New moon western horizon shortly after sunset and before moonset. A lunation or synodic month is the average time from one new moon to the next. In the J2000.0 epoch, the average length of a lunation is 29.530588 days (or 29 days, 12 hours, 44 minutes, and 2.8 seconds). However, the length of any one synodic month can vary from 29.26 to 29.80 days due to the perturbing effects of the Sun's gravity on the Moon's eccentric orbit. In a lunar calendar, each month corresponds to a lunation. Each lunar cycle can be assigned a unique lunation number to identify it. The
History of mathematics the Roman Kingdom and included 356 days plus a leap year every other year. In contrast, the lunar calendar of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the solar year, a discrepancy that was solved by adding an extra month into the calendar after the 23rd of February. This calendar was supplanted by the Julian calendar, a solar calendar organized by Julius Caesar (100–44 BC) and devised by Sosigenes of Alexandria to include a leap day every four years in a 365-day cycle. This calendar, which contained an error of 11 minutes and 14 seconds, was