpinnings of all models until 's theory of in the 20th century.

18th and 19th century From the time of Hipparchus and Ptolemy, the year was based on two equinoxes (or two solstices) a number of years apart, to average out both observational errors and the effects of (irregular of the axis of of the earth, the main cycle being 18.6 years) and the movement of the Sun caused by the gravitational pull of the planets. These effects did not begin to be understood until Newton's time. To model short variations of the time between equinoxes (and prevent them from confounding efforts to measure long term variations) requires either precise observations or an elaborate theory of the motion of the Sun. The necessary theories and mathematical tools came together in the 18th century due to the work of Pierre- Simon de Laplace, Joseph Louis Lagrange, and other specialists in . They were able to express the of the Sun as

2 L0 = A0 + A1T + A2T days where T is the time in Julian . The inverse of the derivative

of L0, dT/dL0 gives the length of the tropical year as a linear function of T. When this is computed, an expression giving the length of the tropical year as function of T results. Two equations are given in the table. Both equations estimate that the tropical year gets roughly a half shorter each century.

Tropical year coefficients

Name Equation on which T = 0

Leverrier (Meeus & Savoie, Y = 365.24219647 − January 0.5, 1900, 1992, p. 42) 6.24×10−6 T Time

Y = 365.24219879 − Newcomb (1898, p. 9–10) January 0, 1900, mean time 6.14×10−6 T Newcomb's tables were successful enough that they were used by the joint American-British Astronomical for the Sun, , , and through 1983. (Seidelmann, 1992, p. 317)

20th and 21st centuries The length of the mean tropical year is derived from a model of the solar system, so any advance that improves the solar system model potentially improves the accuracy of the mean tropical year. Many new observing instruments became available, including

 artificial

 tracking of deep probes such as Pioneer 4 beginning in 1959 (Jet Propulsion Laboratory 2005)

 radars able to measure other planets beginning in 1961 (Butrica, 1996)

 lunar laser ranging since the 1969 left the first of a series of which allow greater accuracy than reflectorless

 artificial satellites such as LAGEOS (1976) and the Global Positioning System (initial operation in 1993)

 Very Long Baseline Interferometry which finds precise directions to in distant , and allows determination of the Earth's orientation with respect to these objects whose distance is so great they can be considered to show minimal space motion (McCarthy & Seidelmann, 2009, p. 265)

The complexity of the model used for the solar system must be limited to the available computation facilities. In the 1920s punched card equipment came into use by L. J. Comrie in Britain. At the American Ephemeris an electromagnetic computer, the IBM Selective Sequence Electronic Calculator was used since 1948. When modern computers became available, it was possible to compute ephemerides using numerical integration rather than general theories; numerical integration came into use in 1984 for the joint US-UK . (McCarthy & Seidelmann, 2009, p. 32) Einstein's General provided a more accurate theory, but the accuracy of theories and observations did not require the refinement provided by this theory (except for the advance of the perihelion of Mercury) until 1984. Time scales incorporated general relativity beginning in the 1970s. (McCarthy & Seidelmann, 2009, p. 37) A key development in understanding the tropical year over long periods of time is the discovery that the rate of rotation of the earth, or equivalently, the length of the mean solar day, is not constant. William Ferrel in 1864 and Charles-Eugène Delaunay in 1865 indicated the rotation of the Earth was being retarded by . In 1921 William H Shortt invented the Shortt-Synchronome , the most accurate commercially produced ; it was the first clock capable of measuring variations in the Earth's rotation. The next major time-keeping advance was the , first built by Warren Marrison and J. W. Horton in 1927; in the late 1930s quartz began to replace pendulum clocks as time standards. (McCarthy and Seidelmann, 2009, ch. 9) A series of experiments beginning in the late 1930s led to the development of the first by and J. V. L. Parry in 1955. Their clock was based on a transition in the cesium . (McCarthy & Seidelmann, 2009, pp. 157–9) Due to the accuracy the General Conference on Weights and Measures in 1960 redefined the second in terms of the cesium transition.[1] The atomic second, often called the SI second, was intended to agree with the ephemeris second based on Newcomb's work, which in turn makes it agree with the mean solar second of the mid-19th century. (McCarthy & Seidelman, 2009, pp. 81–2, 191–7)

Time scales

As mentioned in , advances in time-keeping have resulted in various time scales. One useful time scale is (especially the UT1 variant), which is the mean at 0 degrees longitude (the meridian). One second of UT is 1/86,400 of a mean solar day. This time scale is known to be somewhat variable. Since all civil count actual solar days, all civil calendars are based on UT. The other time scale has two parts. (ET) is the independent variable in the equations of motion of the solar system, in particular, the equations in use from 1960 to 1984. (McCarthy & Seidelmann, 2009, p. 378) That is, the length of the second used in the solar system calculations could be adjusted until the length that gives the best agreement with observations is found. With the introduction of atomic clocks in the 1950s, it was found that ET could be better realized as atomic time. This also means that ET is a uniform time scale, as is atomic time. ET was given a new name, (TT), and for most purposes ET = TT = International Atomic Time + 32.184 SI seconds. As of January 2010, TT is ahead of UT1 by about 66 seconds. (International Earth Rotation Service, 2010; McCarthy & Seidelman, 2009, pp. 86–7). As explained below, long term estimates of the length of the tropical year were used in connection with the reform of the , which resulted in the Gregorian calendar. Of course the participants in that reform were unaware of the non-uniform rotation of the Earth, but now this can be taken into account to some . The amount that TT is ahead of UT1 is known as Δ T, or Delta T. The table below gives Morrison and Stephenson's (S & M) 2004 estimates and standard errors (σ) for dates significant in the process of developing the Gregorian calendar. Year Nearest S & M Year ΔT σ

Julian calendar begins −44 0 2h56m20s 4m20s

First Council of Nicaea 325 300 2h8m 2m

Gregorian calendar begins 1583 1600 2m 20s

low precision extrapolation 4000 4h13m

low precision extrapolation 10,000 2d11h

The low precision extrapolations are computed with an expression provided by Morrison and Stephenson ΔT = −20 + 32t2 where t is measured in Julian centuries from 1820. The extrapolation is provided only to show ΔT is not negligible when evaluating the calendar for long periods; Borkowski (1991, p. 126) cautions that "many researchers have attempted to fit a parabola to the measured ΔT values in order to determine the of the deceleration of the Earth's rotation. The results, when taken together, are rather discouraging."

Length of tropical year An oversimplified definition of the tropical year would be the time required for the Sun, beginning at a chosen ecliptic longitude, to make one complete cycle of the seasons and return to the same ecliptic longitude. Before considering an example, the equinox must be examined. There are two important planes in solar system calculations, the plane of the ecliptic (the Earth's orbit around the Sun), and the plane of the celestial (the Earth's equator projected into space). These two planes intersect in a line. The direction along the line from the Earth in the general direction of the sign (Ram) is the Northward equinox, and is given the symbol ♈ (the symbol looks like the horns of aram). The opposite direction, along the line in the general direction of the sign , is the Southward equinox and is given the symbol ♎. Because of precession and nutation these directions change, compared to the direction of distant stars and galaxies, whose directions have no measurable motion due to their great distance (see International Celestial Reference Frame). The ecliptic longitude of the Sun is the between ♈ and the Sun, measured eastward along the ecliptic. This creates a complicated , because as the Sun is moving, the direction the angle is measured from is also moving. It is convenient to have a fixed (with respect to distant stars) direction to measure from; the direction of

♈ at January 1, 2000 fills this role and is given the symbol ♈0. Using the oversimplified definition, there was an equinox on , 2009, 11:44:43.6 TT. The 2010 was March 20, 17:33:18.1 TT, which gives a of 365 d 5 h 49 m 30s. (Astronomical Applications Dept., 2009) While the Sun moves, ♈ moves in the opposite direction . When the Sun and ♈ met at the 2010 March equinox, the Sun had moved east 359°59'09" while ♈ had moved 51" for a total of 360° (all with respect to ♈0). (Seidelmann, 1992, p. 104, expression for pA) If a different starting longitude for the Sun is chosen, the duration for the Sun to return to the same longitude will be different. This is because although ♈ changes at a nearly steady rate[2] there is considerable variation in the angular speed of the Sun. Thus, the 50 or so arcseconds that the Sun does not have to move to complete the tropical year "saves" varying amounts of time depending on the position in the orbit.

Mean equinox tropical year As already mentioned, there is some choice in the length of the tropical year depending on the point of reference that one selects. But during the period when return of the Sun to a chosen longitude was the method in use by astronomers, one of the equinoxes was usually chosen because the instruments were most sensitive there. When tropical year measurements from several successive years are compared, variations are found which are due to nutation, and to the planetary perturbations acting on the Sun. Meeus and Savoie (1992, p. 41) provided the following examples of intervals between northward equinoxes:

days hours Min s

1985–1986 365 5 48 58

1986–1987 365 5 49 15

1987–1988 365 5 46 38

1988–1989 365 5 49 42

1989–1990 365 5 51 06

Until the beginning of the 19th century, the length of the tropical year was found by comparing equinox dates that were separated by many years; this approach yielded the meantropical year. (Meeus & Savoie, 1992, p. 42) Values of mean time intervals between equinoxes and solstices were provided by Meeus and Savoie (1992, p. 42) for the years 0 and 2000. Year 0 Year 2000

Between two Northward equinoxes 365.242137 days 365.242374 days

Between two Northern solstices 365.241726 365.241626

Between two Southward equinoxes 365.242496 365.242018

Between two Southern solstices 365.242883 365.242740

Mean tropical year 365.242310 365.242189 (Laskar's expression)

Mean tropical year current value

The mean tropical year on January 1, 2000 was 365.2421897 or 365 days, 5 hours, 48 minutes, 45.19 seconds. This changes slowly; an expression suitable for calculating the length in days for the distant is 365.2421896698 − 6.15359×10−6T − 7.29×10−10T2 + 2.64×10−10T3 where T is in Julian centuries of 36,525 days measured from noon January 1, 2000 TT (in negative numbers for dates in the past). (McCarthy & Seidelmann, 2009, p. 18.; Laskar, 1986) Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360°. The process for finding an expression for the length of the tropical year is to first find an expression for the Sun's mean longitude (with respect to ♈), such as Newcomb's expression given above, or Laskar's expression (1986, p. 64). When viewed over a 1 year period, the mean longitude is very nearly a linear function of Terrestrial Time. To find the length of the tropical year, the mean longitude is differentiated, to give the angular speed of the Sun as a function of Terrestrial Time, and this angular speed is used to compute how long it would take for the Sun to move 360°. (Meeus & Savoie, 1992, p. 42).

The Gregorian calendar, as used for civil purposes, is an international standard. It is a that is designed to maintain synchrony with the vernal equinox tropical year.[3] It has a cycle of 400 years (146,097 days). Each cycle repeats the , dates, and weekdays. The average year length is 146,097/400 = 365+97/400 = 365.2425 days per year, a close approximation to the mean tropical year, and an even closer approximation to the current vernal equinox tropical year. (Seidelmann, 1992, pp. 576–81) The Gregorian calendar is a reformed version of the Julian calendar. By the time of the reform in 1582, the date of the vernal equinox had shifted about 10 days, from about March 21 at the time of the First Council of Nicaea in 325, to about March 11. According to North, the real motivation for reform was not primarily a matter of getting agricultural cycles back to where they had once been in the seasonal cycle; the primary concern of Christians was the correct observance of . The rules used to compute the used a conventional date for the vernal equinox (March 21), and it was considered important to keep March 21 close to the actual equinox. (North, 1983, pp. 75–76) If society in the still attaches importance to the synchronization between the civil calendar and the seasons, another reform of the calendar will eventually be necessary. According to Blackburn and Holford-Strevens (who used Newcomb's value for the tropical year) if the tropical year remained at its 1900 value of 365.24219878125 days the Gregorian calendar would be 3 days, 17 min, 33 s behind the Sun after 10,000 years. Aggravating this error, the length of the tropical year (measured in Terrestrial Time) is decreasing at a rate of approximately 0.53 s per 100 tropical years. Also, the mean solar day is getting longer at a rate of about 1.5 ms per 100 tropical years. These effects will cause the calendar to be nearly a day behind in 3200. A possible reform would be to omit the leap day in 3200, keep 3600 and 4000 as leap years, and thereafter make all centennial years common except 4500, 5000, 5500, 6000, etc. The effects are not sufficiently predictable to form more precise proposals. (Blackburn & Holford-Strevens, 2003, p. 692) Borkowski (1991, p. 121) states "because of high uncertainty in the Earth's rotation it is premature at to suggest any reform that would reach further than a few thousand years into the future." He estimates that in 4000 the Gregorian year (which counts actual solar days) will be behind the tropical year by 0.8 to 1.1 days. (p. 126) EARTH'S ROTATION

An animation showing the rotation of the Earth around its own axis.

Southern over the Residencia “hotel” at ESO’s Paranal Observatory in Chile

Earth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates from the west towards the east. As viewed from the North or polestar Polaris, the Earth turns counter-clockwise.

The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the where the Earth's axis of rotation meets its surface. This point is distinct from the Earth's North Magnetic Pole. The South Pole is the other point where the Earth's axis of rotation intersects its surface, in Antarctica.

The Earth rotates once in about 24 hours with respect to the sun and once every 23 hours 56 minutes and 4 seconds with respect to the stars (see below). Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moonhas on Earth's rotation. Atomic clocks show that a modern day is longer by about 1.7 than a century ago,[2] slowly increasing the rate at which UTC is adjusted by leap seconds.

History

Among the ancient Greeks, several of the Pythagorean school believed in the rotation of the earth rather than the apparent diurnal rotation of the heavens. The first was Philolaus(470-385 BCE) though his system was complicated, including a counter- earth rotating daily about a central fire.[3]

A more conventional picture was that supported by Hicetas, Heraclides and Ecphantus in the fourth century BCE who assumed that the earth rotated but did not suggest that the earth revolved about the sun. In the third century, Aristarchus of Samos suggested the sun's central place.

However, Aristotle in the fourth century criticized the ideas of Philolaus as being based on theory rather than observation. He established the idea of a sphere of fixed stars that rotated about the earth.[4] This was accepted by most of those who came after, in particular Claudius Ptolemy (2nd century CE), who thought the earth would be devastated by gales if it rotated.[5]

In 499 CE, the Indian astronomer wrote that the rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth. He provided the following analogy: "Just as a man in a boat going in one direction sees the stationary things on the bank as moving in the opposite direction, in the same way to a man at Lanka the fixed stars appear to be going westward."[6][7]

In the Middle Ages, Thomas Aquinas accepted Aristotle's view[8] and so, reluctantly, did John Buridan [9] and Nicole Oresme [10] in the fourteenth century. Not until in 1543 adopted a heliocentric world system did the earth's rotation begin to be established. Copernicus pointed out that if the movement of the earth is violent, then the movement of the stars must be very much more so. He acknowledged the contribution of the Pythagoreans and pointed to examples of relative motion. For Copernicus this was the first step in establishing the simpler pattern of planets circling a central sun.[11]

This was not accepted immediately even by many astronomers due to the widespread conformance to Aristotle and the Bible. Tycho Brahe, who produced accurate observations on which Kepler based his laws, used Copernicus's work as the basis of a system assuming a stationary earth. In 1600, William Gilbert strongly supported the earth's rotation in his treatise on the earth's magnetism[12] and thereby influenced many of his contemporaries.[13] Those like Gilbert who did not openly support or reject the motion of the earth about the sun are often called "semi-Copernicans".[14] A century after Copernicus, Riccioli disputed the model of a rotating earth due to the lack of then- observable eastward deflections in falling bodies;[15] such deflections would later be called the Coriolis effect. However, the contributions of Kepler, Galileo and Newton gathered support for the theory of the rotation of the Earth.

Empirical tests

The earth's rotation implies that the equator bulges and the poles are flattened. In his Principia, Newton predicted this flattening would occur in the ratio of 1:230, and pointed to the 1673 pendulum measurements by Richer as corroboration of the change in gravity,[16] but initial measurements of meridian lengths by Picard and Cassini at the end of the 17th century suggested the opposite. However measurements by Maupertuis and the French Geodetic Mission in the 1730s established the flattening, thus confirming both Newton and the Copernican position.[17]

In the Earth's rotating frame of reference, a freely moving body follows an apparent path that deviates from the one it would follow in a fixed frame of reference. Because of thisCoriolis effect, falling bodies veer slightly eastward from the vertical plumb line below their point of release, and projectiles veer right in the northern hemisphere (and left in the southern) from the direction in which they are shot. The Coriolis effect is mainly observable at a meteorological scale, where it is responsible for the differing rotation direction ofcyclones in the northern and southern hemispheres.

Hooke, following a 1679 suggestion from Newton, tried unsuccessfully to verify the predicted eastward deviation of a body dropped from a height of 8.2 meters, but definitive results were only obtained later, in the late 18th and early 19th century, by Giovanni Battista Guglielmini in Bologna, Johann Friedrich Benzenberg in Hamburg and Ferdinand Reich in Freiberg, using taller towers and carefully released weights.[n 1] A ball dropped from a height of 158.5 m (520 ft) departed by 27.4 mm (1.08 in) from the vertical compared with a calculated value of 28.1 mm (1.11 in).

The most celebrated test of Earth's rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of a lead-filled brass sphere suspended 67 mfrom the top of the Panthéon in Paris. Because of the Earth's rotation under the swinging pendulum, the pendulum's plane of oscillation appears to rotate at a rate depending on . At the latitude of Paris the predicted and observed shift was about 11 degrees clockwise per . Foucault pendulums now swing in museums around the world.

Rotation period

A 3571 second exposure of the northern sky.

True solar day

Earth's relative to the Sun (true noon to true noon) is its true solar day or apparent solar day. It depends on the Earth's orbital motion and is thus affected by changes in the eccentricity and inclination of Earth's orbit. Both vary over thousands of years so the annual variation of the true solar day also varies. Generally, it is longer than the mean solar day during two periods of the year and shorter during another two. [n 2] The true solar day tends to be longer near perihelion when the Sun apparently moves along the ecliptic through a greater angle than usual, taking about 10 seconds longer to do so. Conversely, it is about 10 seconds shorter near aphelion. It is about20 seconds longer near a solstice when the projection of the Sun's apparent movement along the ecliptic onto the celestial equatorcauses the Sun to move through a greater angle than usual. Conversely, near an equinox the projection onto the equator is shorter by about 20 seconds. Currently, the perihelion and solstice effects combine to lengthen the true solar day near December 22 by 30 meansolar seconds, but the solstice effect is partially cancelled by the aphelion effect near June 19 when it is only 13 seconds longer. The effects of the equinoxes shorten it nearMarch 26 and September 16 by 18 seconds and 21 seconds, respectively.[18][19][20]

Mean solar day

The average of the true solar day during the course of an entire year is the mean solar day, which contains 86,400 mean solar seconds. Currently, each of these seconds is slightly longer than an SI second because Earth's mean solar day is now slightly longer than it was during the 19th century due to tidal friction. The average length of the mean solar day since the introduction of the in 1972 has been about 0 to 2 ms longer than 86,400 SI seconds.[21][22][23] Random fluctuations due to core-mantle coupling have an amplitude of about 5 ms.[24][25] The mean solar second between 1750 and 1892 was chosen in 1895 by as the independent in his Tables of the Sun. These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second. In 1967 the SI second was made equal to the ephemeris second.[26]

The apparent solar time is a measure of the Earth's rotation and the difference between it and the mean solar time is known as the .

Stellar and sidereal day

On a prograde like the Earth, the stellar day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again but the Sun is not (1→2 = one stellar day). It is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service(IERS), is 86,164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s, 0.997 269 663 237 16 mean solar days).[27][n 3] Earth's rotation period relative to the precessing or moving mean vernal equinox, named sidereal day, is86,164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s, 0.997 269 566 329 08 mean solar days).[27] Thus the sidereal day is shorter than the stellar day by about 8.4 ms.[29]

Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. The mean solar day in SI seconds is available from the IERS for the periods 1623–2005[30] and 1962–2005.[31]

Recently (1999–2010) the average annual length of the mean solar day in excess of 86,400 SI seconds has varied between 0.25 ms and1 ms, which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (seeFluctuations in the length of day).

Angular speed

The angular speed of Earth's rotation in inertial space is (7.2921150 ± 0.0000001) ×10−5 per SI second (mean solar second).[27]Multiplying by (180°/π radians)×(86,400 seconds/mean solar day) yields 360.9856°/mean solar day, indicating that Earth rotates more than 360° relative to the fixed stars in one solar day. Earth's movement along its nearly circular orbit while it is rotating once around its axis requires that Earth rotate slightly more than once relative to the fixed stars before the mean Sun can pass overhead again, even though it rotates only once (360°) relative to the mean Sun.[n 4] Multiplying the value in rad/s by Earth's equatorial radius of 6,378,137 m (WGS84 ellipsoid) (factors of 2π radians needed by both cancel) yields an equatorial speed of 465.1 m/s, 1,674.4 km/h or 1,040.4 mi/h.[32] Some sources state that Earth's equatorial speed is slightly less, or1,669.8 km/h.[33] This is obtained by dividing Earth's equatorial circumference by 24 hours. However, the use of only one circumference unwittingly implies only one rotation in inertial space, so the corresponding time unit must be a sidereal hour. This is confirmed by multiplying by the number of sidereal days in one mean solar day,1.002 737 909 350 795,[27] which yields the equatorial speed in mean solar hours given above of 1,674.4 km/h.

The tangential speed of Earth's rotation at a point on Earth can be approximated by multiplying the speed at the equator by the cosine of the latitude.[34] For example, the Kennedy Space Center is located at 28.59° North latitude, which yields a speed of: 1,674.4 kilometres per hour (1,040.4 mph) × cos (28.59) = 1,470.23 kilometres per hour (913.56 mph) Changes in rotation Earth's (or obliquity) and its relation to the rotation axis and plane of orbit as viewed from the Sun during theNorthward equinox.

Deviation of day length from SI based day, 1962–2010

The Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. The Earth's crust also moves with respect to the Earth's rotation axis; this is called polar motion.

Precession is a rotation of the Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies. The polar motion is primarily due to free core nutationand the Chandler wobble.

Over millions of years, the rotation is significantly slowed by gravitational interactions with the Moon; both rotational energy and angular momentum are being slowly transferred to the Moon: see . However some large scale events, such as the 2004 Indian Ocean earthquake, have caused the rotation to speed up by around 3 by affecting the Earth's of inertia.[35] Post-glacial rebound, ongoing since the last Ice , is also changing the distribution of the Earth's thus affecting the moment of inertia of the Earth and, by the conservation of angular momentum, the Earth's rotation period.[36]

Measurement

The permanent monitoring of the Earth's rotation is done these days via very-long- baseline interferometry coordinated with the Global Positioning System, laser ranging, and other satellite techniques. This provides an absolute reference for the determination of universal time, precession, and nutation.[37] Origin

An artist's rendering of the protoplanetary disk.

That the Earth rotates is a vestige of the original angular momentum of the cloud of dust, rocks, and gas that coalesced to form the Solar System. This primordial cloud was composed of hydrogen and helium produced in the Big Bang, as well as heavier elements ejected bysupernovas. As this interstellar dust is inhomogeneous, any asymmetry during gravitational accretion results in the angular momentum of the eventual planet.[38] The current rotation period of the Earth is the result of this initial rotation and other factors, including tidal friction and the hypothetical impact of Theia. SIDEREAL YEAR

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. This differs from the solar or tropical year which has length equal to the time interval between vernal equinoxes in successive years. It was equal to 365.256363004 SI days[1] at noon 1 January 2000 (J2000.0). This is 6 hours and 9.1626 minutes longer than the standard calendar year of 365 SI days, and 20 min 24.5128 s longer than the mean tropical year at J2000.0.[1] The word "sidereal" is derived from the Latin sidus meaning "star".

Apparent motion of the Sun against the stars

As the Earth orbits the Sun, the apparent position of the Sun against the stars gradually moves along the ecliptic, passing through the twelve traditional of thezodiac, and returning to its starting point after one sidereal year. This motion is difficult to observe directly because the stars cannot be seen when the Sun is in the sky. However, if one looks regularly at the sky before , the annual motion is very noticeable: the last stars seen to rise are not always the same, and within a or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible.

This effect is easier to measure than the north/south movement of the position of (except in high-latitude regions), which defines the seasonal cycle and the tropical yearon which the Gregorian calendar is based. For this reason many cultures started their year on the first day a particular special star (, for instance) could be seen in the east at dawn. In Hesiod's Works and Days, the of the year for sowing, harvest, and so on are given by reference to the first visibility of stars. Such a calendar effectively uses the sidereal year.

The Greek astronomer Hipparchus is regarded as the one who defined precession. Therefore, it is believed that, before Hipparchus, the years measured by the stars (sidereal years) were thought to be the same as years measured by the seasons (tropical years). Many ancient cultures seem to have discovered the phenomenon of the precession, forming the basis for various world-age myths.