If eclipses occur when the Sun, the Moon and the Earth lie on a straight line, why do they not occur on every new moon and full moon day?

The eclipses of the Sun and the Moon occur during new moon and full moon respectively. A solar eclipse does not occur at every new moon, because the Moon orbits in a plane which is inclined to the ecliptic, the plane of orbit of the Earth around the Sun.

The angle between the planes is about five degrees and hence the Moon can pass well above or below the Sun. The line of intersection of the planes is called the line of nodes.

There are only two points where the Moon’s orbit intersects the ecliptic plane. The nodes move along the orbit from west to east, going completely around the ecliptic in about 19years.

For an eclipse to occur, the Moon has to be near one of the nodes. This does not happen on all new moon and full moon days.