1. Astronomical Coordinate Systems
Liying Huang
20 May 2011
Astronomical coordinate systems are coordinate systems used in astronomy to describe the location of objects in the sky and in the universe. The most commonly occurring such systems are coordinate systems on the celestial sphere, but extragalactic coordinates systems are also important for describing more distant objects. 1

2. Coordinate systems on the celestial sphere
Horizontal coordinate system
Equatorial coordinate system
Ecliptic coordinate system
Galactic coordinate system

3. Horizontal coordinate system
One of the simplest ways of placing a star on the night sky is the coordinate system based on altitude or azimuth, thus called the Alt-Az or horizontal coordinate system. The reference circles for this system are the horizon and the celestial meridian, both of which may be most easily graphed for a given location using the celestial sphere.
In simplest terms, the altitude is the angle made from the position of the celestial object (e.g. star) to the point nearest it on the horizon. The azimuth is the angle from the northernmost point of the horizon (which is also its intersection with the celestial meridian) to the point on the horizon nearest the celestial object. Usually azimuth is measured eastwards from due north. So east has az=90°, south has az=180°, west has az=270° and north has az=360° (or 0°). An object's altitude and azimuth change as the earth rotates.
HORIZONTAL COORDINATES. Azimuth, from the North point (red) -also from the South point toward the West (blue). Altitude, green.

4. Equatorial coordinate system
based on Earth rotation

5. The equatorial coordinate system is another system that uses two angles to place an object on the sky: right ascension and declination.

6. Ecliptic coordinate system
The ecliptic coordinate system is based on the ecliptic plane, i.e., the plane which contains our Sun and Earth's average orbit around it, which is tilted at 23°26' from the plane of Earth's equator. The great circle at which this plane intersects the celestial sphere is the ecliptic, and one of the coordinates used in the ecliptic coordinate system, the ecliptic latitude, describes how far an object is to ecliptic north or to ecliptic south of this circle. On this circle lies the point of the vernal equinox (also called the first point of Aries); ecliptic longitude is measured as the angle of an object relative to this point to ecliptic east. Ecliptic latitude is generally indicated by φ, whereas ecliptic longitude is usually indicated by λ.
based on Solar System rotation

7. Galactic coordinate system
As a member of the Milky Way Galaxy, we have a clear view of the Milky Way from Earth. Since we are inside the Milky Way, we don't see the galaxy's spiral arms, central bulge and so forth directly as we do for other galaxies. Instead, the Milky Way completely encircles us. We see the Milky Way as a band of faint starlight forming a ring around us on the celestial sphere. The disk of the galaxy forms this ring, and the bulge forms a bright patch in the ring. You can easily see the Milky Way's faint band from a dark, rural location.
Our galaxy defines another useful coordinate system — the galactic coordinate system. This system works just like the others we've discussed. It also uses two coordinates to specify the position of an object on the celestial sphere. The galactic coordinate system first defines a galactic latitude, the angle an object makes with the galactic equator. The galactic equator has been selected to run through the center of the Milky Way's band. The second coordinate is galactic longitude, which is the angular separation of the object from the galaxy's "prime meridian," the great circle that passes through the Galactic center and the galactic poles. The galactic coordinate system is useful for describing an object's position with respect to the galaxy's center. For example, if an object has high galactic latitude, you might expect it to be less obstructed by interstellar dust.
based on Milky Way rotation

8. Extragalactic coordinate systems
4/26/2017
Extragalactic coordinate systems
supergalactic coordinate system
comoving coordinates

9. Supergalactic coordinate system
By convention, supergalactic latitude and supergalactic longitude are usually denoted by SGB and SGL, respectively, by analogy to b and l conventionally used for galactic coordinates. The zero point for supergalactic longitude is defined by the intersection of this plane with the galactic plane.
The north supergalactic pole (SGB=90°) lies at galactic coordinates (l =47.37°, b =+6.32°). In the equatorial coordinate system (epoch J2000), this is approximately (RA=18.9 h, Dec=+15.7°).
The zero point (SGB=0°, SGL=0°) lies at (l=137.37°, b=0°). In J2000 equatorial coordinates, this is approximately (2.82 h, +59.5°).
based on plane of local supercluster of galaxies

11. Summary Table

12. Comoving coordinates
While general relativity allows one to formulate the laws of physics using arbitrary coordinates, some coordinate choices are more natural (e.g. they are easier to work with). Comoving coordinates are an example of such a natural coordinate choice. They assign constant spatial coordinate values to observers who perceive the universe as isotropic. Such observers are called "comoving" observers because they move along with the Hubble flow.
A comoving observer is the only observer that will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer.
Most large lumps of matter, such as galaxies, are nearly comoving, i.e., their peculiar velocities (due to gravitational attraction) are low.
The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time. The comoving spatial coordinates tell us where an event occurs while cosmological time tells us when an event occurs. Together, they form a complete coordinate system, giving us both the location and time of an event.
Space in comoving coordinates is usually referred to as being "static", as most bodies on the scale of galaxies or larger are approximately comoving, and comoving bodies have static, unchanging comoving coordinates. So for a given pair of comoving galaxies, while the proper distance between them would have been smaller in the past and will become larger in the future due to the expansion of space, the comoving distance between them remains constant at all times.
The expanding Universe has an increasing scale factor which explains how constant comoving distances are reconciled with proper distances that increase with time.
valid to particle horizon
This unrealistic "God's Eye" view of the Universe shows a rotating Cosmic Microwave Background, as measured by NASA's WMAP probe, at about 13.8 light years (in comoving coordinates) from us. Shown inside are hundreds of thousands of quasars and galaxies found by the Sloan Digital Sky Survey (SDSS).

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14. References
Astronomical coordinate systems,
Dimitri Mihalas and James Binney. Galactic Astronomy. Structure and Kinematics. Second edition 1981, W.H. Freeman, San Francisco. ISBN
F. Schmeidler, Fundamentals of Spherical Astronomy. Ch. 2 in Compendium of Practical Astronomy, by G.D. Roth (ed.), revised translation of Handbuch für Sternfreunde, 4th edition, p. 9-35, 1994, Spinger Verlag, ISBN
Basics of the supergalactic coordinate system:
K. Fisher Original 3/2006 Rev. 7/17/2006
Dr. Mary Kay Hemenway on the History of Astronomy [HQ]
Comoving Coordinates, wikipedia,2011 14

15. Thank you !!!