In Majewski et al. 2003 (Paper I) we present the first all-sky view of the tidal streams of the Sgr dwarf as seen in the 2MASS database. Since tidal debris is closely confined to the Sgr orbital plane, in Paper I we introduce a longitudinal coordinate system as illustrated in Fig. 1 below. This coordinate system is an intuitive system in which to study the tidal tails of the dwarf.
The Sgr coordinate system is diagrammed above in Fig. 1 for a Galactic halo for which q = 0.9 (note that the Sgr stream is no longer thought to pass within 10 kpc of the Sun). The origin of the longitudinal coordinate &Lambda is located at the position of the Sun (8.0 kpc from the Galactic Center), and &Lambda = 0 in the direction of the Sgr dwarf core. &Lambda increases clockwise along trailing debris in the Sgr orbital plane as shown. The left-handed Cartesian coordinate system X_Sgr, Y_Sgr, Z_Sgr is also centered on the location of the Sun, with X_Sgr positive in the direction of Sgr, Y_Sgr positive in the direction of &Lambda = 90, and Z_Sgr positive in the direction of the Sagittarius orbital pole located at (l,b) = (273.75,-13.46). The angular coordinate &Beta is the "latitudinal" angle, and is positive in the direction of +Z_Sgr.
Note that there has been some confusion regarding the sign of the Z_SGR and &Beta coordinates. Majewski et al. (2003) used Z_SGR positive in the direction of the antipole (i.e., [l,b]~[93,+13]) and &Beta positive in the direction of the pole. The public transform coordinate code previously available on this website used similar conventions to Majewski et al. (2003). The updated version of the public transform coordinate code now available defines both Z_SGR and &Beta to be positive in the direction of the pole.
A variant of this system is occasionally employed in our papers, which is centered at the Galactic Center. In this frame, the origin of all coordinates is at the Galactic Center, and is rotated about the Sgr plane pole axis by about 14 degrees so that X_Sgr,GC and &Lambda _GC = 0 lie in the Galactic plane. Coordinates in this system are often referred to as (e.g.) &Lambda 4, X4, Y4, Z4, etc.