The Metonic Star
Each glowing dot is a new moon, placed on the zodiac at the degree where the Sun and Moon met, and the picture spirals outward one turn per year for 19 years. Each line joins a new moon to the one twelve months later, which lands about 11 degrees earlier, so the lines sweep backwards into twelve arms. After 235 new moons the cycle closes: the last new moon falls on almost the same degree, and the same calendar date, as the first.
| Lunations in the cycle | 235 |
|---|---|
| Mean synodic month | 29.53 days |
| 235 months vs 19 years | 6,939.69 vs 6,939.60 days |
| Years with a 13th month | 7 of 19 |
What you are looking at
The wheel is the tropical zodiac, with 0° Aries on the left and the signs running counterclockwise, as on a birth chart. The Earth sits in the middle. Every dot is one new moon, the moment the Moon passes between the Earth and the Sun, placed at the degree the Sun held at that instant. The faint gold spiral underneath is the Sun's own path, one turn per year, and every new moon sits on it like a bead on a thread.
The innermost dot is the starting new moon and the outermost is the 235th after it, 19 turns later. The dashed gold ray shows how close they come: within half a degree. For example, the new moon of 10 October 2026 in Libra returns on 10 October 2045, still in Libra. The new moon of 6 January 2000 came back on 6 January 2019.
The other ways to join the dots tell the same story. Joining each new moon to the next draws a nested polygon of about twelve sides per year that slowly turns backwards. Joining each one to the same month a year later draws zigzags: eleven degrees back in an ordinary year, a jump forward after a year that needed a thirteenth month. The seven leap months are ringed in rose. Switch the spiral off to give each year its own ring.
The math
A lunation, from one new moon to the next, averages 29.530589 days. Twelve of them make a lunar year of about 354.37 days, roughly 11 days short of the 365.24 day solar year. That is why each year's new moons land about 11 degrees earlier on the wheel, and why a calendar built on the Moon drifts through the seasons unless it adds an extra month now and then.
The Metonic cycle is the near coincidence that fixes it. 235 lunations average 6,939.69 days and 19 tropical years are 6,939.60 days, so the two clocks agree to about 2 hours over 19 years. Since 235 is 12 times 19 plus 7, seven of every 19 years need a 13th month to keep the new moons in step with the seasons, which is the rule the Hebrew calendar still follows. The Greek astronomer Meton of Athens proposed the cycle in 432 BC, and the same 19-year count sits behind the golden number in the tables used to date Easter.
The 2 hours is an average. Real lunations stretch and shrink by several hours with the shapes of the Moon's and Earth's orbits, so in any one cycle the 235th new moon can arrive anywhere from several hours early to about half a day late. The piece measures the real figure for the cycle you choose and states it when the drawing finishes.
How it is computed
The new moons are found with astronomy-engine, the same library the app's on-device engines use and check against the Swiss Ephemeris. Each new moon is the instant the Moon's apparent longitude equals the Sun's, and the dot sits at the Sun's apparent tropical longitude at that instant, the degree an ephemeris prints. The piece takes the first new moon on or after your start date and the 235 after it.
The radius of each dot is its time in the cycle, so 19 years make 19 turns. The faint spiral is the Sun's longitude sampled once a day across the same span. For the closing figure the piece also finds the exact instant the Sun completes its 19th return to the starting degree and compares it with the 235th new moon. In the yearly view a year runs from the anniversary of the first new moon, so each year holds 12 or 13 new moons.
Questions
What is the Metonic cycle?
It is the 19-year period after which the phases of the Moon fall on the same calendar dates again, because 19 solar years and 235 lunar months are almost exactly the same length. Meton of Athens described it in 432 BC.
Does the new moon really come back to the same date?
Very nearly. The new moon of 10 October 2026 returns on 10 October 2045, and the new moon of 6 January 2000 returned on 6 January 2019. The exact time can differ by several hours, so occasionally the return falls on the next or previous calendar day.
Why does each year's pattern step backwards?
Twelve lunar months are about 354 days, roughly 11 days shorter than a year, so after twelve new moons the Sun has not quite come back round. Each new moon lands about 11 degrees earlier in the zodiac than the one a year before.
Do astrologers use the Metonic cycle?
Astrologers note that a new or full moon tends to recur at the same degree about every 19 years, and some read that return as an echo of the earlier lunation in a person's chart. That is a tradition of interpretation. The piece only shows where the new moons fall.