Does the Eastern Orthodox Church use the Gregorian Calendar?

yes, it does use the Gregorian calendar

http://en.wikipedia.org/wiki/Julian_calendar

The Eastern Orthodox Church does not use the Gregorian Calendar as its primary liturgical calendar. Instead, it follows the Julian Calendar, which was introduced by Julius Caesar in 45 BCE. This calendar was used by both the Western and Eastern civilizations until 1582, when Pope Gregory XIII introduced the Gregorian Calendar to correct inaccuracies in the Julian Calendar.

To determine if a specific date in the Eastern Orthodox Church falls on the Gregorian or Julian Calendar, you can follow these steps:

1. Find the date you're interested in.
2. Determine if it is a fixed or movable feast. Fixed feasts have specific dates each year, while movable feasts depend on the date of Easter, which is determined according to specific rules.
3. If the feast is fixed, it will fall on the same calendar date regardless of the calendar being used. Therefore, it will be the same on both the Gregorian and Julian Calendars.
4. If the feast is movable, you will need to consult a liturgical calendar that indicates which calendar system is being used for that particular feast. This helps you determine if it falls on the Gregorian or Julian Calendar.

Keep in mind that some Eastern Orthodox churches, particularly those that are in communion with the Catholic Church, might use the Gregorian Calendar for civil or administrative purposes but maintain the Julian Calendar for liturgical observances. It is always best to consult the specific practices of the local Eastern Orthodox church you are referring to.