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It is convenient to specify the positions of the sun, moon, and planets in the sky using
a pair of angular coordinates, and , which are measured with respect to the
ecliptic, rather than the celestial equator. Let denote a celestial object, and the
projection of the line onto the plane of the ecliptic, --see Fig. 6. The coordinate , which
is known as *ecliptic latitude*, is the angle subtended between and . Objects north
of the ecliptic plane have positive ecliptic latitudes, and *vice versa*. The coordinate ,
which is known as *ecliptic longitude*, is the angle subtended between and
. Ecliptic longitude increases from west to east (*i.e.*, in the same direction that the sun travels
around the ecliptic). (Again, in this treatise, is measured relative
to the mean equinox at date, unless specified otherwise.)
Note that the basis vectors in the ecliptic coordinate system are
, , and , whereas the corresponding basis vectors in the
celestial coordinate system are
, , and --see Figs. 3 and 5. By analogy with Eqs. (1)-(3), we can write

where is a unit vector which is directed from to .
Hence, it follows from Eqs. (1), (4), and (5) that

These expressions specify the transformation from celestial to ecliptic
coordinates. The inverse transformation follows from Eqs. (2), (3), and (6)-(8):

Figures 15 and 16 show all stars of visible magnitude less than lying
within of the ecliptic. Table 1 gives the ecliptic longitudes, ecliptic latitudes, and
visible magnitudes of a selection
of these stars which lie within of the ecliptic. The figures and table can
be used
to convert ecliptic longitude and latitude into approximate position
in the sky against the backdrop of the fixed stars.

** Next:** Signs of the Zodiac
** Up:** Spherical Astronomy
** Previous:** Ecliptic Circle
Richard Fitzpatrick
2010-07-21