Astronomical background

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The motion of the Moon in its orbit is very complicated and its period is not constant. Moreover, many cultures (most notably those using the ancient Hebrew (Jewish) calendar and the Islamic calendar) start a month with the first appearance of the thin crescent of the new moon after sunset over the western horizon. The date and time of this actual observation depends on the exact geographical longitude as well as latitude, atmospheric conditions, the visual acuity of the observers, etc. Therefore the beginning and lengths of months in these calendars can not be accurately predicted. Most Jews currently follow a precalculated calendar, but the Karaites rely on actual moon observations.