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Galactic coordinate system
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The galactic coordinate system (GCS) is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane.[1]
Spherical coordinates
[edit]Galactic longitude
[edit]
Longitude (symbol l) measures the angular distance of an object eastward along the galactic equator from the Galactic Center. Analogous to terrestrial longitude, galactic longitude is usually measured in degrees (°).
Galactic latitude
[edit]Latitude (symbol b) measures the angle of an object northward of the galactic equator (or midplane) as viewed from Earth. Analogous to terrestrial latitude, galactic latitude is usually measured in degrees.
Definition
[edit]The first galactic coordinate system was used by William Herschel in 1785. A number of different coordinate systems, each differing by a few degrees, were used until 1932, when Lund Observatory assembled a set of conversion tables that defined a standard galactic coordinate system based on a galactic north pole at RA 12h 40m, dec +28° (in the B1900.0 epoch convention) and a 0° longitude at the point where the galactic plane and equatorial plane intersected.[1]
In 1958, the International Astronomical Union (IAU) defined the galactic coordinate system in reference to radio observations of galactic neutral hydrogen through the hydrogen line, changing the definition of the Galactic longitude by 32° and the latitude by 1.5°.[1] In the equatorial coordinate system, for equinox and equator of 1950.0, the north galactic pole is defined at right ascension 12h 49m, declination +27.4°, in the constellation Coma Berenices, with a probable error of ±0.1°.[2] Longitude 0° is the great semicircle that originates from this point along the line in position angle 123° with respect to the equatorial pole. The galactic longitude increases in the same direction as right ascension. Galactic latitude is positive towards the north galactic pole, with a plane passing through the Sun and parallel to the galactic equator being 0°, whilst the poles are ±90°.[3] Based on this definition, the galactic poles and equator can be found from spherical trigonometry and can be precessed to other epochs; see the table.
| Right ascension | Declination | Constellation | ||||
| North Pole +90° latitude |
12h 51.4m | +27.13° | Coma Berenices (near 31 Com) | |||
| South Pole −90° latitude |
0h 51.4m | −27.13° | Sculptor (near NGC 288) | |||
| Center 0° longitude |
17h 45.6m | −28.94° | Sagittarius (in Sagittarius A) | |||
| Anticenter 180° longitude |
5h 45.6m | +28.94° | Auriga (near HIP 27180) | |||
| ||||||
The IAU recommended that during the transition period from the old, pre-1958 system to the new, the old longitude and latitude should be designated lI and bI while the new should be designated lII and bII.[3] This convention is occasionally seen.[4]
Radio source Sagittarius A*, which is the best physical marker of the true Galactic Center, is located at 17h 45m 40.0409s, −29° 00′ 28.118″ (J2000).[2] Rounded to the same number of digits as the table, 17h 45.7m, −29.01° (J2000), there is an offset of about 0.07° from the defined coordinate center, well within the 1958 error estimate of ±0.1°. Due to the Sun's position, which currently lies 56.75±6.20 ly north of the midplane, and the heliocentric definition adopted by the IAU, the galactic coordinates of Sgr A* are latitude +0° 07′ 12″ south, longitude 0° 04′ 06″. Since as defined the galactic coordinate system does not rotate with time, Sgr A* is actually decreasing in longitude at the rate of galactic rotation at the sun, Ω, approximately 5.7 milliarcseconds per year (see Oort constants).
Conversion between equatorial and galactic coordinates
[edit]An object's location expressed in the equatorial coordinate system can be transformed into the galactic coordinate system. In these equations, α is right ascension, δ is declination. NGP refers to the coordinate values of the north galactic pole and NCP to those of the north celestial pole.[5]
The reverse (galactic to equatorial) can also be accomplished with the following conversion formulas.
Where:
Rectangular coordinates
[edit]In some applications use is made of rectangular coordinates based on galactic longitude and latitude and distance. In some work regarding the distant past or future the galactic coordinate system is taken as rotating so that the x-axis always goes to the centre of the galaxy.[6]
There are two major rectangular variations of galactic coordinates, commonly used for computing space velocities of galactic objects. In these systems the xyz-axes are designated UVW, but the definitions vary by author. In one system, the U axis is directed toward the Galactic Center (l = 0°), and it is a right-handed system (positive towards the east and towards the north galactic pole); in the other, the U axis is directed toward the galactic anticenter (l = 180°), and it is a left-handed system (positive towards the east and towards the north galactic pole).[7]
In the constellations
[edit]The galactic equator runs through the following constellations:[8]
See also
[edit]
Wikimedia Commons has media related to Galactic coordinate system.
- Galactic quadrant – One of four circular sectors of the Milky Way galaxy
- Supergalactic coordinate system – Astronomical coordinate system
- Astronomical coordinate systems – System for specifying positions of celestial objects
- Galaxy formation and evolution – Subfield of cosmology
- Milky Way – Galaxy containing the Solar System
References
[edit]- ^ a b c d Blaauw, A.; Gum, C.S.; Pawsey, J.L.; Westerhout, G. (1960). "The new IAU system of galactic coordinates (1958 revision)". Monthly Notices of the Royal Astronomical Society. 121 (2): 123. Bibcode:1960MNRAS.121..123B. doi:10.1093/mnras/121.2.123.
- ^ a b Reid, M.J.; Brunthaler, A. (2004). "The Proper Motion of Sagittarius A*". The Astrophysical Journal. 616 (2): 874, 883. arXiv:astro-ph/0408107. Bibcode:2004ApJ...616..872R. doi:10.1086/424960. S2CID 16568545.
- ^ a b James Binney, Michael Merrifield (1998). Galactic Astronomy. Princeton University Press. pp. 30–31. ISBN 0-691-02565-7.
- ^ For example in Kogut, A.; et al. (1993). "Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps". Astrophysical Journal. 419: 1. arXiv:astro-ph/9312056. Bibcode:1993ApJ...419....1K. doi:10.1086/173453.
- ^ Carroll, Bradley; Ostlie, Dale (2007). An Introduction to Modern Astrophysics (2nd ed.). Pearson Addison-Wesley. pp. 900–901. ISBN 978-0805304022.
- ^ For example Bobylev, Vadim V. (March 2010). "Searching for Stars Closely Encountering with the Solar System". Astronomy Letters. 36 (3): 220–226. arXiv:1003.2160. Bibcode:2010AstL...36..220B. doi:10.1134/S1063773710030060. S2CID 118374161.
- ^ Johnson, Dean R.H.; Soderblom, David R. (1987). "Calculating galactic space velocities and their uncertainties, with an application to the Ursa Major group". Astronomical Journal. 93: 864. Bibcode:1987AJ.....93..864J. doi:10.1086/114370.
- ^ "SEDS Milky Way Constellations".
External links
[edit]- Universal coordinate converter Archived 2004-10-17 at the Wayback Machine.
- Galactic Coordinate System - Wolfram Demonstration
- Galactic coordinates, The Internet Encyclopedia of Science
- Fiona Vincent, Positional Astronomy: Galactic coordinates Archived 2012-09-10 at the Wayback Machine, University of St Andrews
- An Atlas of the Universe
| Location | Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow (→) may be read as "within" or "part of". |  | |||||
|---|---|---|---|---|---|---|---|
| Structure |
| ||||||
| Satellite galaxies | |||||||
| Related | |||||||
Galactic coordinate system
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Fundamentals
Definition and purpose
The galactic coordinate system is a spherical coordinate framework used in astronomy to specify positions of celestial objects relative to the structure of the Milky Way galaxy. It is centered on the Sun, with the fundamental plane defined as the galactic plane—the approximate midplane of the Milky Way's disk—and the north galactic pole positioned perpendicular to this plane. Longitude zero is defined as the direction toward the galactic center in the constellation Sagittarius, enabling a natural alignment with the galaxy's overall geometry. This system was formally defined by the International Astronomical Union (IAU) in its 1958 revision to standardize galactic mapping.[5] The primary purpose of the galactic coordinate system is to facilitate observations and analyses of the Milky Way's internal structure, including the distribution of stars, gas clouds, and other components, as well as studies of galactic dynamics and evolution. Unlike equatorial coordinates, which are tied to Earth's orbit and rotation, or ecliptic coordinates aligned with the solar system's plane, galactic coordinates provide a galaxy-centric perspective that simplifies the interpretation of phenomena such as spiral arms, the galactic bulge, and the disk's thickness. By referencing the galactic plane and center, astronomers can more effectively model the three-dimensional architecture of our galaxy and track motions relative to its rotation.[5][8] Key reference points in the system, transformed to the J2000.0 epoch, include the north galactic pole at right ascension 12h 51.4m and declination +27.13°, and the zero longitude direction toward the galactic center at right ascension 17h 45.6m and declination −28.94°. These positions ensure consistency across observations and are derived from the original IAU definition adjusted for precession and frame changes.[8][5] Visual representations of the system often depict a grid of galactic longitude and latitude lines superimposed on panoramic views of the Milky Way, highlighting how the coordinates curve along the galaxy's disk and converge at the poles and center for intuitive spatial orientation.[8]Historical development
The concept of a galactic plane emerged in the late 18th century through William Herschel's systematic star counts across the sky, which suggested the Milky Way formed a flattened disk-like structure with the Sun positioned near its center.[9] This pioneering effort laid the groundwork for coordinate systems aligned with the galaxy's geometry, though limited by the assumption that star density directly indicated distance.[10] In the 1920s, Harlow Shapley advanced this understanding by analyzing the distribution of globular clusters, determining that the galactic center lay in the direction of Sagittarius and that the Sun was offset by approximately 50,000 light-years from the center.[11] Shapley's work shifted the reference frame away from a Sun-centered model and highlighted the need for coordinates tied to the true galactic structure. Around the same period, Bertil Lindblad contributed to the theoretical foundation by proposing models of differential galactic rotation, influencing early efforts to define a consistent coordinate plane.[12] The first formalized galactic coordinate system, based on optical observations of the Milky Way, was established in 1932 by astronomers at Lund Observatory, providing conversion tables between equatorial and galactic systems.[13] The advent of radio astronomy in the 1950s revealed discrepancies in the 1932 system, as neutral hydrogen mapping at 21 cm wavelength showed the optical plane was tilted due to interstellar dust obscuring visible light toward the galactic center.[8] This prompted the International Astronomical Union (IAU) to adopt a revised system in 1958, defined using radio data to align with the hydrogen distribution; the North Galactic Pole was set at right ascension 12h 49m and declination +27.4° in the B1950.0 epoch, with the zero longitude point toward the galactic center near Sagittarius A. In 1984, the system was updated to the J2000.0 epoch under the FK5 framework, incorporating refined precession models and radio-derived positions for greater accuracy, including the North Galactic Pole at right ascension 12h 51m 26.282s and declination +27° 07′ 42.01″. Subsequent refinements have been minor, primarily addressing precessional effects, while the European Space Agency's Gaia mission, launched in 2013, has integrated high-precision astrometry to enhance the realization of the coordinate frame, enabling sub-milliarcsecond accuracy in positions and proper motions across the galaxy.[14]Spherical coordinates
Galactic longitude
Galactic longitude, denoted as , is an angular coordinate in the galactic coordinate system that specifies the azimuthal position of a celestial object eastward along the galactic equator from the direction to the galactic center. It is measured in degrees, ranging from 0° to 360°, and increases counterclockwise when viewed from the north galactic pole. The reference direction for is precisely defined as the line from the Sun to the galactic center, corresponding to the position of Sagittarius A* in the constellation Sagittarius. This definition was established by the International Astronomical Union (IAU) in 1958 to standardize measurements based on radio observations of neutral hydrogen.[5][15] Key reference points along the galactic equator highlight its orientation relative to the galaxy's structure: points toward the direction of the galaxy's rotation, in the constellation Cygnus; marks the galactic anticenter in Auriga; and aligns with the anti-rotation direction toward Vela. These positions divide the sky into four galactic quadrants, facilitating the mapping of galactic features. Galactic longitude must be distinguished from analogous coordinates in other systems, such as ecliptic longitude, to ensure accurate interpretation in astronomical catalogs and observations.[16][17][4] In relation to galactic structure, longitude values trace major components like spiral arms, providing insight into the Milky Way's morphology. For instance, the Scutum-Centaurus arm is prominent at longitudes near , while the Perseus arm extends across longitudes around in the inner quadrants. Such alignments aid in studying density waves and star formation regions without requiring exhaustive listings of all features.[18] The longitude arises from the projection of a position vector onto the galactic plane in spherical coordinates. In the associated Cartesian system—origin at the Sun, with the positive X-axis toward the galactic center (), positive Y-axis in the direction of galactic rotation (), and positive Z-axis toward the north galactic pole—the longitude is given bywhere is the two-argument arctangent function yielding values from 0° to 360°, and are the components in the galactic plane after projection (i.e., excluding the Z-component for the azimuthal angle). The complementary coordinate, galactic latitude , measures the perpendicular offset from this plane. The forward transformation from spherical to Cartesian coordinates is
with as the distance from the Sun.[16][2]
Galactic latitude
Galactic latitude, denoted as , is the angular coordinate in the galactic coordinate system that measures the north-south deviation of a celestial object's position from the galactic plane. It ranges from to , with lying in the plane itself, positive values extending northward toward the north galactic pole (NGP) at , and negative values southward toward the south galactic pole (SGP) at .[19][20] This coordinate is essential for classifying stellar populations within the Milky Way, as it reflects their vertical distribution relative to the galactic plane. Objects with low absolute latitudes (, for example) are typically associated with the thin disk, where young stars, gas, and dust are concentrated; intermediate latitudes () often trace the thicker disk components; while high latitudes () predominantly sample the extended stellar halo, comprising older, metal-poor stars.[21] Near the galactic center at low latitudes (, ), populations include the dense bulge, rich in intermediate-age stars.[22] The definition of the galactic plane, and thus the zero point for latitude, has evolved through observations of star counts and neutral hydrogen (HI) surveys. Early determinations relied on optical star counts to approximate the plane's symmetry, but radio HI mapping in the mid-20th century refined it by tracing the distribution of interstellar gas more accurately. The International Astronomical Union (IAU) formalized the system in 1958, placing the NGP at right ascension , declination (B1950.0 epoch), based on integrated HI emission profiles that minimized latitude asymmetry.[23][24] In all-sky maps projected in galactic coordinates, latitude manifests as parallel arcs orthogonal to the galactic equator, illustrating the Milky Way's band-like structure concentrated near . The equator crosses prominent constellations such as Sagittarius (where the galactic center lies at ), Scorpius, and Aquila, with the band widening and dimming at higher latitudes due to increasing distance and lower stellar density.[25] These visualizations highlight how latitude delineates the galaxy's vertical structure, from the dusty plane to the sparse polar caps.Cartesian coordinates
Definition and components
The Galactic Cartesian coordinate system extends the spherical galactic coordinates into a three-dimensional rectangular framework, facilitating vector-based representations of positions within the Milky Way. This heliocentric system places its origin at the solar system barycenter (approximating the Sun's position), with the X-axis directed positively toward the Galactic Center, the Y-axis aligned with the direction of the Galaxy's rotation at 90 degrees from the X-axis in the galactic plane, and the Z-axis oriented perpendicular to that plane toward the North Galactic Pole. It adheres to a right-handed convention, ensuring consistent orientation for mathematical operations in galactic studies.[26] The axes are precisely defined relative to the spherical galactic coordinates: the positive X direction corresponds to galactic longitude , latitude (toward the Galactic Center); the positive Y direction aligns with , (the rotational direction); and the positive Z direction points to (the North Galactic Pole). Positions are expressed as (X, Y, Z) with distances measured in parsecs (pc) or kiloparsecs (kpc), enabling quantitative analysis of spatial distributions. In this framework, the Sun resides at (0, 0, 0), while the Galactic Center lies approximately at (8.0, 0, 0) kpc, implying the Sun's offset from the center is -8.0 kpc along the X-axis in galactocentric coordinates.[26][27][28] This system is widely employed in galactic dynamics for modeling stellar orbits, computing velocity fields, and constructing three-dimensional maps of interstellar matter and star clusters, as it simplifies calculations involving forces and motions perpendicular to the galactic plane. The Cartesian components are derived from spherical galactic coordinates (l, b, and radial distance d) through standard orthogonal projections, converting angular positions into linear vectors without altering the underlying reference frame.[27][7][29]Relation to spherical coordinates
The relation between spherical galactic coordinates—consisting of galactic longitude , galactic latitude , and distance from the Sun—and the corresponding Cartesian coordinates is given by the standard transformations for spherical systems in Euclidean space: where the origin is at the Sun, the -axis points toward the galactic center, the -axis aligns with the direction of galactic rotation, and the -axis points toward the north galactic pole.[27] The inverse transformations, which derive the spherical coordinates from the Cartesian ones, are: These formulas assume a local Euclidean geometry around the Sun, providing an accurate representation for nearby stars and structures within the solar neighborhood.[27] However, at large distances (beyond a few kiloparsecs), the approximations break down due to the Galaxy's disk-like curvature, thickness variations, and overall non-Euclidean structure, which introduce distortions in the coordinate mapping.[30] As an example, consider a star at , , and pc. Substituting into the forward equations yields pc, pc, and pc, illustrating the projection of the spherical position onto the Cartesian frame.Coordinate transformations
From equatorial to galactic
The transformation from equatorial to galactic coordinates is achieved through a rotation of the reference frame, standardized by the International Astronomical Union (IAU) for the J2000.0 epoch. This rotation aligns the equatorial system, defined by the Earth's equator and vernal equinox, with the galactic system, which is oriented toward the Milky Way's plane and center. The process relies on a fixed 3x3 orthogonal rotation matrix , derived from the positions of the North Galactic Pole (NGP) and the ascending node where the galactic plane crosses the celestial equator. The NGP is located at right ascension and declination in J2000.0 equatorial coordinates, while the node (defining galactic longitude ) is at .[31] The rotation matrix for converting from J2000.0 equatorial (FK5) Cartesian coordinates to galactic Cartesian coordinates is given by: This matrix, which ensures the galactic z-axis points toward the NGP and the x-axis toward the galactic center, was originally computed by accounting for precession from the B1950.0 system to J2000.0 using the IAU 1976 precession model and equinox corrections.[8] To perform the conversion, first transform the input equatorial spherical coordinates (in radians) to a unit Cartesian vector in the equatorial system: Next, apply the rotation matrix to obtain the galactic Cartesian vector: Finally, convert the galactic Cartesian vector back to spherical coordinates for galactic longitude (ranging from to ) and latitude (ranging from to ): where returns values in the appropriate quadrant, and all angles are converted to degrees as needed. This intermediate Cartesian step facilitates the linear rotation while preserving the unit sphere geometry.[8] For coordinates not in the J2000.0 epoch, precession must be applied first to adjust to J2000.0 using models such as the IAU 2000 precession-nutation framework, as the rotation matrix is epoch-specific and assumes fixed orientations at J2000.0. Software libraries like Astropy implement this full pipeline, allowing direct transformation via methods such asSkyCoord.transform_to(Galactic()), which internally handles the matrix multiplication and epoch adjustments for precision astronomy applications.[32]