Moon Phases
The Moon orbits Earth about every 29 1/2 days. The cycle begins with a new moon and reaches a full moon half way through the cycle, then begins to recede again until the next new moon.
Solar Eclipses
A solar eclipse only occurs during a new moon. At least twice a year, the orbits of the Moon and Earth line up so part of the Moon's shadow falls somewhere on the Earth's surface and can be seen from that region.
Calculating Solar Eclipses
To calculate a solar eclipse you first plot the orbits of the Moon and Earth to determine when they will align to cast a shadow on Earth. Then you can map the geographic coordinates of the eclipse path to determine where and when the eclipse will be visible.