The date (in the northern hemisphere) when night and day are nearly of the same length and Sun crosses the celestial equator (i.e., declination 0) moving southward (in the northern hemisphere).
http://scienceworld.wolfram.com/astronomy/AutumnalEquinox.html
October’s Full Moon is the “Harvest Moon” (English), “Hunter’s Moon” (Native American), “Travel Moon”, “Dying Grass Moon”, “Blood Moon”, or “Sharad Poornima”.
November’s Full Moon is the “Hunter’s Moon” (English), “Beaver Moon” (Native American), “Frost Moon”, “Snow Moon” , or “Kartik Poornima”.
December’s Full Moon is the “Oak Moon”, “Cold Moon”, “Frost Moon”, “Long Night’s Moon”, “Moon Before Yule”, or “Margashira Poornima.
“Considered by many to be the best meteor shower in the heavens, the Geminids are known for producing up to 60 multicolored meteors per hour at their peak. The peak of the shower is on December 13 & 14, although some meteors should be visible from December 6 – 19. This year, a nearly new moon will provide an excellent viewing experience in the early morning hours. The radiant point for this shower will be in the constellation Gemini. Best viewing is usually to the east after midnight.”
http://www.seasky.org/astronomy/astronomy_calendar_2009.html
The winter solstice is the shortest day of the year, respectively, in the sense that the length of time elapsed between sunrise and sunset on this day is a minimum for the year. Of course, daylight saving time means that the first Sunday in April has 23 hours and the last Sunday in October has 25 hours, but these human meddlings with the calendar and do not correspond to the actual number of daylight hours.
http://scienceworld.wolfram.com/astronomy/WinterSolstice.html