Why Isn't the Mid-Autumn Moon Always a Full Moon?
― The Calendar Fixes a Date, Not the Moon's Shape
On moon-viewing night, the weather forecaster sometimes says, "This year's harvest moon is not a full moon." It sounds odd, but the calendar is not wrong. The date is set first, from the positions of the Sun and Moon, and the moment of full moon arrives later and may not line up. On top of that, the Moon does not circle at a constant speed.
It is early autumn. You set out rice dumplings and look up at the sky from the veranda. Tonight is the Mid-Autumn moon.
But look closely: the right edge of the Moon seems slightly flat. The next night, the Moon may look rounder.
Did you get the date wrong? No, the calendar is not wrong. The two were never guaranteed to line up exactly.
There are just two main reasons
The Mid-Autumn moon is the night of the 15th day of the 8th month in the old calendar. The day that contains the moment of new moon counts as day 1, and the night is 15 days on from there. So it is a rule about dates. It does not mean "the day the Moon is perfectly round."
The Moon's path is a slightly squashed loop. It moves faster when close to Earth and slower when far away. So the time from new moon to full moon can be about 14 days in one year and about 15.5 days in another.
When these two drift apart, the full-moon moment may not have arrived yet on the 15th night, or may already have passed. Let's look at each in turn.
The starting day can shift by a whole day
In the old calendar, the day containing the moment of new moon was day 1 of the month. Here is the catch. The new moon might happen in the morning, or just before midnight.
If the new moon falls just after midnight, nearly the whole of day 1 is still ahead. If it falls at 11 p.m., day 1 has only one hour left. So the starting point can shift by almost a full day.
Figure 1 lays out that counting in one straight line. The downward arrow at the left end is the moment of new moon, and the upward arrow on the right is the moment of full moon. Depending on where in the day the new moon falls, the full moon can be pushed out of the 15th-day box.
The closer the Moon, the faster it moves
The other reason is the shape of the Moon's path. It is not a perfect circle but a slightly squashed loop. Between its closest and farthest points from Earth, the distance changes by about 10%.
The Moon moves fast when near and slowly when far. It moves so that the line joining Earth and Moon sweeps out the same area in the same time.
Figure 2 shows this. The left side is the far, slow part, and the right side is the near, fast part. The two lightly shaded wedges cover the same number of days. Their shapes differ, but their areas are about the same.
Even when the Moon is off the full-moon moment, it is short of full by only a little. That is hard to notice with the naked eye, and you can barely tell even by comparing photos. On moon-viewing night, simply enjoy it as it is.
Summary
The Mid-Autumn moon is not a day picked by the Moon's shape. It is the 15th day counted from the moment of new moon, a rule about dates. The moment of full moon, on the other hand, is set by how the Moon moves. In some years it comes about 14 days after new moon, and in others it takes 15.5 days. Because the two are set for different reasons, they coincide in some years and are a day apart in others.
The harvest moon is a night the calendar chose.
The full moon is a moment the Moon chose.
For how the Moon's shape changes each day, see Why Does the Moon's Shape Change Every Day?. For another story of the calendar and the sky falling out of step, see Why Is the Autumn Equinox Sometimes September 23 and Sometimes 22?.
- Photograph the Moon with your phone on the moon-viewing night and the nights before and after, from the same spot and at the same zoom.
- Line up the three photos and compare whether the left and right edges of the Moon look round or slightly flat.
- The night the Moon looks roundest is the night closest to that year's full moon.
Phones adjust brightness automatically. Tap the Moon on the screen and lower the brightness to see the edge shape more clearly.
For those who want more ― terms, formulas and links to textbooksEach part is marked with the level it belongs to, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school basic physics and basic earth science
- High school+Advanced high-school material, or a textbook sidebar
- UniversityNot taught in high school; university-level celestial mechanics
- ResearchNot yet taught even at university as settled; something researchers are studying now
Middle schoolTerms: this phenomenon has names
- Saku: the new moon. The moment when the Sun and Moon appear in the same direction.
- Bō: the full moon. The moment when the Sun and Moon line up on opposite sides of Earth.
- Synodic month (sakubō-getsu): the time from one saku to the next. It averages about 29.53 days.
Middle schoolHigh schoolChecking with formulas: how many days from saku to bō?
The quantity in question is the number of days from saku to bō. We first find the average, then see how far the Moon's changing speed moves it either way.
| In symbols | r1² × ω1 ＝ r2² × ω2 |
| In words | Near distance squared × near angular speed ＝ far distance squared × far angular speed |
| Where it comes from | The property of constant areal velocity: the line joining Earth and Moon sweeps equal areas in equal times. It follows from conservation of angular momentum (Kepler's second law). |
| When r (distance from Earth) is smallest | About 363,000 km (36.3 in units of 10,000 km) |
| When r is largest | About 406,000 km (40.6 in units of 10,000 km) |
| Average synodic month | 29.53 days |
| Actual range from saku to bō | About 13.9 to 15.6 days |
What the symbols mean: r1 and r2 are the distances from Earth to the Moon, in units of 10,000 km. ω1 and ω2 are the angles the Moon covers per second at each point, in degrees per second.
| Ratio of far to near distance | 40.6 ÷ 36.3 ≒ 1.12 |
| The ratio of ω is the square of the distance ratio | 1.12 × 1.12 ≒ 1.25 |
| Average days from saku to bō (half a synodic month) | 29.53 ÷ 2 ≒ 14.77 |
| Gap for the longest year | 15.6 － 14.77 ≒ 0.83 |
| Gap for the shortest year | 14.77 － 13.9 ≒ 0.87 |
Near Earth, the Moon sweeps its angle about 1.25 times faster than when far away. As a result, the days from saku to bō swing about 0.8 days either way from the 14.77-day average. Against the fixed box of calendar day 15, the full-moon moment can shift by nearly a whole day either way.
High schoolHigh school+The synodic month and the orbital period are different things
High schoolThe Moon takes about 27.32 days to go once around Earth and return to the same place among the stars. This is the sidereal month. But during that time Earth also moves along its orbit around the Sun. It takes about 29.53 days for the Sun-Moon alignment to repeat, and that is the synodic month.
High school+The Moon's closest point to Earth itself also rotates, making one full turn in about 8.85 years. This is called apsidal precession. So the pairing of the new-moon date with the Moon's near-Earth phase shifts every year, and the days from saku to bō change from year to year.
UniversityThe two-body problem and perturbations of the Moon's motion
In the two-body problem, with only Earth and the Moon, the orbit is a fixed ellipse, and constant areal velocity and the semi-major axis set the period. But the Sun's strong pull acts on the real Moon, so its orbital elements keep changing. These changes are called perturbations, and they produce long-known periodic shifts such as evection and variation. Predicting the Moon's position accurately takes lunar theory with many such terms, or numerical integration. The saku and bō times published by Japan's National Astronomical Observatory rest on this kind of calculation.
📖 Derivations and further reading: Kepler's laws ／ Synodic month
ResearchWhat is still not clearly known
- The past speed of the Moon's recession The Moon now drifts away by about 3.8 cm a year, but this rate depends on the shape of the oceans. Studies estimating how it changed in the past, using bands in rock layers, are still going on.
- The Moon's internal structure Whether there is a molten layer at the centre changes how the Moon deforms under tidal forces. How to interpret the observations still leaves some room.
- The history of the calendar itself How the day of saku was decided in old Japan differed from era to era. Researchers are still matching the dates in old records against modern calculations.
In other words, this article too is an explanation "as far as is known today." The numbers shown are representative values.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: Earth and space (phases of the Moon) | Saku and bō; how the moon-viewing date is set |
| High school | Basic earth science, basic physics (circular motion and celestial bodies) | Constant areal velocity; sidereal vs synodic month |
| High school+ | Physics: mechanics (conservation of angular momentum) | Apsidal precession, and why the days vary by year |
| University | Celestial mechanics, positional astronomy | The two-body problem and perturbations; lunar theory |
| Research | Earth and planetary science | The Moon's recession rate and internal structure |
| ― | Links to daily life | Moon-viewing dates; moon-age displays on calendars |
- National Astronomical Observatory of Japan (国立天文台), Ephemeris Computation Office, "Reki-shō Nenpyō" (暦象年表): notes on new moon, quarter moons, full moon and the Moon's distance
- Synodic month (Japanese Wikipedia)
- Kepler's laws (Japanese Wikipedia)
- Nagasawa Kō (長沢工), 『日の出・日の入りの計算 ― 天体の出没時刻の求め方』 (Calculating Sunrise and Sunset: How to Find Rising and Setting Times of Celestial Bodies), Chijin Shokan (地人書館)
- Watanabe Toshio (渡邊敏夫), 『日本の暦』 (The Calendar of Japan), Yuzankaku (雄山閣)
*This article is a general-audience science explainer. The figures given are rough guides to help you understand the mechanism. For actual times of new and full moon and the date of the moon-viewing night, please check the values published by Japan's National Astronomical Observatory.