# Solar time

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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. [1]

## Introduction

A tall pole vertically fixed in the ground casts a shadow on any sunny day. At one moment during the day, the shadow will point exactly north or south (or disappear when and if the Sun moves directly overhead). That instant is local apparent noon, or 12:00 local apparent time. About 24 hours later the shadow will again point north–south, the Sun seeming to have covered a 360-degree arc around Earth's axis. When the Sun has covered exactly 15 degrees (1/24 of a circle, both angles being measured in a plane perpendicular to Earth's axis), local apparent time is 13:00 exactly; after 15 more degrees it will be 14:00 exactly.

The problem is that in September the Sun takes less time (as measured by an accurate clock) to make an apparent revolution than it does in December; 24 "hours" of solar time can be 21 seconds less or 29 seconds more than 24 hours of clock time. This change is quantified by the equation of time, and is due to the eccentricity of Earth's orbit (as in, Earth's orbit is not perfectly circular, meaning that the EarthSun distance varies throughout the year), and the fact that Earth's axis is not perpendicular to the plane of its orbit (the so-called obliquity of the ecliptic).

The effect of this is that a clock running at a constant 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. [2] 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. [3]

## Apparent solar time

The apparent sun is the true sun as seen by an observer on Earth. [4] Apparent solar time or true solar time [lower-alpha 1] 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. [5] [6] Apparent solar time can be crudely measured by a sundial. The equivalent on Mars is termed Mars local true solar time (LTST). [7] [8]

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.

Length of apparent solar day (1998) [9]
DateDuration in mean solar time
February 1124 hours
March 2624 hours − 18.1 seconds
May 1424 hours
June 1924 hours + 13.1 seconds
July 25/2624 hours
September 1624 hours − 21.3 seconds
November 2/324 hours
December 2224 hours + 29.9 seconds

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

## Mean solar time

Mean solar time is the hour angle of the mean Sun plus 12 hours. This 12 hour offset comes from the decision to make each day start at midnight for civil purposes, whereas the hour angle or the mean sun is measured from the local meridian. [10] 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. [11] :68,326 [12] 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. [13] An apparent solar day can be 20 seconds shorter or 30 seconds longer than a mean solar day. [9] [14] 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 [15]

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

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, [16] a gnomon in China dated 2300 BC, [17] and an Egyptian sundial dated 1500 BC [18] 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. [19] 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. [20]

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. [11] :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 SI seconds, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time. [21] [11] :227–231)

## Notes

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:
• Vince, Samuel (1797). A Complete System Of Astronomy Vol 1. Cambridge University Press. p. 44. What we call apparent time the French call true
• "Comprendre - Concepts fondamentaux - Echelles de temps". Bureau des Longitudes (in French). November 23, 2009. Archived from the original on November 23, 2009. temps vrai [true time]
• Allison, Michael; Schmunk, Robert (June 30, 2015). "Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock". Goddard Institute for Space Studies . National Aeronautics and Space Administration. Archived from the original on September 25, 2015. Retrieved October 8, 2015. the solar hour angle or True Solar Time (TST)

## Related Research Articles

In precise timekeeping, ΔT is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of International Atomic Time. Formally, ΔT is the time difference ΔT = TT − UT between Universal Time and Terrestrial Time. The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day which are dealt with separately.

The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set "due west". This occurs twice each year, around 20 March and 23 September.

Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.

A time standard is a specification for measuring time: either the rate at which time passes or points in time or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

Universal Time 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. UT1 is the same everywhere on Earth. UT1 is required to follow the relationship

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.

In astronomy, the ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

Sidereal time 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".

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

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.

The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconciliation of a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Apparent solar time can be obtained by measurement of the current position of the Sun, as indicated by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.

The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. 1, and has been significantly updated in 1994 and 2009.

The apparent place of an object is its position in space as seen by an observer. Because of physical and geometrical effects it may differ from the "true" or "geometric" position.

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise.

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km (2,900 mi) from Earth's centre, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.

In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. Although there are two such intersections, the equinox associated with the Sun's ascending node is used as the conventional origin of celestial coordinate systems and referred to simply as "the equinox". In contrast to the common usage of spring/vernal and autumnal equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

A tropical year or solar year 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.

Coordinated Universal Time or UTC is the primary time standard globally used to regulate clocks and time. It establishes a reference for the current time, forming the basis for civil time and time zones. UTC facilitates international communication, navigation, scientific research, and commerce.

Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.

## References

1. For the three kinds of time, see (for example) the explanatory section in the almanac Connaissance des Temps for 1902, page 759 Archived August 10, 2011, at the Wayback Machine .
2. "solar time, mean". Glossary, Astronomical Almanac Online. Her Majesty's Nautical Almanac Office and the United States Naval Observatory. 2021.
3. "Leap Seconds". Time Service Department, United States Naval Observatory. 1999. Archived from the original on March 12, 2015.
4. Tatum, J.B. (March 27, 2022). "Celestial Mechanics Chapter 6" (PDF). University of Victoria. Archived (PDF) from the original on September 23, 2015.
5. "solar time, apparent". Glossary, Astronomical Almanac Online. Her Majesty's Nautical Almanac Office and the United States Naval Observatory. 2021.
6. Yallop, B. D.; Hohenker, C. Y. (August 1989). "Astronomical Information Sheet No. 58" (PDF). HM Nautical Almanac Office. Solar Location Diagram.
7. Allison, Michael; Schmunk, Robert (June 30, 2015). "Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock". Goddard Institute for Space Studies . National Aeronautics and Space Administration. Archived from the original on September 25, 2015. Retrieved October 8, 2015.
8. Allison, Michael; McEwen, Megan (2000). "A post-Pathfinder evaluation of areocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies". Planetary and Space Science. 48 (2–3): 215. Bibcode:2000P&SS...48..215A. doi:10.1016/S0032-0633(99)00092-6. hdl:. S2CID   123014765. Archived from the original on June 23, 2015.
9. Jean Meeus (1997), Mathematical astronomy morsels (Richmond, VA: Willmann-Bell) 346. ISBN   0-943396-51-4.
10. Hilton, James L; McCarthy, Dennis D. (2013). "Precession, Nutation, Polar Motion, and Earth Rotation". In Urban, Sean E.; Seidelmann, P. Kenneth (eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. ISBN   978-1-891389-85-6.
11. McCarthy, D. D.; Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGa. ISBN   978-3-527-40780-4.
12. Capitaine, N.; Wallace, P. T.; McCarthy, D. D. (2003). "Expressions to implement the IAU 2000 definition of UT1". Astronomy and Astrophysics. 406 (3): 1135–1149. Bibcode:2003A&A...406.1135C. doi:. S2CID   54008769. (or in pdf form); and for some earlier definitions of UT1 see Aoki, S.; Guinot, B.; Kaplan, G. H.; Kinoshita, H.; McCarthy, D. D.; Seidelmann, P. K. (1982). "The new definition of universal time". Astronomy and Astrophysics. 105 (2): 359–361. Bibcode:1982A&A...105..359A.
13. For a discussion of the slight changes that affect the mean solar day, see the ΔT article.
14. Ricci, Pierpaolo. "The duration of the true solar day". pierpaoloricci.it. Archived from the original on August 26, 2009.
15. Meeus, J. (1998). Astronomical Algorithms. 2nd ed. Richmond VA: Willmann-Bell. p. 183.
16. "A Walk Through Time - Early Clocks". A Walk Through Time - The Evolution of Time Measurement through the Ages. National Institute of Standards and Technology. August 12, 2009.
17. Li, Geng (2015). "Gnomons in Ancient China". In Ruggles, C. (ed.). Handbook of Archaeoastronomy and Ethnoastronomy. pp. 2095–2104. Bibcode:2015hae..book.2095L. doi:10.1007/978-1-4614-6141-8_219. ISBN   978-1-4614-6140-1.
18. Vodolazhskaya, L.N. (2014). "Reconstruction of ancient Egyptian sundials" (PDF). Archaeoastronomy and Ancient Technologies. 2 (2): 1–18. arXiv:.
19. Pingree, David; Reiner, Erica (1974). "A Neo-Babylonian Report on Seasonal Hours". Archiv für Orientforschung. 25: 50–55. ISSN   0066-6440. JSTOR   41636303.
20. Neugebauer, Otto (1975), A History of Ancient Mathematical Astronomy, New York / Heidelberg / Berlin: Springer-Verlag, pp. 984–986, ISBN   978-0-387-06995-1
21. (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 "Time Scales", by L. Essen Archived October 19, 2008, at the Wayback Machine , in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".