What are the Sidereal, Synodic, Tropical, Anomalistic and Draconic months?
In simple terms these are the periods of time that it takes for the Moon to compete a cycle, traveling from one ‘observable’ reference point, back to the same point. Unfortunately there are a number of different frames of reference, from the perspective of the observer’ and indeed different reference points, and consequently each gives rise to a different type of ‘lunar’ month.
In summary these are:
The actual period of the Moon's orbit as measured in a fixed frame of reference is known as a sidereal month, because it is the time it takes the Moon to return to the same position on the celestial sphere among the fixed stars.
The cause of moon phases is that from the Earth we see the part of the Moon that is illuminated by the Sun from different angles as the Moon traverses its orbit. So the appearance depends on the position of the Moon with respect to the Sun (as seen from the Earth). Because the Earth orbits the Sun, it takes the Moon extra time (after completing a sidereal month, i.e. a full circle) to catch up and return to the same position with respect to the Sun. This longer period is called the synodic month.
It is customary to specify positions of celestial bodies with respect to the vernal equinox. Because of precession, this point moves back slowly along the ecliptic. Therefore it takes the Moon less time to return to an ecliptic longitude of zero than to the same point amidst the fixed stars. This slightly shorter period is known as tropical month; The tropical month of the Moon is the analogous tropical year of the Sun.
Like all orbits, the Moon's is an ellipse rather than a circle. However, the orientation (as well as the shape) of this orbit is not fixed. In particular, the position of the extreme points (the line of the apsides: perigee and apogee), makes a full circle (lunar precession) in about nine years. It takes the Moon longer to return to the same apsis because it moved ahead during one revolution. This longer period is called the anomalistic month. The apparent diameter of the Moon varies with this period, and therefore this type of month has some relevance for the prediction of eclipses, whose extent, duration, and appearance (whether total or annular) depend on the exact apparent diameter of the Moon.
Draconic (or Draconitic) Month
The orbit of the Moon lies in a plane that is tilted with respect to the plane of the ecliptic: it has an inclination of about five degrees. The line of intersection of these planes defines two points on the celestial sphere: the ascending and descending nodes. The plane of the Moon's orbit precesses over a full circle in about 18.6 years, so the nodes move backwards over the ecliptic with the same period. Hence the time it takes the Moon to return to the same node is again shorter than a sidereal month: this is called the draconic or draconitic month. It is important for predicting eclipses: these take place when the Sun, Earth and Moon are on a line. The three bodies are only on a line when the Moon is at one of the nodes. At this time a solar or lunar eclipse is possible. The draconic or draconitic month refers to the mythological dragon that lives in the nodes and regularly eats the Sun or Moon during an eclipse.