As seen from around the world, the moon will be at or near its last quarter phase on the morning of December 29. At last quarter, the moon appears half-illuminated in sunshine and half-immersed in the moon’s own shadow. The lit side of the waning moon always points eastward – or in the direction of sunrise.
Relative to the backdrop stars of the zodiac, the moon travels its own angular diameter of about 1/2 degree eastward per hour, or approximately 13 degrees eastward per day. For that reason the moon will be closer to Spica on December 30 than it’ll be on December 29.
The last quarter moon happens on December 29 at 9:34 UTC. In U.S. time zones, that places the time of the last quarter moon on December 29 at 4:34 a.m. EST, 3:34 a.m. CST, 2:34 a.m. MST, 1:34 a.m. PST, 12:34 a.m. AKST and on December 28 at 11:34 p.m. HST.
By definition, and in the language of astronomy, the moon at its last quarter phase is at west quadrature – 90 degrees west of the sun in geocentric ecliptic longitude. Technically speaking, the last quarter moon is not exactly 50 percent illuminated at west quadrature, although the lunar disk certainly looks half lit to the eye. Depending on the month, the illuminated portion of last quarter moon varies from 50.117 percent to 50.138 percent.
To be less ambiguous, we could say the moon at the instant that it lies 90 degrees west of the sun is at west quadrature, rather than at last quarter. However, the term last quarter is synonymous with west quadrature, and the term first quarter moon is synonymous with east quadrature.
The moon is exactly half-illuminated at dichotomy, yet a tiny bit more than half-illuminated at quadrature (quarter moon). The moon always reaches dichotomy (50 percent illumination) a short while before its first quarter phase; and the moon always reaches its last quarter phase shortly before dichotomy.
When the moon is at quadrature (first or last quarter) in Earth’s sky, then it’s the Earth that’s at dichotomy in the moon’s sky – and vice versa.
Bottom line: On December 29 and 30, 2018, let the waning moon introduce you to Spica, the brightest star in the constellation Virgo the Maiden.