Eclipses occur when one body passes in front of another and the shadow of the first falls on the second. If you stand in front of the TV when your sister is trying to watch her favorite program you are eclipsing her.
The ancient astrologers predicted eclipses by looking for cycles. Eclipses have cyclic properties. The ancients considered eclipses to be very bad and they often tried hard to predict them. Unfortunately if the king's astrologer got the day wrong of an eclipse, he would probably have his head cut off!
In modern times we have measured the orbits of the planets around the Sun and our Moon around the Earth. We can predict the position of a planet or a moon with great accuracy using algebra and geometry. You can download programs from the Internet that could predict the positions of the Earth and the Moon relative to the Sun and to predict when the next eclipse will occur. --
You can find some free astronomy software here but I don't think one that tells you about the next eclipse.
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