Equinox (celestial coordinates)

In astronomy, 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 intersections of the ecliptic with the celestial equator, by convention the equinox associated with the sun's ascending node is used as the origin of celestial coordinate systems and referred to simply as the equinox. In contrast to the common usage of spring and fall, or vernal and autumnal, equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

The equinox moves 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 objects 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

Equinox path
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. 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.

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 Astronomical Almanacs.[11]

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.[12] 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.[13]

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 0-935702-68-7.
  5. ^ Astronomy on the Personal Computer, p. 20. Google books. Retrieved July 13, 2007.
  6. ^ Chartrand, Mark R. The Audubon Society Field Guide to the Night Sky. New York: Alfred A. Knopf. p. 53. ISBN 0-679-40852-5.
  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: 765–770. Bibcode:2004A&A...413..765H. doi:10.1051/0004-6361:20031552.
  10. ^ Perryman, M.A.C.; et al. (1997). "The Hipparcos Catalogue". Astronomy & Astrophysics. 323: L49–L52. Bibcode:1997A&A...323L..49P.
  11. ^ Astronomical Almanac for the Year 2019. Washington, DC: United States Naval Observatory. 2018. p. B21-B24,M16. ISBN 978-0-7077-41925.
  12. ^ Barbieri, Cesare (2007). Fundamentals of Astronomy. New York: Taylor and Francis Group. p. 74. ISBN 978-0-7503-0886-1.
  13. ^ 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 (PDF). p. 61-64. ISBN 978-5-9651-0873-2. Retrieved December 23, 2018.

External links

Celestial sphere

In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

The celestial sphere is a practical tool for spherical astronomy, allowing astronomers to specify the apparent positions of objects in the sky if their distances are unknown or irrelevant. In the equatorial coordinate system, the celestial equator divides the celestial sphere into two halves: the northern and southern celestial hemispheres.

Durchmusterung

In astronomy, Durchmusterung or Bonner Durchmusterung (BD), is the comprehensive astrometric star catalogue of the whole sky, compiled by the Bonn Observatory (Germany) from 1859 to 1903.The name comes from Durchmusterung ("run-through examination"), a German word used for a systematic survey of objects or data. The term has sometimes been used for other astronomical surveys, including not only stars but also the search for other celestial objects. Special tasks are the celestial scanning in electromagnetic wavelengths which are shorter or longer than visible light waves.

Ecliptic coordinate system

The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets (except Mercury) and many small Solar System bodies have orbits with 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 (northward) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

First Point of Aries

The First Point of Aries, also known as the Cusp of Aries, is the location of the vernal equinox, used as a reference point in celestial coordinate systems; in diagrams using such coordinate systems, it is often indicated with the symbol ♈︎. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the First Point of Libra, located exactly 180° from it. Due to precession of the equinoxes, currently, the position of the Sun on the March equinox is in Pisces, while that on the September equinox is in Virgo (as of J2000).

Along its yearly path through the zodiac, the Sun meets the celestial equator from south to north at the First Point of Aries, and from north to south at the First Point of Libra. The First Point of Aries is considered to be the celestial "prime meridian" from which right ascension is calculated.

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