Phases of the Moon in the context of "Periodic function"

In astronomy and celestial navigation, an ephemeris (/ɪˈfɛmərɪs/; pl. ephemerides /ˌɛfəˈmɛrɪˌdiːz/; from Latin ephemeris 'diary', from Ancient Greek ἐφημερίς (ephēmerís) 'diary, journal') is a book with tables that gives the trajectory of naturally occurring astronomical objects and artificial satellites in the sky, i.e., the position (and possibly velocity) over time. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available.

The astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with the distance from the origin if applicable. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary ingresses, sidereal time, positions for the mean and true nodes of the moon, the phases of the Moon, and the positions of minor celestial bodies such as Chiron.

An ecclesiastical full moon is formally the 14th day of the ecclesiastical lunar month (an ecclesiastical moon) in an ecclesiastical lunar calendar. The ecclesiastical lunar calendar spans the year with lunar months of 30 and 29 days which are intended to approximate the observed phases of the Moon. Since a true synodic month has a length that can vary from about 29.27 to 29.83 days, the moment of astronomical opposition tends to be roughly 14.75 days after the previous conjunction of the Sun and Moon (the new moon). The ecclesiastical full moons of the Gregorian lunar calendar tend to agree with the dates of astronomical opposition, referred to a day beginning at midnight at 0 degrees longitude, to within a day or so. However, the astronomical opposition happens at a single moment for the entire Earth: The hour and day at which the opposition is measured as having taken place will vary with longitude. In the ecclesiastical calendar, the 14th day of the lunar month, reckoned in local time, is considered the day of the full moon at each longitude.

Beginning in mediaeval times, the age of the ecclesiastical moon was announced daily at the canonical hour of Prime during the reading of the martyrology. This is still done today by those using the extraordinary form of the Roman Rite, (according to the 1962 Roman Breviary).