Editing Solar time

{{Short description|Calculation of elapsed time by the apparent position of the sun}}
{{pp|small=yes}}

{{Use American English|date = April 2019}}
{{Use mdy dates|date=June 2022}}
[[Image:Sidereal day (prograde).svg|right|thumb|300px|On a [[Direct motion|prograde]] planet like the [[Earth]], the [[sidereal time|sidereal day]] is shorter than the '''solar day'''. At time 1, the [[Sun]] and a certain distant [[star]] are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day).  More simply, 1→2 is a complete [[rotation of the Earth]], but because the revolution around the Sun affects the [[angle]] at which the Sun is seen from the Earth, 1→3 is how long it takes [[noon]] to return. [Note that in this diagram, the relative motion, and corresponding angles, are highly exaggerated for illustrative purposes.] ]]

'''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|'''apparent solar time''']] and [[#Mean solar time|'''mean solar time''']] (discussed in this article), and ''[[sidereal time]]'', which is based on the apparent motions of [[star]]s other than the Sun.<ref>For the three kinds of time, see (for example) the explanatory section in the almanac [http://gallica.bnf.fr/ark:/12148/bpt6k210143f.image.f740.langFR ''Connaissance des Temps'' for 1902, page 759] {{webarchive|url=https://web.archive.org/web/20110810025808/http://gallica.bnf.fr/ark:/12148/bpt6k210143f.image.f740.langFR |date=August 10, 2011 }}.</ref>

==Introduction==
[[File:EarthsOrbit_en.png |thumb|The Earth's orbit around the Sun, showing its eccentricity]]

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 [[solar noon|''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 [[Orbital eccentricity|eccentricity]] of Earth's orbit (as in, Earth's orbit is not perfectly circular, meaning that the Earth{{endash}}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{{Snd}}e.g. completing the same number of pendulum swings in each hour{{Snd}}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.<ref>{{cite web|url=https://aa.usno.navy.mil/faq/asa_glossary#solar-time,-mean|work=Glossary, Astronomical Almanac Online|date=2021|publisher=[[Her Majesty's Nautical Almanac Office]] and the [[United States Naval Observatory]]|title=solar time, mean}}</ref> 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 [[International System of Units|SI]] seconds, i.e., about 24.0000006 hours.<ref>{{cite web|url=http://tycho.usno.navy.mil/leapsec.html|title=Leap Seconds|date=1999|website=Time Service Department, United States Naval Observatory|archive-url=https://web.archive.org/web/20150312003149/http://tycho.usno.navy.mil/leapsec.html|archive-date=March 12, 2015}}</ref>

==Apparent solar time==
{{Also|Solar day}}
The '''apparent sun''' is the true sun as seen by an observer on Earth.<ref>{{cite web|url=http://www.astro.uvic.ca/~tatum/celmechs/celm6.pdf|title=Celestial Mechanics Chapter 6|first=J.B.|last=Tatum|website=University of Victoria|archive-url=https://web.archive.org/web/20150923175534/http://www.astro.uvic.ca/~tatum/celmechs/celm6.pdf|date=March 27, 2022|archive-date=September 23, 2015|url-status=live}}</ref> '''Apparent solar time''' or '''true solar time'''{{efn|1= 'apparent' is commonly used in English-language sources, but 'true' is used in French astronomical literature and has become nearly as common in English sources. See:
* {{cite book |last1=Vince |first1=Samuel |title=A Complete System Of Astronomy Vol 1 |date=1797 |publisher=Cambridge University Press |page=44 |url=https://archive.org/details/completesystemof025477mbp/page/44/mode/2up|quote=What we call ''apparent'' time the French call ''true''}}
* {{cite web |title=Comprendre - Concepts fondamentaux - Echelles de temps |url=http://www.bdl.fr/fr/ephemerides/astronomie/Promenade/pages3/325.html#tempsvrai |website=Bureau des Longitudes|language=fr |date=November 23, 2009|archive-url=https://web.archive.org/web/20091123072000/http://www.bdl.fr/fr/ephemerides/astronomie/Promenade/pages3/325.html#tempsvrai |archive-date=November 23, 2009 |quote=''temps vrai'' [true time]}} 
* {{cite web|last1=Allison|first1=Michael|last2=Schmunk|first2=Robert|title=Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock|url=http://www.giss.nasa.gov/tools/mars24/help/notes.html|website=[[Goddard Institute for Space Studies]]|publisher=[[National Aeronautics and Space Administration]]|access-date=October 8, 2015|date=June 30, 2015|url-status=live|archive-url=https://web.archive.org/web/20150925020710/http://www.giss.nasa.gov/tools/mars24/help/notes.html|archive-date=September 25, 2015|quote=the solar hour angle or True Solar Time (TST)}}
}} 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 (astronomy)|meridian]].<ref>{{cite web|url=https://aa.usno.navy.mil/faq/asa_glossary#solar-time,-apparent|work=Glossary, Astronomical Almanac Online|date=2021|publisher=[[Her Majesty's Nautical Almanac Office]] and the [[United States Naval Observatory]]|title=solar time, apparent}}</ref><ref>{{cite web|last1=Yallop|first1=B. D.|last2=Hohenker|first2=C. Y.|date=August 1989|url=https://astro.ukho.gov.uk/nao/aisinfo/ais058.pdf|at=Solar Location Diagram|title=Astronomical Information Sheet No. 58|website=HM Nautical Almanac Office|access-date=June 17, 2022|archive-date=December 23, 2022|archive-url=https://web.archive.org/web/20221223124221/https://astro.ukho.gov.uk/nao/aisinfo/ais058.pdf|url-status=dead}}</ref> Apparent solar time can be crudely measured by a [[sundial]].{{efn|The equivalent on Mars is termed '''Mars local true solar time''' (LTST).<ref>{{cite web|last1=Allison|first1=Michael|last2=Schmunk|first2=Robert|title=Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock|url=http://www.giss.nasa.gov/tools/mars24/help/notes.html|website=[[Goddard Institute for Space Studies]]|publisher=[[National Aeronautics and Space Administration]]|access-date=October 8, 2015|date=June 30, 2015|url-status=live|archive-url=https://web.archive.org/web/20150925020710/http://www.giss.nasa.gov/tools/mars24/help/notes.html|archive-date=September 25, 2015}}</ref><ref>{{cite journal|doi=10.1016/S0032-0633(99)00092-6|url=https://pubs.giss.nasa.gov/abs/al05000n.html|title=A post-Pathfinder evaluation of areocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies|journal=Planetary and Space Science|volume=48|issue=2–3|pages=215|year=2000|last1=Allison|first1=Michael|last2=McEwen|first2=Megan|bibcode=2000P&SS...48..215A|url-status=live|archive-url=https://web.archive.org/web/20150623105917/http://pubs.giss.nasa.gov/abs/al05000n.html|archive-date=June 23, 2015|hdl=2060/20000097895|s2cid=123014765 |hdl-access=free}}</ref>}}

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 [[equinox]]es, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its [[mean motion|average]] for the year; when the Sun is farthest from the equator at both [[solstice]]s, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see [[tropical year]]). 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.

{| class=wikitable
|+ Length of apparent solar day (1998)<ref name=Meeus>Jean Meeus (1997), ''Mathematical astronomy morsels'' (Richmond, VA: Willmann-Bell) 346. {{ISBN|0-943396-51-4}}.</ref>
|-
!Date
!Duration in mean solar time
|-
| February 11 || 24 hours
|-
| March 26 || 24 hours − 18.1 seconds
|-
| May 14 || 24 hours
|-
| June 19 || 24 hours + 13.1 seconds
|-
| July 25/26 || 24 hours
|-
| September 16 || 24 hours − 21.3 seconds
|-
| November 2/3 || 24 hours
|-
| December 22 || 24 hours + 29.9 seconds
|}

These lengths will change slightly in a few years and significantly in thousands of years.

==Mean solar time <span class="anchor" id="Mean time"></span>==
{{Main|Universal Time}}
[[Image:Equation of time.svg|thumb|right|250px|The equation of time—above the x-axis a sundial will appear ''fast'' relative to a clock showing local mean time, and below the axis a sundial will appear ''slow''.]]
'''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.<ref>{{cite book |author1-last=Hilton |author1-first= James L| author2-last=McCarthy| author2-first=Dennis D. | author2-link=Dennis McCarthy (scientist) | chapter = Precession, Nutation, Polar Motion, and Earth Rotation | editor1-last = Urban | editor1-first = Sean E. | editor2-last = Seidelmann | editor2-first = P. Kenneth | title = Explanatory Supplement to the Astronomical Almanac | edition = 3rd | date = 2013 | publisher = University Science Books | location = Mill Valley, CA | isbn=978-1-891389-85-6}}</ref> {{As of|2009}}, this is realized with the [[Universal Time|UT1]] time scale, constructed mathematically from [[very-long-baseline interferometry]] observations of the [[diurnal motion]]s of radio sources located in other galaxies, and other observations.<ref name="time-from-earth-rotation-to-atomic-physics">{{cite book|author-link1=Dennis McCarthy (scientist)|last1=McCarthy|first1=D. D.|last2=Seidelmann|first2=P. K.|date=2009|title=TIME From Earth Rotation to Atomic Physics|location=Weinheim|publisher=[[Wiley-VCH|Wiley-VCH Verlag GmbH & Co. KGa]]|isbn=978-3-527-40780-4}}</ref>{{rp|68,326}}<ref>{{cite journal|author-link1=Nicole Capitaine|last1=Capitaine|first1=N.|last2=Wallace|first2=P. T.|last3=McCarthy|first3=D. D.|date=2003|url=http://www.aanda.org/index.php?option=article&access=bibcode&bibcode=2003A%2526A...406.1135CFUL|title=Expressions to implement the IAU 2000 definition of UT1|journal=Astronomy and Astrophysics|volume=406|issue=3 |pages=1135–1149|doi=10.1051/0004-6361:20030817 |bibcode=2003A&A...406.1135C |s2cid=54008769 |doi-access=free}} (or [http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003A%26A...406.1135C&link_type=ARTICLE&db_key=AST&high= in pdf form]); and for some earlier definitions of UT1 see {{cite journal|last1=Aoki|first1=S.|last2=Guinot|first2=B.|last3=Kaplan|first3=G. H.|last4=Kinoshita|first4=H.|last5=McCarthy|first5=D. D.|last6=Seidelmann|first6=P. K.|date=1982|url=http://articles.adsabs.harvard.edu/full/1982A%26A...105..359A|title=The new definition of universal time|journal=Astronomy and Astrophysics|volume=105|issue=2 |pages=359–361|bibcode=1982A&A...105..359A }}</ref> 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.<ref>For a discussion of the slight changes that affect the mean solar day, see the [[ΔT (timekeeping)|ΔT]] article.</ref> An apparent solar day can be 20 seconds shorter or 30 seconds longer than a mean solar day.<ref name=Meeus/><ref>{{cite web|url=http://www.pierpaoloricci.it/dati/giornosolarevero_eng.htm|title=The duration of the true solar day|first=Pierpaolo|last=Ricci|website=pierpaoloricci.it|archive-url=https://web.archive.org/web/20090826184737/http://www.pierpaoloricci.it/dati/giornosolarevero_eng.htm|archive-date=August 26, 2009|url-status=live}}</ref> 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:

{{blockquote|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''.<ref>Meeus, J. (1998). ''Astronomical Algorithms.'' 2nd ed. Richmond VA: Willmann-Bell. p. 183.</ref>}}

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==
{{See also|History of timekeeping devices}}
[[File:Sun and Moon Nuremberg chronicle.jpg|176px|thumbnail|right|[[Sun]] and [[Moon]], [[Nuremberg Chronicle]], 1493]]
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,<ref>{{cite web |title=A Walk Through Time - Early Clocks |url=https://www.nist.gov/pml/time-and-frequency-division/popular-links/walk-through-time/walk-through-time-early-clocks |work=A Walk Through Time - The Evolution of Time Measurement through the Ages|publisher=[[National Institute of Standards and Technology]] |language=en |date=August 12, 2009}}</ref> a [[gnomon]] in China dated 2300 BC,<ref>{{cite book |last1=Li |first1=Geng |chapter=Gnomons in Ancient China |editor-last=Ruggles |editor-first=C. |title=Handbook of Archaeoastronomy and Ethnoastronomy |date=2015 |pages=2095–2104 |doi=10.1007/978-1-4614-6141-8_219|bibcode=2015hae..book.2095L |isbn=978-1-4614-6140-1 }}</ref> and an Egyptian [[sundial]] dated 1500 BC<ref>{{cite journal|url=http://aaatec.org/documents/article/vl4.pdf|last=Vodolazhskaya|first=L.N.|title=Reconstruction of ancient Egyptian sundials|journal=Archaeoastronomy and Ancient Technologies|date=2014|volume=2|issue=2|pages=1–18|arxiv=1408.0987 }}</ref> are some of the earliest methods for measuring the sun's position.

[[Babylonia]]n astronomers knew that the hours of daylight varied throughout the year. A tablet from 649 BC shows that they used a 2:1 ratio for the longest day to the shortest day, and estimated the variation using a linear zigzag function.<ref>{{cite journal |last1=Pingree |first1=David |last2=Reiner |first2=Erica |title=A Neo-Babylonian Report on Seasonal Hours |journal=Archiv für Orientforschung |date=1974 |volume=25 |pages=50–55 |jstor=41636303 |url=https://www.jstor.org/stable/41636303 |issn=0066-6440}}</ref> 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''.<ref>{{Citation | last = Neugebauer | first = Otto | author-link = Otto Neugebauer | date = 1975 | title = A History of Ancient Mathematical Astronomy | publisher = Springer-Verlag | location = New York / Heidelberg / Berlin | pages = 984–986 | isbn = 978-0-387-06995-1}}</ref> 

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.<ref name="time-from-earth-rotation-to-atomic-physics" />{{rp|9–11}}

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 [[second|SI seconds]], and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.<ref>:(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770 ± 20 cycles), see [http://www.leapsecond.com/history/1968-Metrologia-v4-n4-Essen.pdf "Time Scales", by L. Essen] {{webarchive|url=https://web.archive.org/web/20081019014533/http://www.leapsecond.com/history/1968-Metrologia-v4-n4-Essen.pdf |date=October 19, 2008 }}, in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the [[second|SI second]].  L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".</ref><ref name="time-from-earth-rotation-to-atomic-physics" />{{rp|227–231}})

==See also==
* [[Local mean time]]
* [[Meridian circle]]
* [[Earth rotation]]
* [[Synodic day]]

==Notes==
{{notelist}}

==References==
{{reflist}}

==External links==
*[http://ptaff.ca/soleil/?lang=en_CA Sunrise and Sunset and maximum Sun altitude, all year long, anywhere]
*[http://theorderoftime.org/truetime/solartime.html Astrarium Solar Tempometer]: Apparent solar time in a digital display.

{{Time Topics}}
{{Time measurement and standards}}
{{The Sun}}

[[Category:Time scales]]
[[Category:Day]]
[[Category:Time in astronomy]]