From 916a25f08a6580e3498c1260422ac81660e9ea62 Mon Sep 17 00:00:00 2001 From: turtle89431 Date: Tue, 5 May 2026 04:14:26 -0700 Subject: [PATCH] Scrape wikipedia-science: 9223 new, 3518 updated, 13090 total (kb-cron) --- _index.db | Bin 98959360 -> 98959360 bytes .../wiki/A_series_and_B_series-0.md | 65 ++ .../wiki/Absolute_space_and_time-0.md | 42 ++ .../wiki/Absolute_space_and_time-1.md | 61 ++ data/en.wikipedia.org/wiki/Aevum-0.md | 45 ++ .../wiki/An_Experiment_with_Time-0.md | 33 + .../wiki/An_Experiment_with_Time-1.md | 58 ++ data/en.wikipedia.org/wiki/Arrow_of_time-0.md | 30 + data/en.wikipedia.org/wiki/Arrow_of_time-1.md | 31 + data/en.wikipedia.org/wiki/Arrow_of_time-2.md | 27 + data/en.wikipedia.org/wiki/Arrow_of_time-3.md | 53 ++ .../wiki/Astronomical_year_numbering-0.md | 40 ++ data/en.wikipedia.org/wiki/Atom_(time)-0.md | 23 + .../wiki/B-theory_of_time-0.md | 23 + .../wiki/B-theory_of_time-1.md | 28 + .../en.wikipedia.org/wiki/Centered_world-0.md | 14 + 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zd10k@G&2L;_%+ofjrJNFRV}Nb>v3Kdv~JW9ayFbUhBe(mG^bp1S_qf9oM^@Q$pt!9 zrGyK$r1@m+y4}L6wZl(iO|&;$j`^<2S&$^B9g@Tjh8kPdIH8Y_m3G|Sl-G=vbkFr< zyg@-W=>sW(W0KuuI!$NLrqcOjTbhy*i8_@mEC69>#P|tTBCBHZxjO8(4e<<>B2r{P z?Mwn;XyoR>wj_6;JoV%Oq%SCyYFs$^bX|R(Y8G*9w8?CN@`%Z7y0NE#?Y1G+c)TUw zPlZI%lC`O7BA|(M`dTXA`;2PX^W%7`E>}!Y7qJZsFR=G?I?sLaqFSp~Hw}N!`~9U#UG_V*|K~5- z>i_>;{QtQr_;K&i*WVA2W%y@mV(*T2Zfbno_5Sy~wOHv(Q$OV=ulu=^H8tMJ|g>A9xmvZt!5X(T88OzgWKvOj$;l;e$4x^pyeUFhV`re z$hMt8233~NSAa^ogEVY#4Ly_M)4?gY!!-`Q&XL>z{!kwXrEhDah-x^tT)Vv+`7iWc z_Xxq4D{}9v!{yBu`e)C7#aN@YUJQU6fi>&HtNrBgo-CnIue(2#14QGPYO1df91g~o z7Oe1uB0=ourvl!z(*^7qn|KCnUGKL~4Wq!@-8zeO_rb%K9|#%MP6v(i1PCNESnC6c z!GWEZ%o<>==L4Y`;->v)RYTD1EAK~+etu653yJlb)lI{@a;}iD+I>rBmpiQVu@La= zIN(-3P0)jzvV~c*&B0h{-dL@reAf-TT)`l{#k{^oJgB?(%jKWE``TH;WuwEqhER5@AHq13)7 zgupqkzjFI%ApF`4g;3NJe&ZF&(P7koK@xN%*+{5%cY9^-fh>&rNm~Fa81XVK6Q+Y1&Fb>7y!F_j3Mfj zS5s4g;F8AHjecFogbS%mTP7Kfg|qz>k*{n&{gKxCX!RZ23}?^noPC%3Ec~B(A4(>b=u`Vs`Q`PwhYX?f7U`)^i%)sR)%4!Oq)1qF>A3Z|5BU44cEra1 zN%}@)EyxIpuO!QB2apU4SuY%qrM#rq?8Qp_gVdk$B9Uwu6vv!g?|R@C)4laB;k;u; zPdhTH)-luC_03I-RnX(>uV{{)=gJ>@do}g2&BVa~xnImxqW)aU3?TJN>M)izzTtnc zd%FT5ka<4k%?3z~RGrWL7?q8q@yOdGiz6MrPms^yiD9~UHqDm@8NB)X)yrF!&(+Nf zzbkLA=5y7Tw~vGt2$z{6@hK6; zO&~Sps;1O4>3@h@Caf5PFu%+3eJ_~II2cbtgDqivGW)e3c!NJVc>enyFF(-B$9nlh zFF(}Fr+WF%dil(IJb3mk=0TyJu{#r2oC{tDM$<@#$}KgRXf zxxUEt<6J+%^(C%%Drf)bbMNoOFP`PYi#0V9f4}ml{NeY47oV$q_{X1ngvh;D>HP1X zdpAoHmPCbW3FH0`gN{ B}}} + + +In other words, reactant A and product B are forming into one another based on reaction rate constants k and k'. +To solve for the concentration of A, recognize that the forward reaction ( + + + + + A + + + → + + + k + + + + + B + + + + {\displaystyle {\ce {A ->[{k}] B}}} + +) causes the concentration of A to decrease over time, whereas the reverse reaction ( + + + + + B + + + → + + + + k + ′ + + + + + + A + + + + {\displaystyle {\ce {B ->[{k'}] A}}} + +) causes the concentration of A to increase over time. +Therefore, + + + + + + + d + + + [ + A + ] + + + + + d + t + + + + = + − + k + + + [ + A + ] + + + + + + k + ′ + + + + [ + B + ] + + + + + {\displaystyle {d{\ce {[A]}} \over dt}=-k{\ce {[A]}}+k'{\ce {[B]}}} + +, where brackets around A and B indicate concentrations. +If we say that at + + + + t + = + 0 + , + + + [ + A + ] + + + ( + t + ) + = + + + + [ + A + ] + + + + 0 + + + + + {\displaystyle t=0,{\ce {[A]}}(t)={\ce {[A]}}_{0}} + +, and applying the law of conservation of mass, we can say that at any time, the sum of the concentrations of A and B must be equal to the concentration of + + + + + A + + 0 + + + + + {\displaystyle A_{0}} + +, assuming the volume into which A and B are dissolved does not change: + + + + + + + [ + A + ] + + + + + + + [ + B + ] + + + = + + + + [ + A + ] + + + + 0 + + + ⇒ + + + [ + B + ] + + + = + + + + [ + A + ] + + + + 0 + + + − + + + [ + A + ] + + + + + {\displaystyle {\ce {[A]}}+{\ce {[B]}}={\ce {[A]}}_{0}\Rightarrow {\ce {[B]}}={\ce {[A]}}_{0}-{\ce {[A]}}} + + +Substituting this value for [B] in terms of [A]0 and [A](t) yields + + + + + + + + d + + + [ + A + ] + + + + + d + t + + + + = + − + k + + + [ + A + ] + + + + + + k + ′ + + + + [ + B + ] + + + = + − + k + + + [ + A + ] + + + + + + k + ′ + + ( + + + + [ + A + ] + + + + 0 + + + − + + + [ + A + ] + + + ) + = + − + ( + k + + + + k + ′ + + ) + + + [ + A + ] + + + + + + k + ′ + + + + + [ + A + ] + + + + 0 + + + , + + + {\displaystyle {d{\ce {[A]}} \over dt}=-k{\ce {[A]}}+k'{\ce {[B]}}=-k{\ce {[A]}}+k'({\ce {[A]}}_{0}-{\ce {[A]}})=-(k+k'){\ce {[A]}}+k'{\ce {[A]}}_{0},} + + which becomes the separable differential equation + + + + + + + d + + + [ + A + ] + + + + + − + ( + k + + + + k + ′ + + ) + + + [ + A + ] + + + + + + k + ′ + + + + + [ + A + ] + + + + 0 + + + + + + = + d + t + + + {\displaystyle {\frac {d{\ce {[A]}}}{-(k+k'){\ce {[A]}}+k'{\ce {[A]}}_{0}}}=dt} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md b/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md new file mode 100644 index 000000000..8d6173431 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md @@ -0,0 +1,294 @@ +--- +title: "Relaxation (physics)" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Relaxation_(physics)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:24.533010+00:00" +instance: "kb-cron" +--- + +This equation can be solved by substitution to yield + + + + + + [ + A + ] + + + = + + + + + k + ′ + + − + k + + e + + − + ( + k + + + + k + ′ + + ) + t + + + + + k + + + + k + ′ + + + + + + + + [ + A + ] + + + + 0 + + + + + {\displaystyle {\ce {[A]}}={k'-ke^{-(k+k')t} \over k+k'}{\ce {[A]}}_{0}} + + +== In atmospheric sciences == + +=== Desaturation of clouds === +Consider a supersaturated portion of a cloud. Then shut off the updrafts, entrainment, and any other vapor sources/sinks and things that would induce the growth of the particles (ice or water). Then wait for this supersaturation to reduce and become just saturation (relative humidity = 100%), which is the equilibrium state. The time it takes for the supersaturation to dissipate is called relaxation time. It will happen as ice crystals or liquid water content grow within the cloud and will thus consume the contained moisture. The dynamics of relaxation are very important in cloud physics for accurate mathematical modelling. +In water clouds where the concentrations are larger (hundreds per cm3) and the temperatures are warmer (thus allowing for much lower supersaturation rates as compared to ice clouds), the relaxation times will be very low (seconds to minutes). +In ice clouds the concentrations are lower (just a few per liter) and the temperatures are colder (very high supersaturation rates) and so the relaxation times can be as long as several hours. Relaxation time is given as + + where: +D = diffusion coefficient [m2/s] +N = concentration (of ice crystals or water droplets) [m−3] +R = mean radius of particles [m] +K = capacitance [unitless]. + +== In astronomy == +In astronomy, relaxation time relates to clusters of gravitationally interacting bodies, for instance, stars in a galaxy. The relaxation time is a measure of the time it takes for one object in the system (the "test star") to be significantly perturbed by other objects in the system (the "field stars"). It is most commonly defined as the time for the test star's velocity to change by of order itself. +Suppose that the test star has velocity v. As the star moves along its orbit, its motion will be randomly perturbed by the gravitational field of nearby stars. The relaxation time can be shown to be + + + + + + + + + + T + + r + + + + + + = + + + + 0.34 + + σ + + 3 + + + + + + G + + 2 + + + m + ρ + ln + ⁡ + Λ + + + + + + + + + + ≈ + 0.95 + × + + 10 + + 10 + + + + + + ( + + + σ + + 200 + + + + k + m + + s + + + − + 1 + + + + + + ) + + + + 3 + + + + + + + ( + + + ρ + + + 10 + + 6 + + + + + M + + ⊙ + + + + + + p + c + + + − + 3 + + + + + + ) + + + + − + 1 + + + + + + + ( + + + m + + M + + ⊙ + + + + + ) + + + + − + 1 + + + + + + + ( + + + + ln + ⁡ + Λ + + 15 + + + ) + + + + − + 1 + + + + + y + r + + + + + + + + {\displaystyle {\begin{aligned}T_{r}&={0.34\sigma ^{3} \over G^{2}m\rho \ln \Lambda }\\&\approx 0.95\times 10^{10}\!\left({\sigma \over 200\,\mathrm {km\,s} ^{-1}}\right)^{\!3}\!\!\left({\rho \over 10^{6}\,M_{\odot }\,\mathrm {pc} ^{-3}}\right)^{\!-1}\!\!\left({m \over M_{\odot }}\right)^{\!-1}\!\!\left({\ln \Lambda \over 15}\right)^{\!-1}\!\mathrm {yr} \end{aligned}}} + + +where ρ is the mean density, m is the test-star mass, σ is the 1d velocity dispersion of the field stars, and ln Λ is the Coulomb logarithm. +Various events occur on timescales relating to the relaxation time, including core collapse, energy equipartition, and formation of a Bahcall-Wolf cusp around a supermassive black hole. + +== See also == +Relaxation oscillator +Time constant + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Rotation_period_(astronomy)-0.md b/data/en.wikipedia.org/wiki/Rotation_period_(astronomy)-0.md new file mode 100644 index 000000000..b3dd34232 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Rotation_period_(astronomy)-0.md @@ -0,0 +1,33 @@ +--- +title: "Rotation period (astronomy)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Rotation_period_(astronomy)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:25.739752+00:00" +instance: "kb-cron" +--- + +In astronomy, the rotation period or spin period of a celestial object (e.g., star, planet, moon, asteroid) has two definitions. The first one corresponds to the sidereal rotation period (or sidereal day), i.e., the time that the object takes to complete a full rotation around its axis relative to the background stars (inertial space). The other type of commonly used "rotation period" is the object's synodic rotation period (or solar day), which may differ, by a fraction of a rotation or more than one rotation, to accommodate the portion of the object's orbital period around a star or another body during one day. + + +== Measuring rotation == +For solid objects, such as rocky planets and asteroids, the rotation period is a single value. For gaseous or fluid bodies, such as stars and giant planets, the period of rotation varies from the object's equator to its pole due to a phenomenon called differential rotation. Typically, the stated rotation period for a giant planet (such as Jupiter, Saturn, Uranus, Neptune) is its internal rotation period, as determined from the rotation of the planet's magnetic field. For objects that are not spherically symmetrical, the rotation period is, in general, not fixed, even in the absence of gravitational or tidal forces. This is because, although the rotation axis is fixed in space (by the conservation of angular momentum), it is not necessarily fixed in the body of the object itself. As a result of this, the moment of inertia of the object around the rotation axis can vary, and hence the rate of rotation can vary (because the product of the moment of inertia and the rate of rotation is equal to the angular momentum, which is fixed). For example, Hyperion, a moon of Saturn, exhibits this behaviour, and its rotation period is described as chaotic. + + +== Rotation period of selected objects == + +Orbital velocity values are mean orbital speeds along each planet's orbit around the Sun. + + +== See also == + + +== Notes == + + +== References == + + +== External links == +Murray, Carl D. & Dermott, Stanley F. (1999). Solar System Dynamics. Cambridge University Press. p. 531. ISBN 0-521-57295-9.Note, the rotation periods for Mercury and Earth in this work may be inaccurate. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Saros_(astronomy)-0.md b/data/en.wikipedia.org/wiki/Saros_(astronomy)-0.md new file mode 100644 index 000000000..3196fe751 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Saros_(astronomy)-0.md @@ -0,0 +1,122 @@ +--- +title: "Saros (astronomy)" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Saros_(astronomy)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:27.065142+00:00" +instance: "kb-cron" +--- + +In astronomy, the saros ( ) is a length of time covering exactly 223 synodic months (18 years 11 days and 8 hours), 242 draconic months and 239 anomalistic months. Arising naturally due to synchronization between lunar phase, nodal precession, and apsidal precession, it can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. Every eclipse has an associated saros series and all succeeding or preceding eclipses have a different saros series associated with them - as the eclipse of the same series occurs or occurred with a gap of one saros only. Solar and lunar eclipses have different saros series. +A series of eclipses that are separated by one saros is called a saros series. It corresponds to: + +6,585.321347 solar days +18.029 years +223 synodic months +241.999 draconic months +18.999 eclipse years (38 eclipse seasons of 173.31 days) +238.992 anomalistic months +241.029 sidereal months +The 19 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one saros a new moon will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur. + +== History == +The earliest discovered historical record of what is known as the saros is by Chaldean (neo-Babylonian) astronomers in the last several centuries BCE. It was later known to Hipparchus, Pliny and Ptolemy. +The name "saros" (Greek: σάρος) was applied to the eclipse cycle by Edmond Halley in 1686, who took it from the Suda, a Byzantine lexicon of the 11th century. The Suda says, "[The saros is] a measure and a number among Chaldeans. For 120 saroi make 2220 years (years of 12 lunar months) according to the Chaldeans' reckoning, if indeed the saros makes 222 lunar months, which are 18 years and 6 months (i.e. years of 12 lunar months)." The information in the Suda in turn was derived directly or otherwise from the Chronicle of Eusebius of Caesarea, which quoted Berossus. (Guillaume Le Gentil claimed that Halley's usage was incorrect in 1756, but the name continues to be used.) The Greek word apparently either comes from the Babylonian word sāru meaning the number 3600 or the Greek verb saro (σαρῶ) that means "sweep (the sky with the series of eclipses)". + +The Saros period of 223 lunar months (in Greek numerals, ΣΚΓ′) is in the Antikythera Mechanism user manual on this instrument, made around 150–100 BCE in Greece, as seen in the picture. This number is one of a few inscriptions of the mechanism that are visible with the unaided eye. Above it, the period of the Metonic cycle and the Callippic cycle are also visible. + +== Description == + + + + + + + + + 1 + + saros + + + + + = + 6585.3211 + + days + + + + + + + + = + 15 + + common years + + + + 3 + + leap years + + + + 12.321 + + days + + + + + + + + = + 14 + + common years + + + + 4 + + leap years + + + + 11.321 + + days + + + + + + + + = + 13 + + common years + + + + 5 + + leap years + + + + 10.321 + + days + + + + + + + + {\displaystyle {\begin{aligned}1{\text{ saros}}&=6585.3211{\text{ days}}\\&=15{\text{ common years}}+3{\text{ leap years}}+12.321{\text{ days}}\\&=14{\text{ common years}}+4{\text{ leap years}}+11.321{\text{ days}}\\&=13{\text{ common years}}+5{\text{ leap years}}+10.321{\text{ days}}\end{aligned}}} + + +The saros, a period of 6585.3211 days, is useful for predicting the times at which nearly identical eclipses will occur. Three periodicities related to lunar orbit, the synodic month, the draconic month, and the anomalistic month coincide almost perfectly each saros cycle. For an eclipse to occur, either the Moon must be located between the Earth and Sun (for a solar eclipse) or the Earth must be located between the Sun and Moon (for a lunar eclipse). This can happen only when the Moon is new or full, respectively, and repeat occurrences of these lunar phases result from solar and lunar orbits producing the Moon's synodic period of 29.53059 days. During most full and new moons, however, the shadow of the Earth or Moon falls to the north or south of the other body. Eclipses occur when the three bodies form a nearly straight line. Because the plane of the lunar orbit is inclined to that of the Earth, this condition occurs only when a full or new Moon is near or in the ecliptic plane, that is when the Moon is at one of the two nodes (the ascending or descending node). The period of time for two successive lunar passes through the ecliptic plane (returning to the same node) is termed the draconic month, a 27.21222 day period. The three-dimensional geometry of an eclipse, when the new or full moon is near one of the nodes, occurs every five or six months when the Sun is in conjunction or opposition to the Moon and coincidentally also near a node of the Moon's orbit at that time, or twice per eclipse year. Two eclipses separated by one saros have very similar appearance and duration due to the distance between the Earth and Moon being nearly the same for each event: this is because the saros is also an integer multiple of the anomalistic month of 27.5545 days, the period of the moon with respect to the lines of apsides in its orbit. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Saros_(astronomy)-1.md b/data/en.wikipedia.org/wiki/Saros_(astronomy)-1.md new file mode 100644 index 000000000..9fae4d0a4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Saros_(astronomy)-1.md @@ -0,0 +1,19 @@ +--- +title: "Saros (astronomy)" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Saros_(astronomy)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:27.065142+00:00" +instance: "kb-cron" +--- + +After one saros, the Moon will have completed roughly an integer number of synodic, draconic, and anomalistic periods (223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase and be at the same node and the same distance from the Earth. In addition, because the saros is close to 18 years in length (about 11 days longer), the Earth will be nearly the same distance from the Sun, and tilted to it in nearly the same orientation (same season). Given the date of an eclipse, one saros later a nearly identical eclipse can be predicted. During this 18-year period, about 40 other solar and lunar eclipses take place, but with a somewhat different geometry. One saros equaling 18.03 years is not equal to a perfect integer number of lunar orbits (Earth revolutions with respect to the fixed stars of 27.32166 days sidereal month), therefore, even though the relative geometry of the Earth–Sun–Moon system will be nearly identical after a saros, the Moon will be in a slightly different position with respect to the stars for each eclipse in a saros series. The axis of rotation of the Earth–Moon system exhibits a precession period of 18.59992 years. +The saros is not an integer number of days, but contains the fraction of +1⁄3 of a day. Thus each successive eclipse in a saros series occurs about eight hours later in the day. In the case of an eclipse of the Sun, this means that the region of visibility will shift westward about 120°, or about one third of the way around the globe, and the two eclipses will thus not be visible from the same place on Earth. In the case of an eclipse of the Moon, the next eclipse might still be visible from the same location as long as the Moon is above the horizon. Given three saros eclipse intervals, the local time of day of an eclipse will be nearly the same. This three saros interval (19,755.96 days) is known as a triple saros or exeligmos (Greek: "turn of the wheel") cycle. + +== Saros series == + +Each solar saros series starts with a partial eclipse (Sun first enters the end of the node, when new Moon occurs east of a node) - which means the first eclipse of the saros series occurs within about 15° to 18° of the node before Earth reaches the node and the moon's elongation is also within the gamma range for an eclipse to occur. In each successive saros, the path of the Moon is shifted either northward (when near the descending node) or southward (when near the ascending node) due to the fact that the saros is not an exact integer of draconic months (223 synodic months of a saros is about one hour short of 242 draconic months - hence, the Moon's node shifts eastward by about 0.5º with each cycle). At some point, eclipses are no longer possible and the series terminates (Sun leaves the beginning of the node). An arbitrary solar saros series was designated as solar saros series 1 by compilers of eclipse statistics. This series has finished, but the eclipse of November 16, 1990 BC (Julian calendar) for example is in solar saros series 1. There are different saros series for solar and lunar eclipses. For lunar saros series, the lunar eclipse occurring 58.5 synodic months earlier (February 23, 1994 BC) was assigned the number 1. If there is an eclipse one inex (29 years minus about 20 days) after an eclipse of a particular saros series then it is a member of the next series. For example, the eclipse of October 26, 1961 BC is in solar saros series 2. Saros series, of course, went on before these dates, and it is necessary to extend the saros series numbers backwards to negative numbers even just to accommodate eclipses occurring in the years following 2000 BC (up till the last eclipse with a negative saros number in 1367 BC). It takes between 1226 and 1550 years for the members of a saros series to traverse the Earth's surface from north to south (or vice versa). These extremes allow from 69 to 87 eclipses in each series (most series have 71 or 72 eclipses). From 39 to 59 (mostly about 43) eclipses in a given series will be central (that is, total, annular, or hybrid). At any given time, approximately 40 different saros series will be in progress. +Saros series, as mentioned, are numbered according to the type of eclipse (lunar or solar). In odd numbered series (for solar eclipses) the Sun is near the ascending node, whereas in even numbered series it is near the descending node (this is reversed for lunar eclipse saros series). Generally, the ordering of these series determines the time at which each series peaks, which corresponds to when an eclipse is closest to one of the lunar nodes. For solar eclipses, the 40 series numbered between 117 and 156 are active (series 117 will end in 2054), whereas for lunar eclipses, there are now 41 active saros series numbered between 110 and 150 (series 110 will end in 2027). These numbers can be derived by counting the number of eclipses listed over an 18-year (saros) period from the eclipse catalog sites. + +=== Example === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Saros_(astronomy)-2.md b/data/en.wikipedia.org/wiki/Saros_(astronomy)-2.md new file mode 100644 index 000000000..0e849c238 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Saros_(astronomy)-2.md @@ -0,0 +1,44 @@ +--- +title: "Saros (astronomy)" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Saros_(astronomy)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:27.065142+00:00" +instance: "kb-cron" +--- + +As an example of a single saros series, this table gives the dates of some of the 72 lunar eclipses for saros series 131. This eclipse series began in AD 1427 with a partial eclipse at the southern edge of the Earth's shadow when the Moon was close to its descending node. In each successive saros, the Moon's orbital path is shifted northward with respect to the Earth's shadow, with the first total eclipse occurring in 1950. For the following 252 years, total eclipses occur, with the central eclipse in 2078. The first partial eclipse after this will occur in the year 2220, and the final partial eclipse of the series will occur in 2707. The total lifetime of lunar saros series 131 is 1280 years. Solar saros 138 interleaves with this lunar saros with an event occurring every 9 years 5 days alternating between each saros series. +Because of the +1⁄3 fraction of days in a saros, the visibility of each eclipse will differ for an observer at a given locale. For the lunar saros series 131, the first total eclipse of 1950 had its best visibility for viewers in Eastern Europe and the Middle East because mid-eclipse was at 20:44 UT. The following eclipse in the series occurred about 8 hours later in the day with mid-eclipse at 4:47 UT, and was best seen from North America and South America. The third total eclipse occurred about 8 hours later in the day than the second eclipse with mid-eclipse at 12:43 UT, and had its best visibility for viewers in the Western Pacific, East Asia, Australia and New Zealand. This cycle of visibility repeats from the start to the end of the series, with minor variations. Solar saros 138 interleaves with this lunar saros with an event occurring every 9 years 5 days alternating between each saros series. +For a similar example for solar saros see solar saros 136. + +== Relationship between lunar and solar saros (sar) == +After a given lunar or solar eclipse, after 9 years and 5+1⁄2 days (a half saros, or sar) an eclipse will occur that is lunar instead of solar, or vice versa, with similar properties. +For example, if the Moon's penumbra partially covers the southern limb of the Earth during a solar eclipse, 9 years and 5+1⁄2 days later a lunar eclipse will occur in which the Moon is partially covered by the southern limb of the Earth's penumbra. Likewise, 9 years and 5+1⁄2 days after a total solar eclipse or an annular solar eclipse occurs, a total lunar eclipse will also occur. This 9-year period is referred to as a sar. It includes 111+1⁄2 synodic months, or 111 synodic months plus one fortnight. The fortnight accounts for the alternation between solar and lunar eclipse. For a visual example see this chart (each row is one sar apart). + +== See also == +List of saros series for solar eclipses +List of saros series for lunar eclipses +Eclipse cycle +Exeligmos +Inex +Solar eclipse +Lunar eclipse +Metonic cycle + +== Notes == + +== References == + +== Bibliography == +Jean Meeus and Hermann Mucke (1983) Canon of Lunar Eclipses. Astronomisches Büro, Vienna +Theodor von Oppolzer (1887). Canon der Finsternisse. Vienna +Jean Meeus, Mathematical Astronomy Morsels, Willmann-Bell, Inc., 1997 (Chapter 9, p. 51, Table 9. A Some eclipse Periodicities) + +== External links == + +List of all active saros cycles +NASA – Eclipses and the Saros +Solar and Lunar Eclipses – Xabier Jubier – Interactive eclipse search +Eclipse Search – Search 5,000 years of eclipse data by various attributes +Eclipses, Cosmic Clockwork of the Ancients – Fundamental astronomy of eclipses \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sidereal_time-0.md b/data/en.wikipedia.org/wiki/Sidereal_time-0.md new file mode 100644 index 000000000..8ea70167d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sidereal_time-0.md @@ -0,0 +1,22 @@ +--- +title: "Sidereal time" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Sidereal_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:28.221801+00:00" +instance: "kb-cron" +--- + +Sidereal time ("sidereal" pronounced sy-DEER-ee-əl, sə-) is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars". A sidereal day (also known as the sidereal rotation period) represents the time for one rotation about the planet axis relative to the stars. +Viewed from the same location, a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day. This is similar to how the time kept by a sundial (Solar time) can be used to find the location of the Sun. Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time is reckoned according to the position of the Sun in the sky while sidereal time is based approximately on the position of the fixed stars on the theoretical celestial sphere. +More exactly, sidereal time is the angle, measured along the celestial equator, from the observer's meridian to the great circle that passes through the March equinox (the northern hemisphere's vernal equinox) and both celestial poles, and is usually expressed in hours, minutes, and seconds. In the context of sidereal time, "March equinox" or "equinox" or "first point of Aries" is currently the direction from the center of the Earth along the line formed by the intersection of the Earth's equator and the ecliptic, toward the constellation Pisces; during ancient times it was toward the constellation Aries. Common time on a typical clock (using mean Solar time) measures a slightly longer cycle, affected not only by Earth's axial rotation but also by Earth's orbit around the Sun. +The March equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 25,800 years, so the misnamed "sidereal" day ("sidereal" is derived from the Latin sidus meaning "star") is 0.0084 seconds shorter than the stellar day, Earth's actual period of rotation relative to the fixed stars. The slightly longer stellar period is measured as the Earth rotation angle (ERA), formerly the stellar angle. An increase of 360° in the ERA is a full rotation of the Earth. +A sidereal day on Earth is approximately 86164.0905 seconds (23 h 56 min 4.0905 s or 23.9344696 h). (Seconds are defined as per International System of Units and are not to be confused with ephemeris seconds.) Each day, the sidereal time at any given place and time will be about four minutes shorter than local civil time (which is based on solar time), so that for a complete year the number of sidereal "days" is one more than the number of solar days. + +== Comparison to solar time == + +Solar time is measured by the apparent diurnal motion of the Sun. Local noon in apparent solar time is the moment when the Sun is exactly due south or north (depending on the observer's latitude and the season). A mean solar day (what we normally measure as a "day") is the average time between local solar noons ("average" since this varies slightly over a year). +Earth makes one rotation around its axis each sidereal day; during that time it moves a short distance (about 1°) along its orbit around the Sun. So after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day. +The stars are so far away that Earth's movement along its orbit makes nearly no difference to their apparent direction (except for the nearest stars if measured with extreme accuracy; see parallax), and so they return to their highest point at the same time each sidereal day. +Another way to understand this difference is to notice that, relative to the stars, as viewed from Earth, the position of the Sun at the same time each day appears to move around Earth once per year. A year has about 365.24 solar days but 366.24 sidereal days. Therefore, there is one fewer solar day per year than there are sidereal days, similar to an observation of the coin rotation paradox. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sidereal_time-1.md b/data/en.wikipedia.org/wiki/Sidereal_time-1.md new file mode 100644 index 000000000..096c16955 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sidereal_time-1.md @@ -0,0 +1,176 @@ +--- +title: "Sidereal time" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Sidereal_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:28.221801+00:00" +instance: "kb-cron" +--- + +== Effects of precession == +Earth's rotation is not a simple rotation around an axis that remains always parallel to itself. Earth's rotational axis itself rotates about a second axis, orthogonal to the plane of Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is termed the precession of the equinoxes. Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation. +For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it was conventional to chart the positions of the stars in the sky according to right ascension and declination, which are based on a frame of reference that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well. (The conventional reference frame, for purposes of star catalogues, was replaced in 1998 with the International Celestial Reference Frame, which is fixed with respect to extra-galactic radio sources. Because of the great distances, these sources have no appreciable proper motion.) In this frame of reference, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this frame of reference that the tropical year (or solar year), the year related to Earth's seasons, represents one orbit of Earth around the Sun. The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing frame of reference. + +== Modern definitions == +During the past, time was measured by observing stars with instruments such as photographic zenith tubes and Danjon astrolabes, and the passage of stars across defined lines would be timed with the observatory clock. Then, using the right ascension of the stars from a star catalog, the time when the star should have passed through the meridian of the observatory was computed, and a correction to the time kept by the observatory clock was computed. Sidereal time was defined such that the March equinox would transit the meridian of the observatory at 0 hours local sidereal time. +Beginning during the 1970s, the radio astronomy methods very-long-baseline interferometry (VLBI) and pulsar timing overtook optical instruments for the most precise astrometry. This resulted in the determination of UT1 (mean solar time at 0° longitude) using VLBI, a new measure of the Earth Rotation Angle, and new definitions of sidereal time. These changes became effective 1 January 2003. + +=== Earth rotation angle === +The Earth rotation angle (ERA) measures the rotation of the Earth from an origin on the celestial equator, the Celestial Intermediate Origin, also termed the Celestial Ephemeris Origin, that has no instantaneous motion along the equator; it was originally referred to as the non-rotating origin. This point is very close to the equinox of J2000. +ERA, measured in radians, is related to UT1 by a simple linear relation: + + + + θ + ( + + t + + U + + + ) + = + 2 + π + ( + 0.779 + + 057 + + 273 + + 2640 + + + 1.002 + + 737 + + 811 + + 911 + + 354 + + 48 + ⋅ + + t + + U + + + ) + + + {\displaystyle \theta (t_{U})=2\pi (0.779\,057\,273\,2640+1.002\,737\,811\,911\,354\,48\cdot t_{U})} + +where tU is the Julian UT1 date (JD) minus 2451545.0. +The linear coefficient represents the Earth's rotation speed around its own axis. +ERA replaces Greenwich Apparent Sidereal Time (GAST). The origin on the celestial equator for GAST, termed the true equinox, does move, due to the movement of the equator and the ecliptic. The lack of motion of the origin of ERA is considered a significant advantage. +The ERA may be converted to other units; for example, the Astronomical Almanac for the Year 2017 tabulated it in degrees, minutes, and seconds. +As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″. Since Coordinated Universal Time (UTC) is within a second or two of UT1, this can be used as an anchor to give the ERA approximately for a given civil time and date. + +=== Mean and apparent varieties === + +Although ERA is intended to replace sidereal time, there is a need to maintain definitions for sidereal time during the transition, and when working with older data and documents. +Similarly to mean solar time, every location on Earth has its own local sidereal time (LST), depending on the longitude of the point. Since it is not feasible to publish tables for every longitude, astronomical tables use Greenwich sidereal time (GST), which is sidereal time on the IERS Reference Meridian, less precisely termed the Greenwich, or Prime meridian. There are two varieties, mean sidereal time if the mean equator and equinox of date are used, and apparent sidereal time if the apparent equator and equinox of date are used. The former ignores the effect of astronomical nutation while the latter includes it. When the choice of location is combined with the choice of including astronomical nutation or not, the acronyms GMST, LMST, GAST, and LAST result. +The following relationships are true: + +The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are: + + + + + + G + M + S + T + + ( + + t + + U + + + , + t + ) + = + θ + ( + + t + + U + + + ) + − + + E + + + P + R + E + C + + + + ( + t + ) + + + {\displaystyle \mathrm {GMST} (t_{U},t)=\theta (t_{U})-E_{\mathrm {PREC} }(t)} + + + + + + + G + A + S + T + + ( + + t + + U + + + , + t + ) + = + θ + ( + + t + + U + + + ) + − + + E + + 0 + + + ( + t + ) + + + {\displaystyle \mathrm {GAST} (t_{U},t)=\theta (t_{U})-E_{0}(t)} + +such that θ is the Earth Rotation Angle, EPREC is the accumulated precession, and E0 is equation of the origins, which represents accumulated precession and nutation. The calculation of precession and nutation was described in Chapter 6 of Urban & Seidelmann. +As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″ (6 h 42 m 28.8291 s). The GAST was 6 h 43 m 20.7109 s. For GMST the hour and minute were the same but the second was 21.1060. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sidereal_time-2.md b/data/en.wikipedia.org/wiki/Sidereal_time-2.md new file mode 100644 index 000000000..1db1ba9ff --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sidereal_time-2.md @@ -0,0 +1,133 @@ +--- +title: "Sidereal time" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Sidereal_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:28.221801+00:00" +instance: "kb-cron" +--- + +=== Relationship between solar time and sidereal time intervals === + +If a certain interval I is measured in both mean solar time (UT1) and sidereal time, the numerical value will be greater in sidereal time than in UT1, because sidereal days are shorter than UT1 days. The ratio is: + + + + + + + I + + + m + e + a + n + + s + i + d + e + r + e + a + l + + + + + I + + + U + T + 1 + + + + + + = + + r + ′ + + = + 1.002 + + 737 + + 379 + + 093 + + 507 + + 95 + + + 5.9006 + × + + 10 + + − + 11 + + + t + − + 5.9 + × + + 10 + + − + 15 + + + + t + + 2 + + + + + {\displaystyle {\frac {I_{\mathrm {mean\,sidereal} }}{I_{\mathrm {UT1} }}}=r'=1.002\,737\,379\,093\,507\,95+5.9006\times 10^{-11}t-5.9\times 10^{-15}t^{2}} + +such that t represents the number of Julian centuries elapsed since noon 1 January 2000 Terrestrial Time. + +== Sidereal days compared to solar days on other planets == +Six of the eight solar planets have prograde rotation—that is, they rotate more than once per year in the same direction as they orbit the Sun, so the Sun rises in the east. Venus and Uranus, however, have retrograde rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is: + +or, equivalently: + +When calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign (put another way, in the original formula the length of the sidereal day must be treated as negative). This is due to the solar day being shorter than the sidereal day for retrograde rotation, as the rotation of the planet would be against the direction of orbital motion. +If a planet rotates prograde, and the sidereal day exactly equals the orbital period, then the formula above gives an infinitely long solar day (division by zero). This is the case for a planet in synchronous rotation; in the case of zero eccentricity, one hemisphere experiences eternal day, the other eternal night, with a "twilight belt" separating them. +All the solar planets more distant from the Sun than Earth are similar to Earth in that, since they experience many rotations per revolution around the Sun, there is only a small difference between the length of the sidereal day and that of the solar day – the ratio of the former to the latter never being less than Earth's ratio of 0.997. But the situation is quite different for Mercury and Venus. Mercury's sidereal day is about two-thirds of its orbital period, so by the prograde formula its solar day lasts for two revolutions around the Sun – three times as long as its sidereal day. Venus rotates retrograde with a sidereal day lasting about 243.0 Earth days, or about 1.08 times its orbital period of 224.7 Earth days; hence by the retrograde formula its solar day is about 116.8 Earth days, and it has about 1.9 solar days per orbital period. +By convention, rotation periods of planets are given in sidereal terms unless otherwise specified. + +== See also == +Anti-sidereal time +Earth's rotation +International Celestial Reference Frame +Nocturnal (instrument) +Sidereal month +Sidereal year +Synodic day +Transit instrument + +== Citations == + +== References == +Astronomical Almanac for the Year 2017. Washington and Taunton: US Government Printing Office and The UK Hydrographic Office. 2016. ISBN 978-0-7077-41666. +Bakich, Michael E. (2000). The Cambridge Planetary Handbook. Cambridge University Press. ISBN 0-521-63280-3. +"Earth Rotation Angle". International Earth Rotation and Reference System Service. 2013. Retrieved 20 March 2018. +Explanatory Supplement to the Ephemeris. London, England: Her Majesty's Stationery Office. 1961. +"Time and Frequency from A to Z, S to So". National Institute of Standards and Technology. 12 May 2010. +Urban, Sean E.; Seidelmann, P. Kenneth, eds. (2013). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, California: University Science Books. ISBN 978-1-891389-85-6. + +== External links == + +Web-based Sidereal time calculator \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solar_time-0.md b/data/en.wikipedia.org/wiki/Solar_time-0.md new file mode 100644 index 000000000..b3ed63fcf --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solar_time-0.md @@ -0,0 +1,34 @@ +--- +title: "Solar time" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Solar_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:29.423240+00:00" +instance: "kb-cron" +--- + +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. Traditionally, there are three types of time reckoning based on astronomical observations: apparent solar time and mean solar time (discussed in this article), and sidereal time, which is based on the apparent motions of stars other than the Sun. + +== 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 called 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 Earth–Sun 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 rate – e.g. completing the same number of pendulum swings in each hour – cannot 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. As of 2008, a mean solar day is about 86,400.002 SI seconds, i.e., about 24.0000006 hours. + +== 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. Apparent solar time can be crudely measured by a sundial. +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 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 motion). Second, due to Earth's axial tilt (known as the obliquity of the ecliptic), the Sun's annual motion is along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, 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 for the year; when the Sun is farthest from the equator at both solstices, 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). 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 position of the 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. As of 2009, this is realized with the UT1 time scale, constructed mathematically from very-long-baseline interferometry observations of the diurnal motions 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: + +Consider a first fictitious Sun travelling along the ecliptic with a constant speed and coinciding with the true sun at the perigee and apogee (when the Earth is in perihelion and aphelion, respectively). Then consider a second fictitious Sun travelling along the celestial equator at a constant speed and coinciding with the first fictitious Sun at the equinoxes. This second fictitious sun is the mean Sun. +The length of the mean solar day is slowly increasing due to the tidal acceleration of the Moon by Earth and the corresponding slowing of Earth's rotation by the Moon. + +== History == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solar_time-1.md b/data/en.wikipedia.org/wiki/Solar_time-1.md new file mode 100644 index 000000000..773593b39 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solar_time-1.md @@ -0,0 +1,28 @@ +--- +title: "Solar time" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Solar_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:29.423240+00:00" +instance: "kb-cron" +--- + +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 constructed c. 3500 BC, a gnomon in China dated 2300 BC, and an Egyptian sundial dated 1500 BC are some of the earliest methods for measuring the sun's position. +Babylonian 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 clearly distinguishes the mean solar day and apparent solar day in his Almagest (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 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 (UTC) determines whether a leap second 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.) + +== See also == +Local mean time +Meridian circle +Earth rotation +Synodic day + +== Notes == + +== References == + +== External links == +Sunrise and Sunset and maximum Sun altitude, all year long, anywhere +Astrarium Solar Tempometer: Apparent solar time in a digital display. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solstice-0.md b/data/en.wikipedia.org/wiki/Solstice-0.md new file mode 100644 index 000000000..2db007184 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solstice-0.md @@ -0,0 +1,32 @@ +--- +title: "Solstice" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/Solstice" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:30.644057+00:00" +instance: "kb-cron" +--- + +A solstice is the time when the Sun reaches its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around 20–22 June and 20–22 December. In many countries, the seasons of the year are defined by reference to the solstices and the equinoxes. +The term solstice can also be used in a broader sense, as the day when this occurs. For locations not too close to the equator or the poles, the dates with the longest and shortest periods of daylight are the summer and winter solstices, respectively. Terms with no ambiguity as to which hemisphere is the context are "June solstice" and "December solstice", referring to the months in which they take place every year. + +== Etymology == +The word solstice is derived from the Latin sol ('sun') and sistere ('to stand still'), because at the solstices, the Sun's declination appears to "stand still"; that is, the seasonal movement of the Sun's daily path (as seen from Earth) reaches a northern or southern limit before reversing direction. +Solstice first entered into English in the Middle English period. An older term in English is its calque sunstead (Old English: sunstede), which became rare after the 17th century. Sunstead is cognate with other terms with the same meaning in other Germanic language such as Old Norse: sólstaðr and Middle High German: sunnenstat. A similar English calque of the Latin term is sunstay which was first used in the 16th century and is now also rare. + +== Definitions and frames of reference == + +For an observer at the North Pole, the Sun reaches the highest position in the sky once a year in June. The day this occurs is called the June solstice day. Similarly, for an observer on the South Pole, the Sun reaches the highest position on the December solstice day. When it is the summer solstice at one Pole, it is the winter solstice on the other. The Sun's westerly motion never ceases as Earth is continually in rotation. However, at the moment of solstice the Sun's motion in declination (i.e. vertically) appears to stop for an instant, and then reverse. In that sense, solstice means "sun-standing". +This modern scientific word descends from a Latin scientific word in use in the late Roman Republic of the 1st century BC: solstitium. Pliny uses it a number of times in his Natural History with a similar meaning that it has today. It contains two Latin-language morphemes, sol, "sun", and -stitium, "stoppage". The Romans used "standing" to refer to a component of the relative velocity of the Sun as it is observed in the sky. Relative velocity is the motion of an object from the point of view of an observer in a frame of reference. From a fixed position on the ground, the Sun appears to orbit around Earth. +To an observer in an inertial frame of reference, planet Earth is seen to rotate about an axis and orbit around the Sun in an elliptical path with the Sun at one focus. Earth's axis is tilted with respect to the plane of Earth's orbit and this axis maintains a position that changes little with respect to the background of stars. An observer on Earth therefore sees a solar path that is the result of both rotation and revolution. + +The component of the Sun's motion seen by an earthbound observer caused by the revolution of the tilted axis—which, keeping the same angle in space, is oriented toward or away from the Sun—is an observed daily increment (and lateral offset) of the elevation of the Sun at noon for approximately six months and observed daily decrement for the remaining six months. At maximum or minimum elevation, the relative yearly motion of the Sun perpendicular to the horizon stops and reverses direction. +Outside of the tropics, the maximum elevation occurs at the summer solstice and the minimum at the winter solstice. The path of the Sun, or ecliptic, sweeps north and south between the northern and southern hemispheres. The lengths of time when the sun is up are longer around the summer solstice and shorter around the winter solstice, except near the equator. When the Sun's path crosses the equator, the length of the nights at latitudes +L° and −L° are of equal length. This is known as an equinox. There are two solstices and two equinoxes in a tropical year. + +Because of the variation in the rate at which the sun's right ascension changes, the days of longest and shortest daylight do not coincide with the solstices for locations very close to the equator. At the equator, the longest day is around 23 December and the shortest around 16 September (see graph). Inside the Arctic or Antarctic Circles the sun is up all the time for days or even months. + +== Relationship to seasons == + +The seasons occur because the Earth's axis of rotation is not perpendicular to its orbital plane (the plane of the ecliptic) but currently makes an angle of about 23.44° (called the obliquity of the ecliptic), and because the axis keeps its orientation with respect to an inertial frame of reference. As a consequence, for half the year the Northern Hemisphere is inclined toward the Sun while for the other half year the Southern Hemisphere has this distinction. The two moments when the inclination of Earth's rotational axis has maximum effect are the solstices. +At the June solstice the subsolar point is further north than any other time: at latitude 23.44° north, known as the Tropic of Cancer. Similarly at the December solstice the subsolar point is further south than any other time: at latitude 23.44° south, known as the Tropic of Capricorn. The subsolar point will cross every latitude between these two extremes exactly twice per year. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solstice-1.md b/data/en.wikipedia.org/wiki/Solstice-1.md new file mode 100644 index 000000000..43eb059a4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solstice-1.md @@ -0,0 +1,38 @@ +--- +title: "Solstice" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/Solstice" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:30.644057+00:00" +instance: "kb-cron" +--- + +Also during the June solstice, places on the Arctic Circle (latitude 66.56° north) will see the Sun just on the horizon during midnight, and all places north of it will see the Sun above horizon for 24 hours. That is the midnight sun or midsummer-night sun or polar day. On the other hand, places on the Antarctic Circle (latitude 66.56° south) will see the Sun just on the horizon during midday, and all places south of it will not see the Sun above horizon at any time of the day. That is the polar night. During the December Solstice, the effects on both hemispheres are just the opposite. This sees polar sea ice re-grow annually due to lack of sunlight on the air above and surrounding sea. The warmest and coldest periods of the year in temperate regions are offset by about one month from the solstices, delayed by the earth's thermal inertia. + +== Cultural aspects == + +=== Ancient Greek names and concepts === +The concept of the solstices was embedded in ancient Greek celestial navigation. As soon as they discovered that the Earth was spherical they devised the concept of the celestial sphere, an imaginary spherical surface rotating with the heavenly bodies (ouranioi) fixed in it (the modern one does not rotate, but the stars in it do). As long as no assumptions are made concerning the distances of those bodies from Earth or from each other, the sphere can be accepted as real and is in fact still in use. The Ancient Greeks use the term "ηλιοστάσιο" (heliostāsio), meaning stand of the Sun. +The stars move across the inner surface of the celestial sphere along the circumferences of circles in parallel planes perpendicular to the Earth's axis extended indefinitely into the heavens and intersecting the celestial sphere in a celestial pole. The Sun and the planets do not move in these parallel paths but along another circle, the ecliptic, whose plane is at an angle, the obliquity of the ecliptic, to the axis, bringing the Sun and planets across the paths of and in among the stars.* +Cleomedes states: + +The band of the Zodiac (zōdiakos kuklos, "zodiacal circle") is at an oblique angle (loksos) because it is positioned between the tropical circles and equinoctial circle touching each of the tropical circles at one point ... This Zodiac has a determinable width (set at 8° today) ... that is why it is described by three circles: the central one is called "heliacal" (hēliakos, "of the sun"). +The term heliacal circle is used for the ecliptic, which is in the center of the zodiacal circle, conceived as a band including the noted constellations named on mythical themes. Other authors use Zodiac to mean ecliptic, which first appears in a gloss of unknown author in a passage of Cleomedes where he is explaining that the Moon is in the zodiacal circle as well and periodically crosses the path of the Sun. As some of these crossings represent eclipses of the Moon, the path of the Sun is given a synonym, the ekleiptikos (kuklos) from ekleipsis, "eclipse". + +=== English names === + +The two solstices can be distinguished by different pairs of names, depending on which feature one wants to stress. + +Summer solstice and winter solstice are the most common names, referring to the seasons they are associated with. However, these can be ambiguous since the Northern Hemisphere's summer is the Southern Hemisphere's winter, and vice versa. The Latinate names estival solstice (summer) and hibernal solstice (winter) are sometimes used to the same effect, as are midsummer and midwinter. +June solstice and December solstice refer to the months of year in which they take place, with no ambiguity as to which hemisphere is the context. They are still not universal, however, as not all cultures use a solar-based calendar where the solstices occur every year in the same month (as they do not in the Islamic calendar and Hebrew calendar, for example). +Northern solstice and southern solstice indicate the hemisphere of the Sun's location. The northern solstice is in June, when the Sun is directly over the Tropic of Cancer in the Northern Hemisphere, and the southern solstice is in December, when the Sun is directly over the Tropic of Capricorn in the Southern Hemisphere. These terms can be used unambiguously for other planets. +First point of Cancer and first point of Capricorn refer to the astrological signs that the sun "is entering" (a system rooted in Roman Classical period dates). Due to the precession of the equinoxes, the constellations the sun appears in at solstices are currently Taurus in June and Sagittarius in December. + +=== Solstice terms in East Asia === + +The traditional East Asian calendars divide a year into 24 solar terms (節氣). Xiàzhì (pīnyīn) or Geshi (rōmaji) (Chinese and Japanese: 夏至; Korean: 하지(Haji); Vietnamese: Hạ chí; lit. summer's extreme) is the 10th solar term, and marks the summer solstice. It begins when the Sun reaches the celestial longitude of 90° (around 21 June) and ends when the Sun reaches the longitude of 105° (around 7 July). Xiàzhì more often refers in particular to the day when the Sun is exactly at the celestial longitude of 90°. +Dōngzhì (pīnyīn) or Tōji (rōmaji) (Chinese and Japanese: 冬至; Korean: 동지(Dongji); Vietnamese: Đông chí; lit. winter's extreme) is the 22nd solar term, and marks the winter solstice. It begins when the Sun reaches the celestial longitude of 270° (around 23 December) and ends when the Sun reaches the longitude of 285° (around 5 January). Dōngzhì more often refers in particular to the day when the Sun is exactly at the celestial longitude of 270°. +The solstices (as well as the equinoxes) mark the middle of the seasons in East Asian calendars. Here, the Chinese character 至 means "extreme", so the terms for the solstices directly signify the summits of summer and winter. + +=== Solstice celebrations === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solstice-2.md b/data/en.wikipedia.org/wiki/Solstice-2.md new file mode 100644 index 000000000..35e51bfdf --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solstice-2.md @@ -0,0 +1,17 @@ +--- +title: "Solstice" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/Solstice" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:30.644057+00:00" +instance: "kb-cron" +--- + +The term solstice can also be used in a wider sense, as the date (day) that such a passage happens. The solstices, together with the equinoxes, are connected with the seasons. In some languages they are considered to start or separate the seasons; in others they are considered to be centre points (in England, in the Northern Hemisphere, for example, the period around the northern solstice is known as midsummer). Midsummer's Day, defined as St. Johns Day by the Christian Church, is 24 June, about three days after the solstice itself). Similarly 25 December is the start of the Christmas celebration, and is the day the Sun begins to return to the Northern Hemisphere. The traditional British and Irish main rent and meeting days of the year, "the usual quarter days," were often those of the solstices and equinoxes. +Many cultures celebrate various combinations of the winter and summer solstices, the equinoxes, and the midpoints between them, leading to various holidays arising around these events. During the southern or winter solstice, Christmas is the most widespread contemporary holiday, while Yalda, Saturnalia, Karachun, Hanukkah, Kwanzaa, and Yule are also celebrated around this time. In East Asian cultures, the Dongzhi Festival is celebrated on the winter solstice. For the northern or summer solstice, Christian cultures celebrate the feast of St. John from June 23 to 24 (see St. John's Eve, Ivan Kupala Day), while Modern Pagans observe Midsummer, known as Litha among Wiccans. For the vernal (spring) equinox, several springtime festivals are celebrated, such as the Persian Nowruz, the observance in Judaism of Passover, the rites of Easter in most Christian churches, as well as the Wiccan Ostara. The autumnal equinox is associated with the Jewish holiday of Sukkot and the Wiccan Mabon. +In the southern tip of South America, the Mapuche people celebrate We Tripantu (the New Year) a few days after the northern solstice, on 24 June. Further north, the Atacama people formerly celebrated this date with a noise festival, to call the Sun back. Further east, the Aymara people celebrate their New Year on 21 June. A celebration occurs at sunrise, when the sun shines directly through the Gate of the Sun in Tiwanaku. Other Aymara New Year feasts occur throughout Bolivia, including at the site of El Fuerte de Samaipata. +In the Hindu calendar, two sidereal solstices are named Makara Sankranti which marks the start of Uttarayana and Karka Sankranti which marks the start of Dakshinayana. The former occurs around 14 January each year, while the latter occurs around 14 July each year. These mark the movement of the Sun along a sidereally fixed zodiac (precession is ignored) into Makara, the zodiacal sign which corresponds with Capricorn, and into Karka, the zodiacal sign which corresponds with Cancer, respectively. +The Amundsen–Scott South Pole Station celebrates every year on 21 June a midwinter party, to celebrate that the Sun is at its lowest point and coming back. +The Fremont Solstice Parade takes place every summer solstice in Fremont, Seattle, Washington in the United States. +The reconstructed Cahokia Woodhenge, a large timber circle located at the Mississippian culture Cahokia archaeological site near Collinsville, Illinois, is the site of annual equinox and solstice sunrise observances. Out of respect for Native American beliefs these events do not feature ceremonies or rituals of any kind. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Solstice-3.md b/data/en.wikipedia.org/wiki/Solstice-3.md new file mode 100644 index 000000000..509b3d4ba --- /dev/null +++ b/data/en.wikipedia.org/wiki/Solstice-3.md @@ -0,0 +1,43 @@ +--- +title: "Solstice" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/Solstice" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:30.644057+00:00" +instance: "kb-cron" +--- + +=== Solstice determination === +Unlike the equinox, the solstice time is not easy to determine. The changes in solar declination become smaller as the Sun gets closer to its maximum/minimum declination. The days before and after the solstice, the declination speed is less than 30 arcseconds per day which is less than 1⁄60 of the angular size of the Sun, or the equivalent to just 2 seconds of right ascension. +This difference is hardly detectable with indirect viewing based devices like sextant equipped with a vernier, and impossible with more traditional tools like a gnomon or an astrolabe. It is also hard to detect the changes in sunrise/sunset azimuth due to the atmospheric refraction changes. Those accuracy issues render it impossible to determine the solstice day based on observations made within the 3 (or even 5) days surrounding the solstice without the use of more complex tools. +Accounts do not survive but Greek astronomers must have used an approximation method based on interpolation, which is still used by some amateurs. This method consists of recording the declination angle at noon during some days before and after the solstice, trying to find two separate days with the same declination. When those two days are found, the halfway time between both noons is estimated solstice time. An interval of 45 days has been postulated as the best one to achieve up to a quarter-day precision, in the solstice determination. +In 2012, the journal DIO found that accuracy of one or two hours with balanced errors can be attained by observing the Sun's equal altitudes about S = twenty degrees (or d = about 20 days) before and after the summer solstice because the average of the two times will be early by q arc minutes where q is (πe cosA)/3 times the square of S in degrees (e = earth orbit eccentricity, A = earth's perihelion or Sun's apogee), and the noise in the result will be about 41 hours divided by d if the eye's sharpness is taken as one arc minute. +Guo Shoujing, a Chinese astronomer, found that the taller the gnomon, the more acurately the journey of the sun could be measured. He designed the 12.6 metres (41 ft) gnomon constructed at Gaocheng Astronomical Observatory in 1276. The measurements from Gaocheng determined the length of the year to within one minute of the current measurement, a value in accord with the value of the Gregorian Calendar, but obtained 300 years earlier.. +Astronomical almanacs define the solstices as the moments when the Sun passes through the solstitial colure, i.e. the times when the apparent geocentric celestial longitude of the Sun is equal to 90° (June solstice) or 270° (December solstice). The dates of the solstice varies each year and may occur a day earlier or later depending on the time zone. Because the earth's orbit takes slightly longer than a calendar year of 365 days, the solstices occur slightly later each calendar year, until a leap day re-aligns the calendar with the orbit. Thus the solstices always occur between June 20 and 22 and between December 20 and 23 in a four-year-long cycle with the 21st and 22nd being the most common dates, as can be seen in the schedule at the start of the article. +Currently, government organizations like USNO +and IMCCE +publish the date and time of the solstice. + +== In the constellations == +Using the current official IAU constellation boundaries—and taking into account the variable precession speed and the rotation of the ecliptic—the solstices shift through the constellations as follows (expressed in astronomical year numbering in which the year 0 = 1 BC, −1 = 2 BC, etc.): + +The northern solstice passed from Leo into Cancer in year −1458, passed into Gemini in year −10, passed into Taurus in December 1989, and is expected to pass into Aries in year 4609. +The southern solstice passed from Capricornus into Sagittarius in year −130, is expected to pass into Ophiuchus in year 2269, and is expected to pass into Scorpius in year 3597. + +== See also == + +Analemma +Geocentric view of the seasons +Iranian calendars +Perihelion and aphelion +Wheel of the Year +Zoroastrian calendar + +== References == + +== External links == + +Equinoxes and Solstices Calculator (1600 to 2400) +"Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion (2000–2025)". United States Naval Observatory, Astronomical Applications Department. Retrieved December 9, 2015. +Weisstein, Eric (1996–2007). "Summer Solstice". Eric Weisstein's World of Astronomy. Retrieved October 24, 2008. The above plots show how the date of the summer solstice shifts through the Gregorian calendar according to the insertion of leap years. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sunrise_equation-0.md b/data/en.wikipedia.org/wiki/Sunrise_equation-0.md new file mode 100644 index 000000000..566780a0c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sunrise_equation-0.md @@ -0,0 +1,596 @@ +--- +title: "Sunrise equation" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Sunrise_equation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:31.804583+00:00" +instance: "kb-cron" +--- + +The sunrise equation or sunset equation can be used to derive the time of sunrise or sunset for any solar declination and latitude in terms of local solar time when sunrise and sunset actually occur. + +== Geometric equation == +The time at which a celestial object crosses the horizon can be calculated by converting its coordinates from the equatorial coordinate system to the horizontal coordinate system, and then solving the equation for an altitude of zero. We then obtain + + + + + cos + ⁡ + + H + + 0 + + + = + − + tan + ⁡ + ϕ + + tan + ⁡ + δ + + + {\displaystyle \cos H_{0}=-\tan \phi \,\tan \delta } + + +where: + + + + + + H + + 0 + + + + + {\displaystyle H_{0}} + + is the solar hour angle at either sunrise (when the negative value is taken) or sunset (when the positive value is taken); + + + + + ϕ + + + {\displaystyle \phi } + + is the latitude of the observer on the Earth; + + + + + δ + + + {\displaystyle \delta } + + is the Sun's declination. +This gives the geometric rise or set time (ignoring refraction) of the center of the Sun. See below for an equation which accounts for these effects. +The Earth rotates at an angular velocity of 15°/hour. Therefore, the expression + + + + + H + + 0 + + + + / + + + + 15 + + + ∘ + + + + + {\displaystyle H_{0}/\mathrm {15} ^{\circ }} + +, where + + + + + H + + 0 + + + + + {\displaystyle H_{0}} + + is in degrees, gives the interval of time in hours from sunrise to local solar noon or from local solar noon to sunset. +The sign convention is that the observer latitude + + + + ϕ + + + {\displaystyle \phi } + + is 0 at the equator, positive for the Northern Hemisphere and negative for the Southern Hemisphere, and the solar declination + + + + δ + + + {\displaystyle \delta } + + is 0 when the Sun is exactly above the equator, positive during the Northern Hemisphere summer and negative during the Northern Hemisphere winter.The declination of the Sun is nearly, but not exactly, zero at the equinoxes. +The equation has no solution when + + + + + | + + tan + ⁡ + ϕ + + tan + ⁡ + δ + + | + + > + 1 + + + {\displaystyle |\tan \phi \,\tan \delta |>1} + +. This occurs north of the Arctic Circle or south of the Antarctic Circle, during the polar night, when the Sun is not visible above the horizon at local midday. + +=== Hemispheric relation === +Suppose + + + + + ϕ + + N + + + + + {\displaystyle \phi _{N}} + + is a given latitude in Northern Hemisphere, and + + + + + H + + N + + + + + {\displaystyle H_{N}} + + is the corresponding sunrise hour angle that has a negative value, and similarly, + + + + + ϕ + + S + + + + + {\displaystyle \phi _{S}} + + is the same latitude but in Southern Hemisphere, which means + + + + + ϕ + + S + + + = + − + + ϕ + + N + + + + + {\displaystyle \phi _{S}=-\phi _{N}} + +, and + + + + + H + + S + + + + + {\displaystyle H_{S}} + + is the corresponding sunrise hour angle, then it is apparent that + + + + + cos + ⁡ + + H + + S + + + = + − + cos + ⁡ + + H + + N + + + = + cos + ⁡ + ( + − + + 180 + + ∘ + + + − + + H + + N + + + ) + + + {\displaystyle \cos H_{S}=-\cos H_{N}=\cos(-180^{\circ }-H_{N})} + +, +which means + + + + + + H + + N + + + + + + H + + S + + + = + − + + 180 + + ∘ + + + + + {\displaystyle H_{N}+H_{S}=-180^{\circ }} + +. +The above relation implies that on the same day, the lengths of daytime from sunrise to sunset at + + + + + ϕ + + N + + + + + {\displaystyle \phi _{N}} + + and + + + + + ϕ + + S + + + + + {\displaystyle \phi _{S}} + + sum to 24 hours if + + + + + ϕ + + S + + + = + − + + ϕ + + N + + + + + {\displaystyle \phi _{S}=-\phi _{N}} + +, and this also applies to regions where polar days and polar nights occur. This further suggests that the global average of length of daytime on any given day is 12 hours without considering the effect of atmospheric refraction. + +== Generalized equation == + +The equation above neglects the influence of atmospheric refraction and the non-zero angle subtended by the solar disc — i.e. the apparent diameter of the sun. The times of the rising and the setting of the upper solar limb as given in astronomical almanacs correct for this by using the more general equation: + + + + + cos + ⁡ + + H + + 0 + + + = + + + + + sin + ⁡ + + h + + 0 + + + − + sin + ⁡ + ϕ + + sin + ⁡ + δ + + + cos + ⁡ + ϕ + + cos + ⁡ + δ + + + + + + + {\displaystyle \cos H_{0}={\dfrac {\sin h_{0}-\sin \phi \,\sin \delta }{\cos \phi \,\cos \delta }}} + + +where + + + + + h + + 0 + + + + + {\displaystyle h_{0}} + + is the geometric altitude angle of the center of the Sun at the time of rising or setting, which is approximately −0.833° or −50.0 arcminutes, although the exact figure depends on atmospheric conditions along the line of sight. +This equation, as given by Jean Meeus, can be also used for any other solar altitude. The NOAA provides additional approximate expressions for refraction corrections at these other altitudes. There are also alternative formulations, such as a non-piecewise expression by G.G. Bennett used in the U.S. Naval Observatory's "Vector Astronomy Software". +The dip of the horizon in radians, including refraction and the geometric correction for the observer's height above the apparent horizon, can be approximated by: + + + + + ψ + = + + + 2 + + + h + + R + + 0 + + + + + ( + 1 + − + k + ) + + + + + {\displaystyle \psi ={\sqrt {2{\frac {h}{R_{0}}}(1-k)}}} + + +where h is the height of the observer, + + + + + R + + 0 + + + + + {\displaystyle R_{0}} + +is the radius of the Earth, and k is the ratio of the radius of the ray's curvature to the radius of the Earth. This assumes that light rays follow a circular path, which is approximately true when the lapse rate is constant. For a typical value of k of 0.17, this gives + + + + + ψ + = + + 1.75 + + ′ + + + + + height in metres + + + + + {\displaystyle \psi =1.75^{\prime }{\sqrt {\text{height in metres}}}} + + +or + + + + + ψ + = + + 0.97 + + ′ + + + + + height in feet + + + + + {\displaystyle \psi =0.97^{\prime }{\sqrt {\text{height in feet}}}} + + +where the prime ( + + + + + + + ′ + + + + + {\displaystyle ^{\prime }} + +) indicates arcminutes, i.e. 1/60 °. This should be subtracted from the altitude angle. In summary, at sunrise or sunset: + + + + + + h + + 0 + + + = + − + s + − + ψ + + + {\displaystyle h_{0}=-s-\psi } + + +where s is the semidiameter of the Sun, about 16 arcminutes. + +== In Universal Time == +To calculate the time of the sunrise in Universal Time, Meeus recommends the following procedure. The position of the Sun in equatorial coordinates should first be calculated or looked up for the day of interest. For the day D, find: + + + + + + θ + + 0 + + + + + {\displaystyle \theta _{0}} + +: the apparent sidereal time (or Earth Rotation Angle) at 0h Universal Time on day + + + + D + + + {\displaystyle D} + +, \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sunrise_equation-1.md b/data/en.wikipedia.org/wiki/Sunrise_equation-1.md new file mode 100644 index 000000000..0c9a2f2b7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sunrise_equation-1.md @@ -0,0 +1,552 @@ +--- +title: "Sunrise equation" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Sunrise_equation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:31.804583+00:00" +instance: "kb-cron" +--- + + + + + + α + + 1 + + + + + {\displaystyle \alpha _{1}} + + and + + + + + δ + + 1 + + + + + {\displaystyle \delta _{1}} + +, the right ascension and declination on day + + + + D + − + 1 + + + {\displaystyle D-1} + + at 0h Universal Time, + + + + + + α + + 2 + + + + + {\displaystyle \alpha _{2}} + + and + + + + + δ + + 2 + + + + + {\displaystyle \delta _{2}} + +, the right ascension and declination on day + + + + D + + + {\displaystyle D} + +, + + + + + + α + + 3 + + + + + {\displaystyle \alpha _{3}} + + and + + + + + δ + + 3 + + + + + {\displaystyle \delta _{3}} + +, the right ascension and declination on day + + + + D + + + 1 + + + {\displaystyle D+1} + +. +Calculate the approximate time of the sunset using + + + + + cos + ⁡ + + H + + 0 + + + = + + + + + sin + ⁡ + + h + + 0 + + + − + sin + ⁡ + ϕ + + sin + ⁡ + + δ + + 2 + + + + + cos + ⁡ + ϕ + + cos + ⁡ + + δ + + 2 + + + + + + + . + + + {\displaystyle \cos H_{0}={\dfrac {\sin h_{0}-\sin \phi \,\sin \delta _{2}}{\cos \phi \,\cos \delta _{2}}}.} + + +If the right hand side has an absolute value greater than 1, then the Sun does not go below the horizon on that day and + + + + + H + + 0 + + + + + {\displaystyle H_{0}} + + does not exist. +Calculate the transit, sunrise and sunset time in fractions of a day: + + + + + + m + + 0 + + + = + + + + + α + + 2 + + + + + L + − + + θ + + 0 + + + + + 360 + + ∘ + + + + + + + {\displaystyle m_{0}={\frac {\alpha _{2}+L-\theta _{0}}{360^{\circ }}}} + + + + + + + m + + 1 + + + = + + m + + 0 + + + − + + + + H + + 0 + + + + 360 + + ∘ + + + + + + + {\displaystyle m_{1}=m_{0}-{\frac {H_{0}}{360^{\circ }}}} + + + + + + + m + + 2 + + + = + + m + + 0 + + + + + + + + H + + 0 + + + + 360 + + ∘ + + + + + + + {\displaystyle m_{2}=m_{0}+{\frac {H_{0}}{360^{\circ }}}} + + +where L is the geographical longitude expressed as an angle increasing westwards from Greenwich, i.e. the opposite sign convention than is typically used in geography. +These values of m can be multiplied by 24 to give the time of each event in hours, accurate to about ±0.01 days (14 minutes). For greater accuracy, the elevation angle of the Sun should be calculated at the proposed time, and then an adjustment applied to bring it to the desired elevation. The adjustment is: + + + + + Δ + m + = + + + + h + − + + h + + 0 + + + + + + 360 + + ∘ + + + cos + ⁡ + δ + cos + ⁡ + ϕ + sin + ⁡ + H + + + + + + {\displaystyle \Delta m={\frac {h-h_{0}}{360^{\circ }\cos \delta \cos \phi \sin H}}} + + +where + + + + + H + = + θ + − + L + − + α + + + {\displaystyle H=\theta -L-\alpha } + + is the hour angle, + + + + + θ + = + + θ + + 0 + + + + + + 360.985647 + + ∘ + + + m + + + {\displaystyle \theta =\theta _{0}+360.985647^{\circ }m} + + is the sidereal time at Greenwich in degrees, +h is the altitude of the Sun in degrees at m, + + + + + α + + + {\displaystyle \alpha } + + is the result of linear interpolation between + + + + + α + + 1 + + + + + {\displaystyle \alpha _{1}} + +, + + + + + α + + 2 + + + + + {\displaystyle \alpha _{2}} + + and + + + + + α + + 3 + + + + + {\displaystyle \alpha _{3}} + +, + + + + + δ + + + {\displaystyle \delta } + + is similarly interpolated between + + + + + δ + + 1 + + + + + {\displaystyle \delta _{1}} + +, + + + + + δ + + 2 + + + + + {\displaystyle \delta _{2}} + + and + + + + + δ + + 3 + + + + + {\displaystyle \delta _{3}} + +. +The final time is then + + + + m + + + Δ + m + + + {\displaystyle m+\Delta m} + +. +Temperature variations in the atmosphere unpredictably affect the amount of refraction, limiting accuracy to about two minutes. + +== See also == +Daytime +Equation of time + +== References == + +== External links == +Sunrise, sunset, or sun position for any location — U.S. only (U.S. NOAA) +Sunrise, sunset and day length for any location — worldwide +Rise/Set/Transit/Twilight Data — U.S. only (U.S. Naval Observatory) +Astronomical Information Center (U.S. Naval Observatory) +Converting Between Julian Dates and Gregorian Calendar Dates +Approximate Solar Coordinates +Algorithms for Computing Astronomical Phenomena +Astronomy Answers: Position of the Sun +A Simple Expression for the Equation of Time +The Equation of Time +Equation of Time +Long-Term Almanac for Sun, Moon, and Polaris V1.11 +Evaluating the Effectiveness of Current Atmospheric Refraction Models in Predicting Sunrise and Sunset Times \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Terrestrial_Time-0.md b/data/en.wikipedia.org/wiki/Terrestrial_Time-0.md new file mode 100644 index 000000000..c0fc7ce7d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Terrestrial_Time-0.md @@ -0,0 +1,409 @@ +--- +title: "Terrestrial Time" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Terrestrial_Time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:32.984785+00:00" +instance: "kb-cron" +--- + +Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. +For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth. +The unit of TT is the SI second, the definition of which is based currently on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it. +TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT is indirectly the basis of UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is 32.184 s ahead of TAI. + +== History == +A definition of a terrestrial time standard was adopted by the International Astronomical Union (IAU) in 1976 at its XVI General Assembly and later named Terrestrial Dynamical Time (TDT). It was the counterpart to Barycentric Dynamical Time (TDB), which was a time standard for Solar system ephemerides, to be based on a dynamical time scale. Both of these time standards turned out to be imperfectly defined. Doubts were also expressed about the meaning of 'dynamical' in the name TDT. +In 1991, in Recommendation IV of the XXI General Assembly, the IAU redefined TDT, also renaming it "Terrestrial Time". TT was formally defined in terms of Geocentric Coordinate Time (TCG), defined by the IAU on the same occasion. TT was defined to be a linear scaling of TCG, such that the unit of TT is the "SI second on the geoid", i.e. the rate approximately matched the rate of proper time on the Earth's surface at mean sea level. Thus the exact ratio between TT time and TCG time was + + + + 1 + − + + L + + + G + + + + + + {\displaystyle 1-L_{\mathrm {G} }} + +, where + + + + + L + + + G + + + + = + + U + + + G + + + + + / + + + c + + 2 + + + + + {\displaystyle L_{\mathrm {G} }=U_{\mathrm {G} }/c^{2}} + + was a constant and + + + + + U + + + G + + + + + + {\displaystyle U_{\mathrm {G} }} + + was the gravitational potential at the geoid surface, a value measured by physical geodesy. In 1991 the best available estimate of + + + + + L + + + G + + + + + + {\displaystyle L_{\mathrm {G} }} + + was 6.969291×10−10. +In 2000, the IAU very slightly altered the definition of TT by adopting an exact value, LG = 6.969290134×10−10. + +== Current definition == +TT differs from Geocentric Coordinate Time (TCG) by a constant rate. Formally it is defined by the equation + + + + + + T + T + + = + + + ( + + + 1 + − + + L + + + G + + + + + + ) + + + × + + T + C + G + + + + E + , + + + {\displaystyle \mathrm {TT} ={\bigl (}1-L_{\mathrm {G} }{\bigr )}\times \mathrm {TCG} +E,} + + +where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, + + + + + L + + + G + + + + + + {\displaystyle L_{\mathrm {G} }} + + is the constant difference in the rates of the two time scales, and + + + + E + + + {\displaystyle E} + + is a constant to resolve the epochs (see below). + + + + + L + + + G + + + + + + {\displaystyle L_{\mathrm {G} }} + + is defined as exactly 6.969290134×10−10. Due to the term + + + + 1 + − + + L + + + G + + + + + + {\displaystyle 1-L_{\mathrm {G} }} + + the rate of TT is very slightly slower than that of TCG. +The equation linking TT and TCG more commonly has the form given by the IAU, + + + + + + T + T + + = + + T + C + G + + − + + L + + + G + + + + × + + + ( + + + + J + + D + + T + C + G + + + + − + 2443144.5003725 + + + ) + + + × + 86400 + , + + + {\displaystyle \mathrm {TT} =\mathrm {TCG} -L_{\mathrm {G} }\times {\bigl (}\mathrm {JD_{TCG}} -2443144.5003725{\bigr )}\times 86400,} + + +where + + + + + J + + D + + T + C + G + + + + + + {\displaystyle \mathrm {JD_{TCG}} } + + is the TCG time expressed as a Julian date (JD). The Julian Date is a linear transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is not simplified. The use of a Julian Date specifies the epoch fully. The above equation is often given with the Julian Date 2443144.5 for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier + + + + + L + + + G + + + + + + {\displaystyle L_{\mathrm {G} }} + +). The value 2443144.5003725 is exactly in accord with the definition. +Time coordinates on the TT and TCG scales are specified conventionally using traditional means of specifying days, inherited from non-uniform time standards based on the rotation of Earth. Specifically, both Julian Dates and the Gregorian calendar are used. For continuity with their predecessor Ephemeris Time (ET), TT and TCG were set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TT instant 1977-01-01T00:00:32.184 and TCG instant 1977-01-01T00:00:32.184 exactly correspond to the International Atomic Time (TAI) instant 1977-01-01T00:00:00.000. This is also the instant at which TAI introduced corrections for gravitational time dilation. +TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation + + + + + + J + + D + + T + T + + + + = + + E + + + J + D + + + + + + + + ( + + + + J + + D + + T + C + G + + + + − + + E + + + J + D + + + + + + ) + + + × + + + ( + + + 1 + − + + L + + + G + + + + + + ) + + + , + + + {\displaystyle \mathrm {JD_{TT}} =E_{\mathrm {JD} }+{\bigl (}\mathrm {JD_{TCG}} -E_{\mathrm {JD} }{\bigr )}\times {\bigl (}1-L_{\mathrm {G} }{\bigr )},} + + +where + + + + + E + + + J + D + + + + + + {\displaystyle E_{\mathrm {JD} }} + + is 2443144.5003725 exactly. + +== Realizations == +TT is a theoretical ideal, not dependent on a particular realization. For practical use, physical clocks must be measured and their readings processed to estimate TT. A simple offset calculation is sufficient for most applications, but in demanding applications, detailed modeling of relativistic physics and measurement uncertainties may be needed. + +=== TAI === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Terrestrial_Time-1.md b/data/en.wikipedia.org/wiki/Terrestrial_Time-1.md new file mode 100644 index 000000000..76a9b41cc --- /dev/null +++ b/data/en.wikipedia.org/wiki/Terrestrial_Time-1.md @@ -0,0 +1,71 @@ +--- +title: "Terrestrial Time" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Terrestrial_Time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:32.984785+00:00" +instance: "kb-cron" +--- + +The main realization of TT is supplied by TAI. The BIPM TAI service, performed since 1958, estimates TT using measurements from an ensemble of atomic clocks spread over the surface and low orbital space of Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings shown by that particular group of atomic clocks at the time. Estimates of TAI are also provided in real time by the institutions that operate the participating clocks. Because of the historical difference between TAI and ET when TT was introduced, the TAI realization of TT is defined thus: + + + + + + T + T + ( + T + A + I + ) + = + T + A + I + + + 32.184 + + s + + . + + + {\displaystyle \mathrm {TT(TAI)=TAI+32.184~s} .} + + +The offset 32.184 s arises from history. The atomic time scale A1 (a predecessor of TAI) was set equal to UT2 at its conventional starting date of 1 January 1958, when ΔT (ET − UT) was about 32 seconds. The offset 32.184 seconds was the 1976 estimate of the difference between Ephemeris Time (ET) and TAI, "to provide continuity with the current values and practice in the use of Ephemeris Time". +TAI is never revised once published and TT(TAI) has small errors relative to TT(BIPM), on the order of 10-50 microseconds. +The GPS time scale has a nominal difference from atomic time (TAI − GPS time = +19 seconds), so that TT ≈ GPS time + 51.184 seconds. This realization introduces up to a microsecond of additional error, as the GPS signal is not precisely synchronized with TAI, but GPS receiving devices are widely available. + +=== TT(BIPM) === +Approximately annually since 1992, the International Bureau of Weights and Measures (BIPM) has produced better realizations of TT based on reanalysis of historical TAI data. BIPM's realizations of TT are named in the form "TT(BIPM08)", with the digits indicating the year of publication. They are published in the form of a table of differences from TT(TAI), along with an extrapolation equation that may be used for dates later than the table. The latest as of July 2024 is TT(BIPM23). + +=== Pulsars === +Researchers from the International Pulsar Timing Array collaboration have created a realization TT(IPTA16) of TT based on observations of an ensemble of pulsars up to 2012. This new pulsar time scale is an independent means of computing TT. The researchers observed that their scale was within 0.5 microseconds of TT(BIPM17), with significantly lower errors since 2003. The data used was insufficient to analyze long-term stability, and contained several anomalies, but as more data is collected and analyzed, this realization may eventually be useful to identify defects in TAI and TT(BIPM). + +=== Other standards === +TT is in effect a continuation of (but is more precisely uniform than) the former Ephemeris Time (ET). It was designed for continuity with ET, and it runs at the rate of the SI second, which was itself derived from a calibration using the second of ET (see, under Ephemeris time, Redefinition of the second and Implementations). The JPL ephemeris time argument Teph is within a few milliseconds of TT. +TT is slightly ahead of UT1 (a refined measure of mean solar time at Greenwich) by an amount known as ΔT = TT − UT1. ΔT was measured at +67.6439 seconds (TT ahead of UT1) at 0 h UTC on 1 January 2015; and by retrospective calculation, ΔT was close to zero about the year 1900. ΔT is expected to continue to increase, with UT1 becoming steadily (but irregularly) further behind TT in the future. In fine detail, ΔT is somewhat unpredictable, with 10-year extrapolations diverging by 2-3 seconds from the actual value. + +== Relativistic relationships == +Observers in different locations, that are in relative motion or at different altitudes, can disagree about the rates of each other's clocks, owing to effects described by the theory of relativity. As a result, TT (even as a theoretical ideal) does not match the proper time of all observers. +In relativistic terms, TT is described as the proper time of a clock located on the geoid (essentially mean sea level). +However, +TT is now actually defined as a coordinate time scale. +The redefinition did not quantitatively change TT, but rather made the existing definition more precise. In effect it defined the geoid (mean sea level) in terms of a particular level of gravitational time dilation relative to a notional observer located at infinitely high altitude. +The present definition of TT is a linear scaling of Geocentric Coordinate Time (TCG), which is the proper time of a notional observer who is infinitely far away (so not affected by gravitational time dilation) and at rest relative to Earth. TCG is used to date mainly for theoretical purposes in astronomy. From the point of view of an observer on Earth's surface the second of TCG passes in slightly less than the observer's SI second. The comparison of the observer's clock against TT depends on the observer's altitude: they will match on the geoid, and clocks at higher altitude tick slightly faster. + +== See also == +Barycentric Coordinate Time +Geocentric Coordinate Time + +== Notes == + +== References == + +== External links == +BIPM technical services: Time Metrology +Time and Frequency from A to Z \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tropical_year-0.md b/data/en.wikipedia.org/wiki/Tropical_year-0.md new file mode 100644 index 000000000..5fd8cf887 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tropical_year-0.md @@ -0,0 +1,34 @@ +--- +title: "Tropical year" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/Tropical_year" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:34.155727+00:00" +instance: "kb-cron" +--- + +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 – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons. For example, it is the time from vernal equinox to the next vernal equinox, or from summer solstice to the next summer solstice. It is the type of year used by tropical solar calendars. +The tropical year is one type of astronomical year and a particular orbital period. Another type is the sidereal year (or sidereal orbital period), which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars, resulting in a duration of 20 minutes and 24.7 seconds longer than the tropical year due to the precession of the equinoxes. +Since antiquity, astronomers have progressively refined the definition of the tropical year. The entry for "year, tropical" in the Astronomical Almanac Online Glossary states: + +the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds. +An equivalent, more descriptive definition is "The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever the longitude reaches a multiple of 360 degrees, the mean Sun crosses the vernal equinox and a new tropical year begins". +The mean tropical year in 2000 was 365.24219 ephemeris days, each ephemeris day lasting 86,400 SI seconds. This is 365.24217 mean solar days. For this reason, the calendar year is an approximation of the solar year: the Gregorian calendar (with its rules for catch-up leap days) is designed to resynchronize the calendar year with the solar year at regular intervals. + +== History == + +=== Origin === +The word "tropical" comes from the Greek tropikos meaning "turn". Thus, the tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead, and where it appears to "turn" in its annual seasonal motion. Because of this connection between the tropics and the seasonal cycle of the apparent position of the Sun, the word "tropical" was lent to the period of the seasonal cycle. The early Chinese, Hindus, Greeks, and others made approximate measures of the tropical year. + +=== Early value, precession discovery === +In the 2nd century BC, Hipparchus measured 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 1/300 of a day less than 365.25 days (365 days, 5 hours, 55 minutes, 12 seconds, or 365.24667 days). Hipparchus used this method because he was better able to detect the time of the equinoxes, compared to that of the solstices. +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 years later, by Islamic astronomers. Since this discovery, a distinction has been made between the tropical year and the sidereal year. + +=== Middle Ages and the Renaissance === +During the Middle Ages and Renaissance, several progressively better tables were published that allowed computation of the positions of the Sun, Moon and planets relative to the fixed stars. An important application of these tables was the reform of the calendar. +The Alfonsine Tables, published in 1252, were based on the theories of Ptolemy and were revised and updated after the original publication. The length of the tropical year was given as 365 solar days, 5 hours, 49 minutes, 16 seconds (≈ 365.24255 days). This length was used in devising the Gregorian calendar of 1582. +In Uzbekistan, Ulugh Beg's Zij-i Sultani was published in 1437 and gave an estimate of 365 solar days, 5 hours, 49 minutes, 15 seconds (365.242535 days). +In the 16th century, Copernicus put forward a heliocentric cosmology. Erasmus Reinhold used Copernicus' theory to compute the Prutenic Tables in 1551, and gave a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days), based on the length of a sidereal year and the presumed rate of precession. This was actually less accurate than the earlier value of the Alfonsine Tables. +Major advances in the 17th century were made by Johannes Kepler and Isaac Newton. In 1609 and 1619, Kepler published his three laws of planetary motion. In 1627, Kepler used the observations of Tycho Brahe and Waltherus to produce the most accurate tables up to that time, the Rudolphine Tables. He evaluated the mean tropical year as 365 solar days, 5 hours, 48 minutes, 45 seconds (365.24219 days). +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 Edmond Halley published in 1693 and 1749 and provided the underpinnings of all solar system models until Albert Einstein's theory of General relativity in the 20th century. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tropical_year-1.md b/data/en.wikipedia.org/wiki/Tropical_year-1.md new file mode 100644 index 000000000..4d4047a53 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tropical_year-1.md @@ -0,0 +1,31 @@ +--- +title: "Tropical year" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/Tropical_year" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:34.155727+00:00" +instance: "kb-cron" +--- + +=== 18th and 19th century === +From the time of Hipparchus and Ptolemy, the year was based on two equinoxes (or two solstices) some years apart, to average out both observational errors and periodic variations (caused by the gravitational pull of the planets, and the small effect of nutation on the equinox). These effects did not begin to be understood until Newton's time. To model short-term variations of the time between equinoxes (and prevent them from confounding efforts to measure long-term variations) requires precise observations and an elaborate theory of the apparent 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 celestial mechanics. They were able to compute periodic variations and separate them from the gradual mean motion. They could express the mean longitude of the Sun in a polynomial such as: + +L0 = A0 + A1T + A2T2 days +where T is the time in Julian centuries. The derivative of this formula is an expression of the mean angular velocity, and the inverse of this gives an expression for the length of the tropical year as a linear function of T. +Two equations are given in the table. Both equations estimate that the tropical year gets roughly a half-second shorter each century. + +Newcomb's tables were sufficiently accurate that they were used by the joint American-British Astronomical Almanac for the Sun, Mercury, Venus, and Mars through 1983. + +=== 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 satellites +tracking of deep space probes such as Pioneer 4 beginning in 1959 +radars able to measure the distance to other planets beginning in 1961 +lunar laser ranging since the 1969 Apollo 11 left the first of a series of retroreflectors which allow greater accuracy than reflectorless measurements +artificial satellites such as LAGEOS (1976) and the Global Positioning System (initial operation in 1993) +very long baseline interferometry which finds precise directions to quasars in distant galaxies, 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. +The complexity of the model used for the Solar System must be limited to the available computational facilities. In the 1920s, punched card equipment came into use by L. J. Comrie in Britain. For 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 almanacs. +Albert Einstein's General Theory of Relativity 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. +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 predicted that the rotation of the Earth is being retarded by tides. This could be verified by observation only in the 1920s with the very accurate Shortt–Synchronome clock and later in the 1930s when quartz clocks began to replace pendulum clocks as time standards. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tropical_year-2.md b/data/en.wikipedia.org/wiki/Tropical_year-2.md new file mode 100644 index 000000000..3acf1407b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tropical_year-2.md @@ -0,0 +1,34 @@ +--- +title: "Tropical year" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/Tropical_year" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:34.155727+00:00" +instance: "kb-cron" +--- + +== Time scales and calendar == +Apparent solar time is the time indicated by a sundial, and is determined by the apparent motion of the Sun caused by the rotation of the Earth around its axis as well as the revolution of the Earth around the Sun. Mean solar time is corrected for the periodic variations in the apparent velocity of the Sun as the Earth revolves in its orbit. The most important such time scale is Universal Time, which is the mean solar time at 0° longitude (the IERS Reference Meridian). Civil time is based on UT (actually UTC), and civil calendars count mean solar days. +However, the rotation of the Earth itself is irregular and is slowing down, with respect to more stable time indicators: specifically, the motion of planets and atomic clocks. +Ephemeris time (ET) is the independent variable in the equations of motion of the Solar System, in particular, the equations from Newcomb's work, and this ET was in use from 1960 to 1984. These ephemerides were based on observations made in solar time over a period of several centuries, and as a consequence represent the mean solar second over that period. The SI second, defined in atomic time, 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. ET as counted by atomic clocks was given a new name, Terrestrial Time (TT), and for most purposes ET = TT = TAI + 32.184 SI seconds. Since the era of the observations, the rotation of the Earth has slowed down and the mean solar second has grown somewhat longer than the SI second. As a result, the time scales of TT and UT1 build up a growing difference: the amount that TT is ahead of UT1 is known as ΔT, or Delta T. As of 5 July 2022, TT is ahead of UT1 by 69.28 seconds. +As a consequence, the tropical year following the seasons on Earth, as counted in solar days of UT, is increasingly out of sync with expressions for equinoxes in ephemerides in TT. +As explained below, long-term estimates of the length of the tropical year were used in connection with the reform of the Julian calendar, which resulted in the Gregorian calendar. Participants in that reform were unaware of the non-uniform rotation of the Earth, but now this can be taken into account to some degree. The table below gives Morrison and Stephenson's estimates and standard errors (σ) for ΔT at dates significant in the process of developing the Gregorian calendar. + +The low-precision extrapolations are computed with an expression provided by Morrison and Stephenson: + +ΔT in seconds = −20 + 32t2 +where t is measured in Julian centuries from 1820. The extrapolation is provided only to show that ΔT is not negligible when evaluating the calendar for long periods; Borkowski cautions that "many researchers have attempted to fit a parabola to the measured ΔT values to determine the magnitude of the deceleration of the Earth's rotation. The results, when taken together, are rather discouraging." + +== Length of tropical year == + +One 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. + +=== Mean time interval between equinoxes === + +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 equator (the Earth's equator projected into space). These two planes intersect in a line. One direction points to the so-called vernal, northward, or March equinox which is given the symbol ♈︎ (the symbol looks like the horns of a ram because it used to be toward the constellation Aries). The opposite direction is given the symbol ♎︎ (because it used to be toward Libra). Because of the precession of the equinoxes 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 angle between ♈︎ and the Sun, measured eastward along the ecliptic. This creates a relative and not an absolute measurement, because as the Sun is moving, the direction from which the angle is measured is also moving. It is convenient to have a fixed (with respect to distant stars) direction to measure from; the direction of ♈︎ at noon January 1, 2000, fills this role and is given the symbol ♈︎0. +There was an equinox on March 20, 2009, 11:44:43.6 TT. The 2010 March equinox was March 20, 17:33:18.1 TT, which gives an interval – and a duration of the tropical year – of 365 days, 5 hours, 48 minutes, 34.5 seconds. 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 west 51" for a total of 360° (all with respect to ♈︎0). This is why the tropical year is 20 minutes shorter than the sidereal year. +When tropical year measurements from several successive years are compared, variations are found which are due to the perturbations by the Moon and planets acting on the Earth, and to nutation. Meeus and Savoie provided the following examples of intervals between March (northward) equinoxes: + +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 mean tropical year. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tropical_year-3.md b/data/en.wikipedia.org/wiki/Tropical_year-3.md new file mode 100644 index 000000000..0a696b1ea --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tropical_year-3.md @@ -0,0 +1,96 @@ +--- +title: "Tropical year" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/Tropical_year" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:34.155727+00:00" +instance: "kb-cron" +--- + +=== Different tropical year definitions === +If a different starting longitude for the Sun is chosen than 0° (i.e. ♈︎), then the duration for the Sun to return to the same longitude will be different. This is a second-order effect of the circumstance that the speed of the Earth (and conversely the apparent speed of the Sun) varies in its elliptical orbit: faster in the perihelion, slower in the aphelion. The equinox moves with respect to the perihelion (and both move with respect to the fixed sidereal frame). From one equinox passage to the next, or from one solstice passage to the next, the Sun completes not quite a full elliptic orbit. The time saved depends on where it starts in the orbit. If the starting point is close to the perihelion (such as the December solstice), then the speed is higher than average, and the apparent Sun saves little time for not having to cover a full circle: the "tropical year" is comparatively long. If the starting point is near aphelion, then the speed is lower and the time saved for not having to run the same small arc that the equinox has precessed is longer: that tropical year is comparatively short. +The "mean tropical year" is based on the mean sun, and is not exactly equal to any of the times taken to go from an equinox to the next or from a solstice to the next. +The following values of time intervals between equinoxes and solstices were provided by Meeus and Savoie for the years 0 and 2000. These are smoothed values which take account of the Earth's orbit being elliptical, using well-known procedures (including solving Kepler's equation). They do not take into account periodic variations due to factors such as the gravitational force of the orbiting Moon and gravitational forces from the other planets. Such perturbations are minor compared to the positional difference resulting from the orbit being elliptical rather than circular. + +=== Mean tropical year current value === +The mean tropical year on January 1, 2000, was 365.2421897 or 365 ephemeris days, 5 hours, 48 minutes, 45.19 seconds. This changes slowly; an expression suitable for calculating the length of a tropical year in ephemeris days, between 8000 BC and 12000 AD, is + + + + + 365.2421896698 + − + 6.15359 + × + + 10 + + − + 6 + + + T + − + 7.29 + × + + 10 + + − + 10 + + + + T + + 2 + + + + + 2.64 + × + + 10 + + − + 10 + + + + T + + 3 + + + + + {\displaystyle 365.2421896698-6.15359\times 10^{-6}T-7.29\times 10^{-10}T^{2}+2.64\times 10^{-10}T^{3}} + + +where T is in Julian centuries of 36,525 days of 86,400 SI seconds measured from noon January 1, 2000, TT. +Modern astronomers define the tropical year as the 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. When viewed over one year, 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°. +The above formulae give the length of the tropical year in ephemeris days (equal to 86,400 SI seconds), not solar days. It is the number of solar days in a tropical year that is important for keeping the calendar synchronized with the seasons (see below). + +== Calendar year == +The Gregorian calendar, as used for civil and scientific purposes, is an international standard. It is a solar calendar that is designed to maintain synchrony with the mean tropical year. It has a cycle of 400 years (146,097 days). Each cycle repeats the months, 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 of 365.2422 days. +The Gregorian calendar is a reformed version of the Julian calendar organized by the Catholic Church and enacted in 1582. By the time of the reform, 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. The motivation for the change was the correct observance of Easter. The rules used to compute the date of Easter used a conventional date for the vernal equinox (March 21), and it was considered important to keep March 21 close to the actual equinox. +If society in the future 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 between three hours and four days 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 seconds per century, the mean solar day is getting longer at a rate of about 1.5 ms per century, and length of the "tropical millennium" is decreasing by about 0.06 solar days per millennium (neglecting the oscillatory changes in the real length of the tropical year). These effects will cause the calendar to be as much as one day behind the Sun in 3200. As a result, many have suggested that the number of leap days should decrease as time goes on. One possible reform that has been proposed involves omitting the leap day in 3200, keeping 3600 and 4000 as leap years, and making all centennial years common except 4500, 5000, 5500, 6000, etc. (i.e. making centennial leap years occur once every 500 years instead of 400 starting from the year 4000), but the quantity ΔT is not sufficiently predictable to form more precise proposals. + +== See also == +Anomalistic year +Gregorian calendar +Sidereal and tropical astrology + +== Notes == + +== References == + +== Further reading == +Dershowitz, N.; Reingold, E.M. (2008). Calendrical calculations (3rd ed.). Cambridge University Press. ISBN 978-0-521-70238-6. +Meeus, Jean (August 10, 2009) [1998]. Astronomical Algorithms (2nd, with corrections as of August 10, 2009 ed.). Richmond, VA: Willmann-Bell. ISBN 978-0-943396-61-3. +Meeus, Jean (2002). More astronomical astronomy morsels. Richmond, VA: Willmann-Bell. ISBN 0-943396-74-3. Contains updates to Meeus & Savoie 1992. +Simon, J. L.; Bretagnon, P.; Chapront, J.; Chapront-Touze, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and the planets". Astronomy and Astrophysics. 282: 663–683. Bibcode:1994A&A...282..663S. ISSN 0004-6361. Referenced in Astronomical almanac for the year 2011 and contains expressions used to derive the length of the tropical year. + +== External links == + Media related to Tropical year at Wikimedia Commons \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tzolkinex-0.md b/data/en.wikipedia.org/wiki/Tzolkinex-0.md new file mode 100644 index 000000000..9e124ceba --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tzolkinex-0.md @@ -0,0 +1,31 @@ +--- +title: "Tzolkinex" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Tzolkinex" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:35.358456+00:00" +instance: "kb-cron" +--- + +The tzolkinex is an eclipse cycle equal to a period of two saros (13,170.636 days) minus one inex (10,571.946 days). As consecutive eclipses in an inex series belongs to the next consecutive saros series, each consecutive tzolkinex belongs to the previous saros series. +The tzolkinex is equal to 2598.691 days (about 7 years, 1 month and 12 days). It is related to the tritos in that a period of one tritos plus one tzolkinex is exactly equal to one saros. It is also related to the inex in that a period of one inex plus one tzolkinex is exactly equal to two saros. +It corresponds to: + +88 synodic months +95.49723 draconic months +7.49723 eclipse years (15 eclipse seasons) +94.31081 anomalistic months. +Because of the non-integer number of anomalistic month each eclipse varies in type, i.e. total vs. annular, and greatly varies in length. From remainder of 0.31081, being near 1⁄3, every third tzolkinex comes close to an even number of anomalistic months, but occurs during a different season, and in the opposite hemisphere, thus they may be of the same type (annular vs. total) but otherwise do not have a similar character. + + +== Details == +It was first studied by George van den Bergh (1951). The name was suggested by Felix Verbelen (2001) because its length is nearly 10 Tzolk'ins (260-day periods). +It alternates hemispheres with each cycle, occurring at alternating nodes, each successive occurrence is one saros less than the last. + + +== See also == +Eclipse cycle + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Universal_Time-0.md b/data/en.wikipedia.org/wiki/Universal_Time-0.md new file mode 100644 index 000000000..0f095c3c1 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Universal_Time-0.md @@ -0,0 +1,32 @@ +--- +title: "Universal Time" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Universal_Time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:36.566553+00:00" +instance: "kb-cron" +--- + +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 with respect to the International Celestial Reference Frame (ICRF), called the Earth Rotation Angle (ERA, which serves as the replacement for Greenwich Mean Sidereal Time). UT1 is the same everywhere on Earth. UT1 is required to follow the relationship + +where Tu = (Julian UT1 date − 2451545.0). + +== History == +Prior to the introduction of standard time, each municipality throughout the clock-using world set its official clock, if it had one, according to the local position of the Sun (see solar time). This served adequately until the introduction of rail travel in Britain, which made it possible to travel fast enough over sufficiently long distances as to require continuous re-setting of timepieces as a train progressed in its daily run through several towns. Starting in 1847, Britain established Greenwich Mean Time (GMT), the mean solar time at Greenwich, England, to solve this problem: all clocks in Great Britain were set to this time regardless of local solar noon. Using telescopes, GMT was calibrated to the mean solar time at the prime meridian through the Royal Observatory, Greenwich. Chronometers or telegraphy were used to synchronize these clocks. + +As international commerce increased, the need for an international standard of time measurement emerged. Several authors proposed a "universal" or "cosmic" time (see Time zone § Worldwide time zones). The development of Universal Time began at the International Meridian Conference. At the end of this conference, on 22 October 1884, the recommended base reference for world time, the "universal day", was announced to be the local mean solar time at the Royal Observatory in Greenwich, counted from 0 hours at Greenwich mean midnight. This agreed with the civil Greenwich Mean Time used on the island of Great Britain since 1847. In contrast, astronomical GMT began at mean noon, i.e. astronomical day X began at noon of civil day X. The purpose of this was to keep one night's observations under one date. The civil system was adopted as of 0 hours (civil) 1 January 1925. Nautical GMT began 24 hours before astronomical GMT, at least until 1805 in the Royal Navy, but persisted much later elsewhere because it was mentioned at the 1884 conference. Greenwich was chosen because by 1884 two-thirds of all nautical charts and maps already used it as their prime meridian. +During the period between 1848 and 1972, all of the major countries adopted time zones based on the Greenwich meridian. +In 1928, the term Universal Time (UT) was introduced by the International Astronomical Union to refer to GMT, with the day starting at midnight. The term was recommended as a more precise term than Greenwich Mean Time, because GMT could refer to either an astronomical day starting at noon or a civil day starting at midnight. As the general public had always begun the day at midnight, the timescale continued to be presented to them as Greenwich Mean Time. +When introduced, broadcast time signals were based on UT, and hence on the rotation of the Earth. In 1955 the BIH adopted a proposal by William Markowitz, effective 1 January 1956, dividing UT into UT0 (UT as formerly computed), UT1 (UT0 corrected for polar motion) and UT2 (UT0 corrected for polar motion and seasonal variation). UT1 was the version sufficient for "many astronomical and geodetic applications", while UT2 was to be broadcast over radio to the public. +UT0 and UT2 soon became irrelevant due to the introduction of Coordinated Universal Time (UTC). Starting in 1956, WWV broadcast an atomic clock signal stepped by 20 ms increments to bring it into agreement with UT1. The error from UT1 of up to 20 ms is on the same order of magnitude as the differences between UT0, UT1, and UT2. By 1960, the U.S. Naval Observatory, the Royal Greenwich Observatory, and the UK National Physical Laboratory had developed UTC, with a similar stepping approach. The 1960 URSI meeting recommended that all time services should follow the lead of the UK and US and broadcast coordinated time using a frequency offset from cesium aimed to match the predicted progression of UT2 with occasional steps as needed. Starting 1 January 1972, UTC was defined to follow UT1 within 0.9 seconds rather than UT2, marking the decline of UT2. +Modern civil time generally follows UTC. In some countries, the term Greenwich Mean Time persists in common usage to this day in reference to UT1, in civil timekeeping as well as in astronomical almanacs and other references. Whenever a level of accuracy better than one second is not required, UTC can be used as an approximation of UT1. The difference between UT1 and UTC is known as DUT1. + +=== Adoption in various countries === +The table shows the dates of adoption of time zones based on the Greenwich meridian, including half-hour zones. + +Apart from Nepal Standard Time (UTC+05:45), the Chatham Standard Time Zone (UTC+12:45) used in New Zealand's Chatham Islands and the officially unsanctioned Central Western Time Zone (UTC+8:45) used in Eucla, Western Australia and surrounding areas, all time zones in use are defined by an offset from UTC that is a multiple of half an hour, and in most cases a multiple of an hour. + +== Measurement == + +Historically, Universal Time was computed from observing the position of the Sun in the sky. But astronomers found that it was more accurate to measure the rotation of the Earth by observing stars as they crossed the meridian each day. Nowadays, UT in relation to International Atomic Time (TAI) is determined by very-long-baseline interferometry (VLBI) observations of the positions of distant celestial objects (stars and quasars), a method which can determine UT1 to within 15 microseconds or better. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Universal_Time-1.md b/data/en.wikipedia.org/wiki/Universal_Time-1.md new file mode 100644 index 000000000..5f8ff7a67 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Universal_Time-1.md @@ -0,0 +1,52 @@ +--- +title: "Universal Time" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Universal_Time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:13:36.566553+00:00" +instance: "kb-cron" +--- + +The rotation of the Earth and UT are monitored by the International Earth Rotation and Reference Systems Service (IERS). The International Astronomical Union also is involved in setting standards, but the final arbiter of broadcast standards is the International Telecommunication Union, or ITU. +The rotation of the Earth is somewhat irregular and also is very gradually slowing due to tidal acceleration. Furthermore, the length of the second was determined from observations of the Moon between 1750 and 1890. All of these factors cause the modern mean solar day, on the average, to be slightly longer than the nominal 86,400 SI seconds, the traditional number of seconds per day. As UT is thus slightly irregular in its rate, astronomers introduced Ephemeris Time, which has since been replaced by Terrestrial Time (TT). Because Universal Time is determined by the Earth's rotation, which drifts away from more precise atomic-frequency standards, an adjustment (called a leap second) to this atomic time is needed since (as of 2019) 'broadcast time' remains broadly synchronised with solar time. Thus, the civil broadcast standard for time and frequency usually follows International Atomic Time closely, but occasionally step (or "leap") in order to prevent them from drifting too far from mean solar time. +Barycentric Dynamical Time (TDB), a form of atomic time, is now used in the construction of the ephemerides of the planets and other Solar System objects, for two main reasons. First, these ephemerides are tied to optical and radar observations of planetary motion, and the TDB time scale is fitted so that Newton's laws of motion, with corrections for general relativity, are followed. Next, the time scales based on Earth's rotation are not uniform and therefore, are not suitable for predicting the motion of bodies in the Solar System. + +== Versions == +UT1 is the principal form of Universal Time. However, there are also several other infrequently used time standards that are referred to as Universal Time, which agree within 0.03 seconds of UT1: + +UT0 is Universal Time determined at an observatory by observing the diurnal motion of stars or extragalactic radio sources, and also from ranging observations of the Moon and artificial Earth satellites. The location of the observatory is considered to have fixed coordinates in a terrestrial reference frame (such as the International Terrestrial Reference Frame) but the position of the rotational axis of the Earth wanders over the surface of the Earth; this is known as polar motion. UT0 does not contain any correction for polar motion, while UT1 does include them. The difference between UT0 and UT1 is on the order of a few tens of milliseconds. The designation UT0 is no longer in common use. +UT1R is a smoothed version of UT1, filtering out periodic variations due to tides. It includes 62 smoothing terms, with periods ranging from 5.6 days to 18.6 years. UT1R is still in use in the technical literature but rarely used elsewhere. +UT2 is a smoothed version of UT1, filtering out periodic seasonal variations. It is mostly of historic interest and rarely used anymore. It is defined by where t is the time as a fraction of the Besselian year. + +== See also == + +Airy mean time on Mars +Earth orientation parameters +List of international common standards +Unix time + +== Notes == + +== Citations == + +== References == +"Common Units and Conversions in Earth Orientation". IERS Rapid Service / Prediction Center, U.S. Naval Observatory. Retrieved 16 June 2022. +Arias, E. F.; Guinot, B.; Quinn, T. J. (29 May 2003). Rotation of the Earth and Time scales (PDF). ITU-R Special Rapporteur Group Colloquium on the UTC Time Scale. +"Earth Rotation Variations Due to Zonal Tides". Paris: Earth Orientation Center. Retrieved 2 October 2011. +Galison, Peter (2003). Einstein's clocks, Poincaré's maps: Empires of time. New York: W.W. Norton & Co. ISBN 0-393-02001-0. Discusses the history of time standardization. +Guinot, Bernard (July 2011). "Solar time, legal time, time in use". Metrologia. 48 (4): S181–S185. Bibcode:2011Metro..48S.181G. doi:10.1088/0026-1394/48/4/S08. S2CID 121852011. +HM Nautical Almanac Office (April 2015). "World Time Zone Map". Archived from the original on 3 May 2014. Retrieved 11 April 2015. +Howse, Derek (1980). Greenwich Time and the discovery of the longitude. Oxford Univ Press. pp. 154–5.. Names have not been updated. +Howse, Derek (1997). Greenwich Time and the Longitude. Phillip Wilson. ISBN 0-85667-468-0. +McCarthy, Dennis D. (July 1991). "Astronomical Time" (PDF). Proceedings of the IEEE. 79 (7): 915–920. doi:10.1109/5.84967. Archived (PDF) from the original on 9 October 2022. +McCarthy, Dennis; Seidelmann, P. Kenneth (2009). TIME—From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-40780-4. +O'Malley, Michael (1996). Keeping watch: A history of American time. Washington DC: Smithsonian. ISBN 1-56098-672-7. +Seidelmann, P. Kenneth (1992). Explanatory supplement to the Astronomical Almanac. Mill Valley, California: University Science Books. ISBN 0-935702-68-7. +Urban, Sean; Seidelmann, P. Kenneth, eds. (2013). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, California: University Science Books. +"UT1R". International Earth Rotation and Reference System Service. Retrieved 6 March 2013. +"Terrestrial Time (TT)". Astronomical Applications Department. United States Naval Observatory. Retrieved 16 June 2022. + This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 22 January 2022. + +== External links == +Time Lord by Clark Blaise: a biography of Sanford Fleming and the idea of standard time \ No newline at end of file