Celestial Coordinate Systems

SLALIB has routines to perform transformations of celestial positions between different spherical coordinate systems, including those shown in the following table:

horizon - azimuth elevation horizontal north L

$$\alpha,\delta$$ equatorial R.A. Dec. equator equinox R

$$h,\delta$$ local equ. H.A. Dec. equator meridian L

$$\lambda,\beta$$ ecliptic ecl. long. ecl. lat. ecliptic equinox R

$$l^{I\!I},b^{I\!I}$$ galactic gal. long. gal. lat. gal. equator gal. centre R

supergalactic SGL,SGB SG long. SG lat. SG equator node w. gal. equ. R

Transformations between $[\,h,\delta\,]$ and $[\,Az,El~]$ can be performed by calling sla_E2H and sla_H2E, or, in double precision, sla_DE2H and sla_DH2E. There is also a routine for obtaining zenith distance alone for a given $[\,h,\delta\,]$,sla_ZD, and one for determining the parallactic angle, sla_PA. Three routines are included which relate to altazimuth telescope mountings. For a given $[\,h,\delta\,]$ and latitude, sla_ALTAZ returns the azimuth, elevation and parallactic angle, plus velocities and accelerations for sidereal tracking. The routines sla_PDA2H and sla_PDQ2H predict at what hour angle a given azimuth or parallactic angle will be reached.

The routines sla_EQECL and sla_ECLEQ transform between ecliptic coordinates and $[\,\alpha,\delta\,]$; there is also a routine for generating the equatorial to ecliptic rotation matrix for a given date: sla_ECMAT.

For conversion between Galactic coordinates and $[\,\alpha,\delta\,]$ there are two sets of routines, depending on whether the $[\,\alpha,\delta\,]$ is old-style, B1950, or new-style, J2000; sla_EG50 and sla_GE50 are $[\,\alpha,\delta\,]$ to $[\,l^{I\!I},b^{I\!I}\,]$ and vice versa for the B1950 case, while sla_EQGAL and sla_GALEQ are the J2000 equivalents.

Finally, the routines sla_GALSUP and sla_SUPGAL transform $[\,l^{I\!I},b^{I\!I}\,]$ to de Vaucouleurs supergalactic longitude and latitude and vice versa.

It should be appreciated that the table, above, constitutes a gross oversimplification. Apparently simple concepts such as equator, equinox etc. are apt to be very hard to pin down precisely (polar motion, orbital perturbations ...) and some have several interpretations, all subtly different. The various frames move in complicated ways with respect to one another or to the stars (themselves in motion). And in some instances the coordinate system is slightly distorted, so that the ordinary rules of spherical trigonometry no longer strictly apply.

These caveats apply particularly to the bewildering variety of different $[\,\alpha,\delta\,]$ systems that are in use. Figure 1 shows how some of these systems are related, to one another and to the direction in which a celestial source actually appears in the sky. At the top of the diagram are the various sorts of mean place found in star catalogues and papers; at the bottom is the observed $[\,Az,El~]$, where a perfect theodolite would be pointed to see the source; and in the body of the diagram are the intermediate processing steps and coordinate systems. To help understand this diagram, and the SLALIB routines that can be used to carry out the various calculations, we will look at the coordinate systems involved, and the astronomical phenomena that affect them.

 

Figure 1: Relationship Between Celestial Coordinates