Lunar calendar average length of the synodic month is days. Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively “"hollow"” and “"full"”). The distribution of "hollow" and "full" months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed: These fractions can be used to construct a lunar calendar, or in combination with a solar calendar
Lunar month month because it is the cycle of the visible phases of the Moon. Most of the following types of lunar month, except the distinction between the sidereal and tropical months, were first recognized in Babylonian lunar astronomy. The period of the Moon's orbit as defined with respect to the celestial sphere of apparently fixed stars (nowadays the International Celestial Reference Frame (ICRF)) is known as a sidereal month because it is the time it takes the Moon to return to a similar position among the stars (): days (27 d 7 h 43 min 11.6 s). This type of month