Jews are called to fast from sunup to sundown.
http://www.torah.org/learning/yomtov/yomkippur/vol1no39.htmlThe day after Rosh HaShana, the third day of Tishrei, is the Fast of Gedalya. The Gemora in Rosh HaShana explains that we first see this fast mentioned in Zecharia 8:19, when the verse speaks about "...the fast of the seventh...." As the seventh month (starting from Nissan) is the month of Tishrei, the fast mentioned in that verse is referring to Tzom Gedalya, the third day of Tishrei. (See #s 27 and 30 for more information on this verse.) On this day, the Gemora says, Gedalya ben Achikam was killed by Yishmael ben Nesania. The Gemora concludes that this fast teaches us that the death of a righteous person is on par with the burning and destruction of the Holy Temple.