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# Ecliptic Coordinates

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
 (8) (9) (10)

where is a unit vector which is directed from to . Hence, it follows from Eqs. (1), (4), and (5) that
 (11) (12)

These expressions specify the transformation from celestial to ecliptic coordinates. The inverse transformation follows from Eqs. (2), (3), and (6)-(8):
 (13) (14)

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