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Encyclopedia > Tropical year

A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). The precise length of time depends on which point of the ecliptic one chooses: starting from the (northern) vernal equinox, one of the four cardinal points along the ecliptic, yields the vernal equinox year; averaging over all starting points on the ecliptic yields the mean tropical year. By ancient tradition, the Sun is the light in the heavens whose presence is day and whose absence is night. ... Earth, also known as the Earth, Terra, and (mostly in the 19th century) Tellus, is the third planet outward from the Sun. ... The plane of the Ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... In astronomy and navigation, the celestial sphere is an imaginary rotating sphere of gigantic radius, concentric with the Earth. ... Illumination of Earth by Sun on the day of equinox In astronomy, the vernal equinox (spring equinox, March equinox, or northward equinox) is the moment when the sun appears to cross the celestial equator, heading northward. ...


On Earth, we notice the progress of the tropical year from the slow motion of the Sun from south to north and back; the word "tropical" is derived from Greek tropos meaning "turn". The tropics of Cancer and Capricorn mark the extreme north and south latitudes the Sun reaches during this cycle. The position of the Sun can be measured by the variation from day to day of the length of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most "natural" way of measuring the year in the sense that the variations of insolation drive the seasons. The tropics are the geographic region of the Earth centered on the equator and limited in latitude by the two tropics: the Tropic of Cancer in the north and the Tropic of Capricorn in the southern hemisphere. ... A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... The Tropic of Cancer (cancer (♋) is Latin for crab), one of the five major circles of latitude that mark maps of the Earth, is the parallel of latitude that runs 23° 26 22 north of the Equator. ... The Tropic of Capricorn is one of the five major circles of latitude that mark maps of the Earth. ... Latitude, denoted by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ... The gnomon is the part of a sundial which casts the shadow. ...


Because the vernal equinox moves back along the ecliptic due to precession, a tropical year is shorter than a sidereal year (in 2000, the difference was 20.409 minutes; it was 20.400 min in 1900). Precession (also called gyroscopic precession) is the phenomenon by which the axis of a spinning object (e. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... This article is about the year 2000. ... 1900 is a common year starting on Monday. ...

Contents


Subtleties

The motion of the Earth in its orbit (and therefore the apparent motion of the Sun among the stars) is not completely regular due to gravitational perturbations by the Moon and planets. Therefore the time between successive passages of a specific point on the ecliptic will vary. Moreover, the speed of the Earth in its orbit varies (because the orbit is elliptic rather than circular). Furthermore, the position of the equinox on the orbit changes due to precession. As a consequence (explained below) the length of a tropical year depends on the specific point that you select on the ecliptic (as measured from, and moving together with, the equinox) that the Sun should return to. In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... It has been suggested that Law of universal gravitation be merged into this article or section. ... Perturbation is a term used in astronomy to describe alterations to an objects orbit caused by gravitational interactions with other bodies. ... Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ... A planet in common parlance is a large object in orbit around a star that is not a star itself. ...


Therefore astronomers defined a mean tropical year, that is an average over all points on the ecliptic; it has a length of about 365.2422 SI days. Besides this, tropical years have been defined for specific points on the ecliptic: in particular the vernal equinox year, that start and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days. The International System of Units (abbreviated SI from the French phrase, Système International dUnités) is the most widely used system of units. ... A day is any of several different units of time. ...


An additional complication: We can measure time either in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks, or dynamical days defined by the motion of the Moon and planets; or in mean "natural" days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean natural day is steadily getting longer as measured by clocks (or conversely, clock days are steadily getting shorter, as measured by a sundial). One must use the mean natural day because the "instantaneous" natural day varies regularly over time, as the equation of time shows. The second (symbol s) is a unit for time, and one of seven SI base units. ... During the course of the year, the time as read from a sundial can run ahead of clock time by as much as 16 min 33 s (around October 31–November 1) or fall behind by as much as 14 min 6 s (around February 11–12). ...


As explained at Error in Statement of Tropical Year, using the value of the "mean tropical year" to refer to the vernal equinox year defined above, is strictly speaking an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year Newcomb-style of 365.2422 SI days. The vernal equinox year of 365.2424 natural days is also important, because it is the basis of most solar calendars, but it is not the "tropical year" of modern astronomers.


The number of natural days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal point of shape changes in the Earth's orbit's happen to almost cancel out.


In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2422 SI days.


Current mean value

At the epoch J2000 (1 January 2000, 12h TT), the mean tropical year was: In astronomy, an epoch is a moment in time for which celestial coordinates or orbital elements are specified. ... This article is about terrestrial time; for other meanings of TT, see TT (disambiguation). ...

365.242 189 670 SI days.

Due to changes in the precession rate and in the orbit of the Earth, there exists a steady change in the length of the tropical year. This can be expressed with a polynomial in time; the linear term is:

−0.000 000 061 62×a days (a in Julian years from 2000),

or about 5 ms/year, which means that 2000 years ago the tropical year was 10 seconds longer. A Julian year is the length of an average year in the Julian calendar, 365. ...


Note: these and following formulae use days of exactly 86400 SI seconds. a is measured in Julian years (365.25 days) from the epoch (2000). The time scale is Terrestrial Time which is based on atomic clocks; this is different from Universal Time, which follows the somewhat unpredictable rotation of the Earth. The (small but accumulating) difference (called ΔT) is relevant for applications that refer to time and days as observed from Earth, like calendars and the study of historical astronomical observations such as eclipses. A Julian year is the length of an average year in the Julian calendar, 365. ... This article is about terrestrial time; for other meanings of TT, see TT (disambiguation). ... Universal Time (UT) is a timescale based on the rotation of the Earth. ... Delta T and delta-T are ASCII substitutes for the formal ΔT, which is Terrestrial Time minus Universal Time. ... A calendar is a system for naming periods of time, typically days. ... Astronomy is probably the oldest of the natural sciences, dating back to antiquity, with its origins in the religious practices of pre-history: vestiges of these are still found in astrology, a discipline long interwoven with astronomy, and not completely separate from it until about 1750‑1800 in the Western... Total solar eclipse in Zambia, 2001 An eclipse (Greek verb: ecleipo = cease to exist) is an astronomical event that occurs when one celestial object moves into the shadow of another. ...


Different lengths

As already mentioned, there is some choice in the length of the tropical year depending on the point of reference that one selects. The reason is that, while the precession of the equinoxes is fairly steady, the apparent speed of the Sun during the year is not. When the Earth is near the perihelion of its orbit (presently, around January 34), it (and therefore the Sun as seen from Earth) moves faster than average; hence the time gained when reaching the approaching point on the ecliptic is comparatively small, and the "tropical year" as measured for this point will be longer than average. This is the case if one measures the time for the Sun to come back to the southern solstice point (around December 2122), which is close to the perihelion. This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... January 3 is the 3rd day of the year in the Gregorian Calendar. ... January 4 is the 4th day of the year in the Gregorian Calendar. ... Solstice is an astronomical term regarding the position of the Sun in relation to the celestial equator. ... December 21 is the 355th day of the year (356th in leap years) in the Gregorian Calendar. ... December 22 is the 356th day of the year (357th in leap years) in the Gregorian Calendar. ...


Conversely, the northern solstice point presently is near the aphelion, where the Sun moves slower than average. Hence the time gained because this point has approached the Sun (by the same angular arc distance as happens at the southern solstice point) is notably greater: so the tropical year as measured for this point is shorter than average. The equinoctial points are in between, and at present the tropical years measured for these are closer to the value of the mean tropical year as quoted above. As the equinox completes a full circle with respect to the perihelion (in about 21,000 years), the length of the tropical year as defined with reference to a specific point on the ecliptic oscillates around the mean tropical year. This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... Illumination of Earth by Sun on the day of equinox In astronomy, an equinox is defined as the moment when the sun reaches one of two intersections between the ecliptic and the celestial equator. ... Illumination of Earth by Sun on the day of equinox In astronomy, an equinox is defined as the moment when the sun reaches one of two intersections between the ecliptic and the celestial equator. ...


Current values and their annual change of the time of return to the cardinal ecliptic points are [1]:

  • vernal equinox: 365.24237404 + 0.00000010338×a days
  • northern solstice: 365.24162603 + 0.00000000650×a days
  • autumn equinox: 365.24201767 − 0.00000023150×a days
  • southern solstice: 365.24274049 − 0.00000012446×a days

Notice that the average of these four is 365.2422 SI days (the mean tropical year). This figure is currently getting smaller, which means years get shorter, when measured in seconds. Now, actual days get slowly and steadily longer, as measured in seconds. So the number of actual days in a year is decreasing too.


The differences between the various types of year are relatively minor for the present configuration of Earth's orbit. On Mars, however, the differences between the different types of years are an order of magnitude greater: vernal equinox year = 668.5907 Martian days (sols), summer solstice year = 668.5880 sols, autumn equinox year = 668.5940 sols, winter solstice year = 668.5958 sols, with the tropical year being 668.5921 sols [1]. This is due to Mars' considerably greater orbital eccentricity. It should be noted that Earth's orbit goes through cycles of increasing and decreasing eccentricity over a timescale of about 100,000 years (Milankovitch cycles), and its eccentricity can reach as high as about 0.06, so in the distant future, Earth will also have much more divergent values of the various equinox and solstice years. Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... Various schemes have been used or proposed to keep track of time and date on the planet Mars independently of Earth time and calendars. ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... Milankovitch cycles is the name given to the collective effect of changes in the Earths movements upon its climate. ...


Calendar year

This distinction is relevant for calendar studies. The main Christian moving feast has been Easter. Several different ways of computing the date of Easter were used in early christian times, but eventually the unified rule was accepted that Easter would be celebrated on the Sunday after the first full moon on or after the day of the vernal equinox, which was established to fall on 21 March. The church therefore made it an objective to keep the day of the vernal (spring) equinox on or near 21 March, and the calendar year has to be synchronized with the tropical year as measured by the mean interval between vernal equinoxes. From about AD 1000 the mean tropical year (measured in SI days) has become increasingly shorter than this mean interval between vernal equinoxes (measured in actual days), though the interval between successive vernal equinoxes measured in SI days has become increasingly longer. Computus (Latin for computation) is the calculation of the date of Easter in the Christian calendar. ... The Galileo spacecraft took this composite image on 7 December 1992 on its way to explore the Jupiter system in 1995-97. ... March 21 is the 80th day of the year in the Gregorian Calendar (81st in leap years). ...


Now our current Gregorian calendar has an average year of: The Gregorian calendar is the calendar widely used in the Western world. ...

365 + 97/400 = 365.2425 days.

Although it is close to the vernal equinox year (in line with the intention of the Gregorian calendar reform of 1582), it is slightly too long, and not an optimal approximation when considering the continued fractions listed below. Note that the approximation of 365 + 8/33 used in the Iranian calendar is even better, and 365 + 8/33 was considered in Rome and England as an alternative for the Catholic Gregorian calendar reform of 1582. Events January 15 - Russia cedes Livonia and Estonia to Poland February 24 - Pope Gregory XIII implements the Gregorian Calendar. ... The Iranian calendar (also known as Persian calendar or the Jalaali Calendar) is a solar calendar currently used in Iran and Afghanistan. ...


Moreover, modern calculations show that the vernal equinox year has remained between 365.2423 and 365.2424 calendar days (i.e. mean solar days as measured in Universal Time) for the last four millennia and should remain 365.2424 days (to the nearest ten-thousandth of a calendar day) for some millennia to come. This is due to the fortuitous mutual cancellation of most of the factors affecting the length of this particular measure of the tropical year during the current era.


Approximations

Continued fractions of the decimal value for the vernal equinox year quoted above give successive approaches to the average interval between vernal equinoxes, in terms of fractions of a day. These can be used to intercalate years of 365 days with leap years of 366 days to keep the calendar year synchronized with the vernal equinox: Intercalation is the insertioffn of an extra day, week or month into some calendar years to make the calendar follow the seasons. ... A leap year (or intercalary year) is a year containing an extra day or month in order to keep the calendar year in sync with an astronomical or seasonal year. ...

  • 365 (No intercalated days)
  • 365 + 1/4 (Julian intercalation cycle; 1-in-4)
  • 365 + 7/29 (6 × Julian cycle + 1-in-5; 7-in-29)
  • 365 + 8/33 (Khayyam cycle; 7 × 1-in-4 + 1-in-5)
  • 365 + 143/590 (17 × Khayyam cycle + 7-in-29) etc.

Note that 590 years hence, the year length will have changed, postponing the need for any 7-in-29 subcycle.


See also

A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... A Julian year is the length of an average year in the Julian calendar, 365. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... Various schemes have been used or proposed to keep track of time and date on the planet Mars independently of Earth time and calendars. ...

References

[1] Derived from: Jean Meeus (1991), Astronomical Algorithms, Ch.26 p. 166; Willmann-Bell, Richmond, VA. ISBN 0-943396-35-2 ; based on the VSOP-87 planetary ephemeris. Jean Meeus (born 1928) is a Belgian astronomer. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros= daily) was, traditionally, a table providing the positions (given in a Cartesian coordinate system, or in right ascension and declination or, for astrologers, in longitude along the zodiacal ecliptic), of the Sun, the Moon, and the planets in the sky at...

  • Jean Meeus and Denis Savoie, "The history of the tropical year", Journal of the British Astronomical Association 102 (1992) 40–42.[2]

  Results from FactBites:
 
CalendarHome.com - Tropical year - Calendar Encyclopedia (1531 words)
A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere).
As the equinox completes a full circle with respect to the perihelion (in about 21000 years), the length of the tropical year as defined with reference to a specific point on the ecliptic oscillates around the mean tropical year.
This is due to the fortuitous mutual cancellation of most of the factors affecting the length of this particular measure of the tropical year during the current era.
  More results at FactBites »

 
 

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