The positions of members of our Solar System may best be specified in the ecliptic coordinate system (see Figure 4) since this uses the plane of the ecliptic as the fundamental plane and most members of the Solar System move in orbits close to it. The reference direction is that of the vernal equinox, as in the equatorial system. This is an obvious choice because it lies along the line of intersection of the planes of the Earth's equator and the ecliptic. The ecliptic longitude is the angle measured in the ecliptic round from the vernal equinox in the same sense as that in which the right ascension is measured, and the ecliptic latitude is the angle up from the ecliptic, positive if to the north, or ‘above’ the ecliptic, and negative if to the south, or ‘below’ the ecliptic.

The subroutine EQECL converts coordinates between the ecliptic and equatorial systems. The angles to be converted are input via the variables X (ecliptic longitude or right ascension) and Y (ecliptic latitude or declination), with the results output via P (right ascension or ecliptic longitude) and Q (declination or ecliptic latitude). The formulae are not quite symmetrical in the two pairs of coordinates so that the direction of conversion needs to be specified with a switch.