New moon and full moon: what a lunar phase actually is
A phase is an angle. Seen from the earth, the moon stands some number of degrees away from the sun, and that separation — nothing belonging to the moon itself — is what the eight familiar names describe. At 0° the moon is new; at 180° it is full; the round trip takes an average of 29.53 days. The moon is half lit at every moment of the journey, and what changes is how much of the lit half is turned toward the earth.
A phase is an angle
The angle between sun and moon, measured from the earth, is the elongation. At 0° the moon is new, at 90° at first quarter, at 180° full, at 270° at last quarter. The illuminated fraction follows from that angle alone and can be written as (1 − cos θ) ÷ 2. The straight edge of a half moon is the same geometry seen from another side: the boundary between lit and unlit is a circle drawn right around the moon, and at 90° that circle is viewed edge on.
The angle also fixes the hour. A full moon stands opposite the sun, so it rises as the sun sets, crosses the meridian near midnight and sets at dawn. A new moon keeps the sun company and travels the daytime sky, which is why it cannot be seen at all.
Degrees convert into signs as readily as into hours, since 180° is six signs of the zodiac. That is the whole reason a full moon falls in the sign opposite the sun and the quarters, at 90°, fall three signs away. Phase and moon sign remain separate quantities all the same, and /blog/moon-sign sets out the difference.
Why the month has two lengths
The moon returns to the same sign every 27.32 days and to the same phase every 29.53. The two days and a quarter between the two figures is the cost of chasing a mark that is itself moving, and the arithmetic is short enough to do in a line.
The moon covers about 13.18° of the ecliptic a day and the sun about 0.99°, so the gap between them opens by 12.19° a day, and 360 divided by 12.19 is 29.53. The figure is not fitted afterwards: the mean elongation term inside this site's lunar series advances by exactly 12.19074912° per day, and the synodic month is nothing but its period. The sky turns 15° in an hour, so that same 12.19° is also why the moon rises about fifty minutes later each night.
Twelve synodic months come to 354.37 days, eleven short of a solar year, which is why lunar calendars need an intercalary month and why lunar festivals walk backwards across the solar one. The customary remedy is nineteen years long: 235 synodic months and nineteen tropical years agree to within about two hours.
Eight names, and what other calendars count instead
This site names eight phases: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent. Quarter counts a quarter of the cycle rather than a quarter of the disc, which is the commonest misreading of the word, since a first-quarter moon is half lit. Gibbous is the Latin gibbus, a hump, and covers everything between half and full.
The English names describe shapes. The Japanese names printed on this site count nights instead, from the old lunar calendar: 三日月, the moon of the third night; 十三夜月, the moon of the thirteenth; 寝待月, the moon of the nineteenth, which rises so late that it is waited for lying down; 有明月, the moon still in the sky at dawn. Fifty minutes a day is the whole of that idiom.
In both systems the names are bands rather than instants. Each of the eight covers one eighth of the synodic month, about 3 days and 17 hours, centred on the phase it is named for.
How the phase is fixed here
The count runs forward from a reference new moon, 6 January 2000 at 18:14 UTC, in mean synodic months. Because the count is a mean one, the true instant of a new or full moon can fall as much as half a day from the centre of its name, which is why no minute-precise table of full moons is published here.
The daily pages print the name of the phase beside a small moon drawn lit on the right while waxing and on the left while waning, and the illuminated fraction is one of the quantities the day's text is written against. A moon sign is a separate computation, belonging to one instant and one person where a phase belongs to a day and to everyone standing in it.
What the tradition puts at each end
A new moon is present and invisible, and the tradition has generally placed there whatever has not yet taken a shape: intention, the beginning of a thing, the plan not yet said aloud. The practice of writing wishes at a new moon is recent; the association behind it is not.
A full moon has nowhere to hide. It stands across the zodiac from the sun and is read as completion and opposition at once, the two facing signs sounding on the same night with equal weight. Reading the waning moon as release and clearing away is a later vocabulary working from the same diagram.
The belief that a full moon disturbs sleep and temper is old and widely distributed. It is carried here as tradition rather than as an established effect. The astronomy on this page is computed; what is read into it is inherited, and the prose written against each day is composed by Claude, an AI, working in that inheritance rather than forecasting from it.