Lunar calendar or crescent moons and others employing detailed calculations. Since each lunation is approximately days (29 days, 12 hours, 44 minutes, 3 seconds, or days), it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of twelve such lunations, a lunar year, is only 354 days, 8 hours, 48 minutes, 34 seconds ( days), purely lunar calendars lose around 11 days per year relative to the Gregorian calendar. In purely lunar calendars like the Islamic calendar, the lack of intercalation causes the lunar months to cycle through all the seasons of
Aryabhatiya to modern astronomy and mathematics. Aryabhata asserted that the Moon, planets, and asterisms shine by reflected sunlight, correctly explained the causes of eclipses of the Sun and the Moon, and calculated values for π and the length of the sidereal year that come very close to modern accepted values. His value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is only 3 minutes 20 seconds longer than the modern scientific value of 365 days 6 hours 9 minutes 10 seconds. A close approximation to π is given as: "Add four to one