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Equinox (celestial coordinates)

January 08, 2023

This article is about the celestial coordinate system. For the moment when the Sun is positioned directly over Earth's equator, see Equinox.

In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator.[1][2][3] 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.

In a cycle of about 25,800 years, the equinox moves westward with respect to the celestial sphere because of perturbing forces; therefore, in order to define a coordinate system, it is necessary to specify the date for which the equinox is chosen. This date should not be confused with the epoch. Astronomical objects show real movements such as orbital and proper motions, and the epoch defines the date for which the position of an object applies. Therefore, a complete specification of the coordinates for an astronomical object requires both the date of the equinox and of the epoch.[4]

The currently used standard equinox and epoch is J2000.0, which is January 1, 2000 at 12:00 TT. The prefix "J" indicates that it is a Julian epoch. The previous standard equinox and epoch was B1950.0, with the prefix "B" indicating it was a Besselian epoch. Before 1984 Besselian equinoxes and epochs were used. Since that time Julian equinoxes and epochs have been used.[5]

Motion of the equinox

 
The precession of the equinox

The equinox moves, in the sense that as time progresses it is in a different location with respect to the distant stars. Consequently, star catalogs over the years, even over the course of a few decades, will list different ephemerides.[6] This is due to precession and nutation, both of which can be modeled, as well as other minor perturbing forces which can only be determined by observation and are thus tabulated in astronomical almanacs.

Precession

Precession of the equinox was first noted by Hipparchus in 129 BC, when noting the location of Spica with respect to the equinox and comparing it to the location observed by Timocharis in 273 BC.[7] It is a long term motion with a period of 25,800 years.

Nutation

Nutation is the oscillation of the ecliptic plane. It was first observed by James Bradley as a variation in the declination of stars. Bradley published this discovery in 1748. Because he did not have an accurate enough clock, Bradley was unaware of the effect of nutation on the motion of the equinox along the celestial equator, although that is in the present day the more significant aspect of nutation.[8] The period of oscillation of the nutation is 18.6 years.

Equinoxes and epochs

Besselian equinoxes and epochs

A Besselian epoch, named after German mathematician and astronomer Friedrich Bessel (1784–1846), is an epoch that is based on a Besselian year of 365.242198781 days, which is a tropical year measured at the point where the Sun's longitude is exactly 280°. Since 1984, Besselian equinoxes and epochs have been superseded by Julian equinoxes and epochs. The current standard equinox and epoch is J2000.0, which is a Julian epoch.

Besselian epochs are calculated according to:

B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781

The previous standard equinox and epoch were B1950.0, a Besselian epoch.

Since the right ascension and declination of stars are constantly changing due to precession, astronomers always specify these with reference to a particular equinox. Historically used Besselian equinoxes include B1875.0, B1900.0, B1925.0 and B1950.0. The official constellation boundaries were defined in 1930 using B1875.0.

Julian equinoxes and epochs

A Julian epoch is an epoch that is based on Julian years of exactly 365.25 days. Since 1984, Julian epochs are used in preference to the earlier Besselian epochs.

Julian epochs are calculated according to:

J = 2000.0 + (Julian date − 2451545.0)/365.25

The standard equinox and epoch currently in use are J2000.0, which corresponds to January 1, 2000 12:00 Terrestrial Time.

J2000.0

The J2000.0 epoch is precisely Julian date 2451545.0 TT (Terrestrial Time), or January 1, 2000, noon TT. This is equivalent to January 1, 2000, 11:59:27.816 TAI or January 1, 2000, 11:58:55.816 UTC.

Since the right ascension and declination of stars are constantly changing due to precession, (and, for relatively nearby stars due to proper motion), astronomers always specify these with reference to a particular epoch. The earlier epoch that was in standard use was the B1950.0 epoch.

When the mean equator and equinox of J2000 are used to define a celestial reference frame, that frame may also be denoted J2000 coordinates or simply J2000. This is different from the International Celestial Reference System (ICRS): the mean equator and equinox at J2000.0 are distinct from and of lower precision than ICRS, but agree with ICRS to the limited precision of the former. Use of the "mean" locations means that nutation is averaged out or omitted. This means that the Earth's rotational North pole does not point quite at the J2000 celestial pole at the epoch J2000.0; the true pole of epoch nutates away from the mean one. The same differences pertain to the equinox.[9]

The "J" in the prefix indicates that it is a Julian equinox or epoch rather than a Besselian equinox or epoch.

Equinox of Date

There is a special meaning of the expression "equinox (and ecliptic/equator) of date". This reference frame is defined by the positions of the ecliptic and the celestial equator as of the date/epoch on which the position of something else (typically a solar system object) is being specified.[10]

Other equinoxes and their corresponding epochs

Other equinoxes and epochs that have been used include:

Epochs and equinoxes for orbital elements are usually given in Terrestrial Time, in several different formats, including:

  • Gregorian date with 24-hour time: 2000 January 1, 12:00 TT
  • Gregorian date with fractional day: 2000 January 1.5 TT
  • Julian day with fractional day: JDT 2451545.0
  • NASA/NORAD's Two-line elements format with fractional day: 00001.50000000

Sidereal time and the equation of the equinoxes

Sidereal time is the hour angle of the equinox. However, there are two types: if the mean equinox is used (that which only includes precession), it is called mean sidereal time; if the true equinox is used (the actual location of the equinox at a given instant), it is called apparent sidereal time. The difference between these two is known as the equation of the equinoxes, and is tabulated in the Astronomical Almanac.[12]

A related concept is known as the equation of the origins, which is the arc length between the Celestial Intermediate Origin and the equinox. Alternatively, the equation of the origins is the difference between the Earth Rotation Angle and the apparent sidereal time at Greenwich.

Diminishing role of the equinox in astronomy

In modern astronomy the ecliptic and the equinox are diminishing in importance as required, or even convenient, reference concepts. (The equinox remains important in ordinary civil use, in defining the seasons, however.) This is for several reasons. One important reason is that it is difficult to be precise what the ecliptic is, and there is even some confusion in the literature about it.[13] Should it be centered on the Earth's center of mass, or on the Earth-Moon barycenter?

Also with the introduction of the International Celestial Reference Frame, all objects near and far are put fundamentally in relationship to a large frame based on very distant fixed radio sources, and the choice of the origin is arbitrary and defined for the convenience of the problem at hand. There are no significant problems in astronomy where the ecliptic and the equinox need to be defined.[14]

References

  1. ^ Astronomical Almanac for the Year 2019. Washington, DC: United States Naval Observatory. 2018. p. M6. ISBN 978-0-7077-41925.
  2. ^ Barbieri, Cesare (2007). Fundamentals of Astronomy. New York: Taylor and Francis Group. p. 31. ISBN 978-0-7503-0886-1.
  3. ^ "IAU Nomenclature for Fundamental Astronomy". Paris Observatory. 2007. Retrieved December 23, 2018.
  4. ^ Seidelmann, P. Kenneh, ed. (1998). Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books. p. 12. ISBN 978-0-935702-68-2.
  5. ^ Montenbruck, Oliver; Pfleger, Thomas (2005). Astronomy on the Personal Computer, p. 20 (corrected 3rd printing of 4th ed.). ISBN 9783540672210. Retrieved January 23, 2019.
  6. ^ Chartrand, Mark R. (1991). The Audubon Society Field Guide to the Night Sky. New York: Alfred A. Knopf. p. 53. Bibcode:1991asfg.book.....C. ISBN 978-0-679-40852-9.
  7. ^ Barbieri, Cesare (2007). Fundamentals of Astronomy. New York: Taylor and Francis Group. p. 71. ISBN 978-0-7503-0886-1.
  8. ^ Barbieri, Cesare (2007). Fundamentals of Astronomy. New York: Taylor and Francis Group. p. 72. ISBN 978-0-7503-0886-1.
  9. ^ Hilton, J. L.; Hohenkerk, C. Y. (2004). "Rotation matrix from the mean dynamical equator and equinox at J2000.0 to the ICRS". Astronomy & Astrophysics. 413 (2): 765–770. Bibcode:2004A&A...413..765H. doi:10.1051/0004-6361:20031552.
  10. ^ Seidelmann, P. K.; Kovalevsky, J. (September 2002). "Application of the new concepts and definitions (ICRS, CIP and CEO) in fundamental astronomy". Astronomy & Astrophysics. 392 (1): 341–351. doi:10.1051/0004-6361:20020931. ISSN 0004-6361.
  11. ^ Perryman, M.A.C.; et al. (1997). "The Hipparcos Catalogue". Astronomy & Astrophysics. 323: L49–L52. Bibcode:1997A&A...323L..49P.
  12. ^ Astronomical Almanac for the Year 2019. Washington, DC: United States Naval Observatory. 2018. p. B21–B24,M16. ISBN 978-0-7077-41925.
  13. ^ Barbieri, Cesare (2007). Fundamentals of Astronomy. New York: Taylor and Francis Group. p. 74. ISBN 978-0-7503-0886-1.
  14. ^ Capitaine, N.; Soffel, M. (2015). "On the definition and use of the ecliptic in modern astronomy". Proceedings of the Journées 2014 "Systèmes de référence spatio-temporels": Recent developments and prospects in ground-based and space astrometry. pp. 61–64. arXiv:1501.05534. ISBN 978-5-9651-0873-2.

External links

    January 08, 2023
    equinox, celestial, coordinates, this, article, about, celestial, coordinate, system, moment, when, positioned, directly, over, earth, equator, equinox, astronomy, equinox, either, places, celestial, sphere, which, ecliptic, intersects, celestial, equator, alt. This article is about the celestial coordinate system For the moment when the Sun is positioned directly over Earth s equator see Equinox In astronomy an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator 1 2 3 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 In a cycle of about 25 800 years the equinox moves westward with respect to the celestial sphere because of perturbing forces therefore in order to define a coordinate system it is necessary to specify the date for which the equinox is chosen This date should not be confused with the epoch Astronomical objects show real movements such as orbital and proper motions and the epoch defines the date for which the position of an object applies Therefore a complete specification of the coordinates for an astronomical object requires both the date of the equinox and of the epoch 4 The currently used standard equinox and epoch is J2000 0 which is January 1 2000 at 12 00 TT The prefix J indicates that it is a Julian epoch The previous standard equinox and epoch was B1950 0 with the prefix B indicating it was a Besselian epoch Before 1984 Besselian equinoxes and epochs were used Since that time Julian equinoxes and epochs have been used 5 Contents 1 Motion of the equinox 1 1 Precession 1 2 Nutation 2 Equinoxes and epochs 2 1 Besselian equinoxes and epochs 2 2 Julian equinoxes and epochs 2 2 1 J2000 0 2 3 Equinox of Date 2 4 Other equinoxes and their corresponding epochs 3 Sidereal time and the equation of the equinoxes 4 Diminishing role of the equinox in astronomy 5 References 6 External linksMotion of the equinox Edit The precession of the equinox The equinox moves in the sense that as time progresses it is in a different location with respect to the distant stars Consequently star catalogs over the years even over the course of a few decades will list different ephemerides 6 This is due to precession and nutation both of which can be modeled as well as other minor perturbing forces which can only be determined by observation and are thus tabulated in astronomical almanacs Precession Edit Precession of the equinox was first noted by Hipparchus in 129 BC when noting the location of Spica with respect to the equinox and comparing it to the location observed by Timocharis in 273 BC 7 It is a long term motion with a period of 25 800 years Nutation Edit Nutation is the oscillation of the ecliptic plane It was first observed by James Bradley as a variation in the declination of stars Bradley published this discovery in 1748 Because he did not have an accurate enough clock Bradley was unaware of the effect of nutation on the motion of the equinox along the celestial equator although that is in the present day the more significant aspect of nutation 8 The period of oscillation of the nutation is 18 6 years Equinoxes and epochs EditBesselian equinoxes and epochs Edit A Besselian epoch named after German mathematician and astronomer Friedrich Bessel 1784 1846 is an epoch that is based on a Besselian year of 365 242198781 days which is a tropical year measured at the point where the Sun s longitude is exactly 280 Since 1984 Besselian equinoxes and epochs have been superseded by Julian equinoxes and epochs The current standard equinox and epoch is J2000 0 which is a Julian epoch Besselian epochs are calculated according to B 1900 0 Julian date 2415020 31352 365 242198781The previous standard equinox and epoch were B1950 0 a Besselian epoch Since the right ascension and declination of stars are constantly changing due to precession astronomers always specify these with reference to a particular equinox Historically used Besselian equinoxes include B1875 0 B1900 0 B1925 0 and B1950 0 The official constellation boundaries were defined in 1930 using B1875 0 Julian equinoxes and epochs Edit A Julian epoch is an epoch that is based on Julian years of exactly 365 25 days Since 1984 Julian epochs are used in preference to the earlier Besselian epochs Julian epochs are calculated according to J 2000 0 Julian date 2451545 0 365 25The standard equinox and epoch currently in use are J2000 0 which corresponds to January 1 2000 12 00 Terrestrial Time J2000 0 Edit The J2000 0 epoch is precisely Julian date 2451545 0 TT Terrestrial Time or January 1 2000 noon TT This is equivalent to January 1 2000 11 59 27 816 TAI or January 1 2000 11 58 55 816 UTC Since the right ascension and declination of stars are constantly changing due to precession and for relatively nearby stars due to proper motion astronomers always specify these with reference to a particular epoch The earlier epoch that was in standard use was the B1950 0 epoch When the mean equator and equinox of J2000 are used to define a celestial reference frame that frame may also be denoted J2000 coordinates or simply J2000 This is different from the International Celestial Reference System ICRS the mean equator and equinox at J2000 0 are distinct from and of lower precision than ICRS but agree with ICRS to the limited precision of the former Use of the mean locations means that nutation is averaged out or omitted This means that the Earth s rotational North pole does not point quite at the J2000 celestial pole at the epoch J2000 0 the true pole of epoch nutates away from the mean one The same differences pertain to the equinox 9 The J in the prefix indicates that it is a Julian equinox or epoch rather than a Besselian equinox or epoch Equinox of Date Edit There is a special meaning of the expression equinox and ecliptic equator of date This reference frame is defined by the positions of the ecliptic and the celestial equator as of the date epoch on which the position of something else typically a solar system object is being specified 10 Other equinoxes and their corresponding epochs Edit Other equinoxes and epochs that have been used include The Bonner Durchmusterung started by Friedrich Wilhelm August Argelander uses B1855 0 The Henry Draper Catalog uses B1900 0 Constellation boundaries were defined in 1930 along lines of right ascension and declination for the B1875 0 epoch Occasionally non standard equinoxes have been used such as B1925 0 and B1970 0 The Hipparcos Catalog uses the International Celestial Reference System ICRS coordinate system which is essentially clarification needed equinox J2000 0 but uses an epoch of J1991 25 For objects with a significant proper motion assuming that the epoch is J2000 0 leads to a large position error Assuming that the equinox is J1991 25 leads to a large error for nearly all objects 11 Epochs and equinoxes for orbital elements are usually given in Terrestrial Time in several different formats including Gregorian date with 24 hour time 2000 January 1 12 00 TT Gregorian date with fractional day 2000 January 1 5 TT Julian day with fractional day JDT 2451545 0 NASA NORAD s Two line elements format with fractional day 00001 50000000Sidereal time and the equation of the equinoxes EditSidereal time is the hour angle of the equinox However there are two types if the mean equinox is used that which only includes precession it is called mean sidereal time if the true equinox is used the actual location of the equinox at a given instant it is called apparent sidereal time The difference between these two is known as the equation of the equinoxes and is tabulated in the Astronomical Almanac 12 A related concept is known as the equation of the origins which is the arc length between the Celestial Intermediate Origin and the equinox Alternatively the equation of the origins is the difference between the Earth Rotation Angle and the apparent sidereal time at Greenwich Diminishing role of the equinox in astronomy EditIn modern astronomy the ecliptic and the equinox are diminishing in importance as required or even convenient reference concepts The equinox remains important in ordinary civil use in defining the seasons however This is for several reasons One important reason is that it is difficult to be precise what the ecliptic is and there is even some confusion in the literature about it 13 Should it be centered on the Earth s center of mass or on the Earth Moon barycenter Also with the introduction of the International Celestial Reference Frame all objects near and far are put fundamentally in relationship to a large frame based on very distant fixed radio sources and the choice of the origin is arbitrary and defined for the convenience of the problem at hand There are no significant problems in astronomy where the ecliptic and the equinox need to be defined 14 References Edit Astronomical Almanac for the Year 2019 Washington DC United States Naval Observatory 2018 p M6 ISBN 978 0 7077 41925 Barbieri Cesare 2007 Fundamentals of Astronomy New York Taylor and Francis Group p 31 ISBN 978 0 7503 0886 1 IAU Nomenclature for Fundamental Astronomy Paris Observatory 2007 Retrieved December 23 2018 Seidelmann P Kenneh ed 1998 Explanatory Supplement to the Astronomical Almanac Mill Valley CA University Science Books p 12 ISBN 978 0 935702 68 2 Montenbruck Oliver Pfleger Thomas 2005 Astronomy on the Personal Computer p 20 corrected 3rd printing of 4th ed ISBN 9783540672210 Retrieved January 23 2019 Chartrand Mark R 1991 The Audubon Society Field Guide to the Night Sky New York Alfred A Knopf p 53 Bibcode 1991asfg book C ISBN 978 0 679 40852 9 Barbieri Cesare 2007 Fundamentals of Astronomy New York Taylor and Francis Group p 71 ISBN 978 0 7503 0886 1 Barbieri Cesare 2007 Fundamentals of Astronomy New York Taylor and Francis Group p 72 ISBN 978 0 7503 0886 1 Hilton J L Hohenkerk C Y 2004 Rotation matrix from the mean dynamical equator and equinox at J2000 0 to the ICRS Astronomy amp Astrophysics 413 2 765 770 Bibcode 2004A amp A 413 765H doi 10 1051 0004 6361 20031552 Seidelmann P K Kovalevsky J September 2002 Application of the new concepts and definitions ICRS CIP and CEO in fundamental astronomy Astronomy amp Astrophysics 392 1 341 351 doi 10 1051 0004 6361 20020931 ISSN 0004 6361 Perryman M A C et al 1997 The Hipparcos Catalogue Astronomy amp Astrophysics 323 L49 L52 Bibcode 1997A amp A 323L 49P Astronomical Almanac for the Year 2019 Washington DC United States Naval Observatory 2018 p B21 B24 M16 ISBN 978 0 7077 41925 Barbieri Cesare 2007 Fundamentals of Astronomy New York Taylor and Francis Group p 74 ISBN 978 0 7503 0886 1 Capitaine N Soffel M 2015 On the definition and use of the ecliptic in modern astronomy Proceedings of the Journees 2014 Systemes de reference spatio temporels Recent developments and prospects in ground based and space astrometry pp 61 64 arXiv 1501 05534 ISBN 978 5 9651 0873 2 External links EditCelestial Coordinate System UTKPortals Astronomy Stars Spaceflight Outer space Solar System Retrieved from https en wikipedia org w index php title Equinox celestial coordinates amp oldid 1130748854, wikipedia, wiki, book, books, library,

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