4 Ecliptic coordinates

The ICRF provides a fixed coordinate system for computing solar system ephemerides. In some cases it may be convenient to use a coordinate system based on a principal plane of the solar system, e.g. a fixed ecliptic, as used in the past. To be consistent with ICRS and its origin, a fixed ecliptic could be defined as a fixed plane through the origin of the ICRS with a fixed inclination $\varepsilon_0$ equal to the mean obliquity at J2000.0. Its value is $\varepsilon_0 = 23^\circ 26' 21\hbox{$.\!\!^{\prime\prime}$ }4059 \pm 0\hbox{$.\!\!^{\prime\prime}$ }0003$ (Fukushima 2001). Each new ephemeris should define its own ecliptic and mean obliquity on the ICRS axes. The transformation from the ICRS (x, y, z) coordinates to the ecliptic fixed coordinates (X, Y, Z) is:

$$y \cos \varepsilon_0 + z \sin \varepsilon_0$$

$$-y \sin \varepsilon_0 + z \cos \varepsilon_0.$$ (3)

The ecliptic remains a convenient basis for a coordinate system for theories of motion in the solar system and its position as a function of time is to be given as the longitude of the node and inclination on the ICRF equator from the ephemerides being used (each might have its own ecliptic). An equinox, as the intersection of the actual moving ecliptic with the intermediate moving equator (see below), can be defined to compute the times of phenomena.