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Note, this file was originally found as http://adswww.colorado.edu/adswww/astro_coord.html, but for fast local access this is a copy of the original file.

Coordinates in the astrophysics data system

by Dr. John Good

The purpose of this document is to provide a brief background on the definitions used in astronomy (and in particular within the ADS Project) for time and position. It is not meant to be comprehensive, but rather to jog the memories of those who used to know the material and provide a starting point for those who are new to the subject.

TIME

In order for time to be useful in astronomy, time must be referenced to some absolute zero point. In everyday life, we use the beginning of the year 1 A.D. In astronomy we use instead a reference of noon on 1 Jan 4713 B.C. at what would later become Greenwich, England. This reference was defined in 1582 by Joseph Scaliger (coinciding with the introduction of the Gregorian calendar) and the choice of 4713 B.C. was for reasons that made sense in 1582 but are pretty much meaningless today.

Using a count in seconds from this reference point is a bit extreme, so instead we introduce the concept of the "Julian Day Number". This is defined as the fractional day offset from the zero reference above (a day is still 60x60x24 = 86400 seconds). A couple of important Julian Dates are 


      JD 2451545.0  =  2000 AD Jan 1.5

      JD 2415020.0  =  1900 AD Jan 0.5
(For mathematical simplicity, we start with day "0" rather than "1").

We don't get into trouble until we insist on referencing time to a year or "epoch" since a year is not an integral number of days (or seconds come to that).

As the period of the Earth's orbit became better known, we could with greater and greater accuracy translate the linear time represented by the Julian Date into a fractional year. Thus we derived an "epoch" measure defined as 


      Besselian epoch  =  B[1900 + (JD - 2415020.31352)/365.242198781]
where 365.242198781 is the length of the year in days to a painful degree of accuracy and 2415020.31352 is the JD of a reference point in time. This epoch measure is named after Friederich Bessel (d. 1846), an early pioneer in the measurement of the precise positions and movements of stars.

Being this precise doesn't really make things all that much easier. The Gregorian calendar we use makes corrections at periodic intervals (i.e. leap years) rather than continuously as does the Besselian epoch measure. Thus the Besselian epoch is always somewhat out of sync with the wall calendar (B1950.0 occured at 1950 Jan 0.923).

The astronomical community therefore decided to take a giant step "backwards" beginning in 1984. At that time the Besselian epoch measure was superceded by the simpler "Julian epoch": 


      Julian epoch  =  J[2000 + (JD - 2451545.0)/365.25]
Historical Note: This is based on the calendar introduced by Julius Ceasar in 46 B.C. (46 B.C. had 445 days to correct for accumulated errors) which assumed years of exacly 365.25 days. The Gregorian calendar introduced by Pope Gregory XIII on Thursday, Oct 15 1582 (the previous day had been Wednesday, Oct 4) has years of 365.241 days (leap years every four year minus one every century plus one every millenium).

While the Julian epoch may seem less "accurate", it isn't really. Either epoch measure is only a convenient approximation to our civil calendar and the Julian epoch corresponds as accurately to the wall calendar as the Besselian for the first hundred years or so ("standard epochs" are typically updated every 50 years).

COORDINATES

All astronomical positions are measured on the sky in spherical coordinates. That is, we use some form of latitude, longitude measure for location. Just as on the Earth you can use either the axis of rotation or the magnetic pole as your reference, on the sky there are a number of alternative reference systems.

Horizontal

The first, which is never used for permanent records (though it is used internally for some telescopes) is the horizontal or horizon coordinate system. In this the "latitude" measure is the angular distance of the object above the horizon and the "longitude" is the angle from North to the point on the horizon directly below the source.

This system, which makes measurement very simple, varies depending on the location of the observer on the Earth and, being fixed to the Earth rather than the sky, forces the stars into continuous motion relative the the coordinate system.

Measurements in this coordinate system are usually referred to as "altitude" and "Azimuth" (alt and Az or z and A).

Equatorial

The simplest sky-fixed coordinate system is referenced to the Earth's equator as projected onto the sky. This system is commonly used in the operation of telescopes, where a motor rotates the instrument backwards around an axis aligned with the Earth's pole at a rate exactly equal to the rotation of the planet (i.e. one revolution in exactly 24 hours). This cancels out the Earth's rotation and keeps the telescope fixed on the target.

In this system, latitude is measured from this "celestial equator" (so the pole star is at +90 degrees). Longitude is not measured relative to Earth longitude zero, however, since the corresponding point on the sky keeps changing during the day. Instead, we use the location on the sky of the Sun on the first day of spring (the point where the Sun crosses the equator on it's way north).

Measurements in this coordinate system are referred to a "Right Ascension" (for longitude) and "Declination" (for latitude) (RA and Dec).

Ecliptic

Any plane (or equivalently, pole) can be used to define a coordinate system. For many applications, the plane of the solar system (as defined by the Earth's orbit) is more useful than the Equatorial plane used above.

From an Earth-centered point of view, this plane is defined by the circle the Sun makes as it appears to travel around the sky through the zodiac during the year (the daily motion having been removed). Latitude is measured away from this plane and longitude is measured from the same location as for Equatorial (the place where the Ecliptic and Equatorial planes cross).

Measurements in this coordinate system are referred to as "Ecliptic Latitude" and "Ecliptic Longitude" (Elat and Elon).

Galactic

In recent years much work has been done which views the Galaxy within which we sit as whole. This gives rise to a new coordinate system whose plane is that of the galactic disk and whose reference longitude is the direction to the center of the Galaxy. Since determination of this plane must be based on the observations of distributed matter rather than specific points, it is more prone to error. In fact, there have been two separate attempts at defining galactic coordinates, the first having now been completely superceded.

Latitude is measured away from this "galactic plane" (the Milky Way on the sky) and longitude from what we now know to be the center of the Galaxy.

Measurements in this coordinate system are referred to as "Galactic Latitude" and "Galactic Longitude" (b and l or Glat and Glon).

Others

There are other coordinate systems that can be defined (and sometimes are for special purposes). The only one of these that has enough currency to warrant mention is the "Supergalactic" coordinate system, based on the distribution of other galaxies (just as Galactic coordinates are based on the distribution of stars in our own Galaxy).

PRECESSION OF EQUATORIAL COORDINATES

Equatorial coordinates, which facilitate measurement and are therefore the most commonly used system, suffer from problems caused by variations in the Earth's rotation. As a consequnce of these variations, there is no fixed Equatorial system but instead a family of systems that evolve with time.

The reason for this is that one of the tidal effects of the Sun and moon on the Earth is to cause it's axis to precess like a dying top. The wobble this produces takes about 26,000 years for one cycle but this is enough to cause serious problems in comparing astronomical measurements taken just a few years apart. Since this effect was first observed (Hipparchus, 125 B.C.) as a change in where the Sun crossed the equator (e.g. the position of the vernal "equinox"), it commonly referred to as "Precession of the Equinoxes" and the mathematical procedure we have to go through to mimic or correct the effect is called "precession".

To avoid having to apply precession calculations all the time, we do not usually use the Equatorial coordinates measured as of the date of observation but rather record positions in the Equatorial coordinates of some "standard epoch". Until 1984, this "standard epoch" was commonly B1950.0. As of that point, the official standard is J2000.0. (B1950 and J2000 are time measurements as defined above.)

At the same time that temporal references were changed, the parameters defining precession were revised as well. If you examine the problem closely, it becomes quite complicated. We measure precession based on motion relative to background stars but then we turn around and measure coordinates based in part on calculations of precession.

As early as 1970, it was known that these parameters were in need of refinement. So in 1984, along with the change to using J2000 as a time reference new precessional parameters were introduced. This composite change of time and positional parameters is frequently referred to as the new "J2000 system".

While all equinox epochs are equally valid for measurement, using standard epochs facilitates intercomparison of datasets. Care must be taken however, since some objects are not fixed to the sky but rather have a measureable "proper motion". For these objects, it is not enough to know where they are but which way they are going and how fast. Since this information is only really known for the actual epoch of the observations, transforming to another equinox can be perilous.

COORDINATE CONVERSION

Problems of precession of Equatorial coordinates aside, conversion between coordinate systems is a straightforward matter of axis rotation in three dimensions. Even precession is in essence the same sort of rotation, though one where the rotation angles vary continuously with time.

All of the coordinate system and precession information for converting between coordinate systems (including Equatorial in either system), has been folded into the standard ADS Coordinate Conversion code and is available to be use in or as an adjunct to an service that wishes to do so.

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