A solar eclipse can occur only when the New Moon occurs close to one of the points (known as nodes) where the Moon's orbit crosses the ecliptic-hence the name.
The Moon's orbit around the Earth is inclined at an angle of just over 5 degrees to the plane of the Earth's orbit around the Sun (the ecliptic). Because of this, at the time of a New Moon, the Moon will usually pass above or below the Sun. A solar eclipse can occur only when the New Moon occurs close to one of the points (known as nodes) where the Moon's orbit crosses the ecliptic-hence the name.
Motion of the Moon and Earth
The Moon's orbit is also elliptical, which means that the distance of the Moon from the Earth can vary by about 6% from its average value. This means that the apparent size of the Moon is sometimes larger or smaller than average, and it is this effect that leads to the difference between total and annular eclipses (the distance of the Earth from the Sun also varies during the year, but this is a smaller effect). On average, the Moon appears to be slightly smaller than the Sun, so the majority (about 60%) of central eclipses are annular. It is only when the Moon is closer to the Earth than average (near its perigee) that a total eclipse occurs.
The Moon orbits the Earth in approximately 27.3 days, relative to a fixed frame of reference. This is known as the sidereal month. However, during one sidereal month, the Earth has moved on in its orbit around the Sun. This means that the average time between one New Moon and the next is longer, and is approximately 29.6 days. This is known as the synodic month, and corresponds to what is commonly called the lunar month.
The Moon crosses from south to north of the ecliptic at its ascending node. However, the nodes of the Moon's orbit are gradually moving in a retrograde motion, due the the action of the Sun's gravity on the Moon's motion, and they make a complete circuit every 18.5 years. This means that the time between each passage of the Moon through the ascending node is slightly shorter than the sidereal month. This period is called the draconitic month.
Finally, the Moon's perigee is moving forwards in its orbit, and makes a complete circuit in about 9 years. The time between one perigee and the next is known as the anomalistic month.
Frequency of Solar Eclipses
The Moon's orbit intersects with the ecliptic at the two nodes that are 180 degrees apart. Therefore, the New Moon occurs close to the nodes at two periods of the year approximately six months apart, and there will always be at least one solar eclipse during these periods. Sometimes the New Moon occurs close enough to a node during two consecutive months. This means that in any given year, there will always be at least two solar eclipses, and there can be as many as five. However, some are visible only as partial eclipses, because the umbra passes either above or below the earth, and others are central only in remote regions of the arctic or antarctic.
Path of an Eclipse
During a central eclipse, the Moon's umbra (or antumbra, in the case of an annular eclipse) moves rapidly from west to east across the Earth. The Earth is also rotating from west to east, but the umbra always moves faster than any given point on the Earth's surface, so it almost always appears to move in a roughly west-east direction across a map of the Earth (there are some rare exceptions to this which can occur during an eclipse of the midnight sun in arctic or antarctic regions).
The width of the track of a central eclipse varies according to the relative apparent diameters of the Sun and Moon. In the most favourable circumstances, when a total eclipse occurs very close to perigee, the track can be over 250 km wide and the duration of totality may be over 7 minutes. Outside of the central track, a partial eclipse can usually be seen over a much larger area of the Earth.